Time crystal - Knowledge

2074: 716: 2036:, supervised by Hans Keßler and Andreas Hemmerich. In periodically driven systems, time-translation symmetry is broken into a discrete time-translation symmetry due to the drive. Discrete time crystals break this discrete time-translation symmetry by oscillating at a multiple of the drive frequency. In the new experiment, the drive (pump laser) was operated continuously, thus respecting the continuous time-translation symmetry. Instead of a subharmonic response, the system showed an oscillation with an intrinsic frequency and a time phase taking random values between 0 and 2π, as expected for spontaneous breaking of continuous time-translation symmetry. Moreover, the observed 1600:: energy in the overall system is conserved, such a crystal does not spontaneously convert thermal energy into mechanical work, and it cannot serve as a perpetual store of work. But it may change perpetually in a fixed pattern in time for as long as the system can be maintained. They possess "motion without energy"—their apparent motion does not represent conventional kinetic energy. Recent experimental advances in probing discrete time crystals in their periodically driven nonequilibrium states have led to the beginning exploration of novel phases of nonequilibrium matter. 2098: 8894: 7543: 93: 8969: 2086: 8884: 7971: 729: 9355: 1286: 7995: 785: 1301:: they have repeated patterns in space and are not invariant under arbitrary translations or rotations. The laws of physics are unchanged by arbitrary translations and rotations. However, if we hold fixed the atoms of a crystal, the dynamics of an electron or other particle in the crystal depend on how it moves relative to the crystal, and particle momentum can change by interacting with the atoms of a crystal — for example in 8007: 1613: 7983: 32: 1217:, as it is a type (or phase) of non-equilibrium matter. Breaking of time symmetry can only occur in non-equilibrium systems. Discrete time crystals have in fact been observed in physics laboratories as early as 2016. One example of a time crystal, which demonstrates non-equilibrium, broken time symmetry is a constantly rotating ring of charged ions in an otherwise lowest-energy state. 1876:. This strongly interacting dipolar spin system was driven with microwave fields, and the ensemble spin state was determined with an optical (laser) field. It was observed that the spin polarization evolved at half the frequency of the microwave drive. The oscillations persisted for over 100 cycles. This 1603:

Time crystals do not evade the Second Law of Thermodynamics, although they spontaneously break "time-translation symmetry", the usual rule that a stable object will remain the same throughout time. In thermodynamics, a time crystal's entropy, understood as a measure of disorder in the system, remains

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The researchers observed a subharmonic oscillation of the drive. The experiment showed "rigidity" of the time crystal, where the oscillation frequency remained unchanged even when the time crystal was perturbed, and that it gained a frequency of its own and vibrated according to it (rather than only

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metals. By analogy, a time crystal arises through the spontaneous breaking of a time-translation symmetry. A time crystal can be informally defined as a time-periodic self-organizing structure. While an ordinary crystal is periodic (has a repeating structure) in space, a time crystal has a repeating

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In February 2024, a team from Dortmund University in Germany built a time crystal from indium gallium arsenide that lasted for 40 minutes, nearly 10 million times longer than the previous record of around 5 milliseconds. In addition, the lack of any decay suggests the crystal could have lasted even

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analogue to common crystals – whereas the atoms in crystals are arranged periodically in space, the atoms in a time crystal are arranged periodically in both space and time. Several different groups have demonstrated matter with stable periodic evolution in systems that are periodically driven. In

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Later, time crystals in open systems, so called dissipative time crystals, were proposed in several platforms breaking a discrete and a continuous time-translation symmetry. A dissipative time crystal was experimentally realized for the first time in 2021 by the group of Andreas Hemmerich at the

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that quantum space–time crystals in equilibrium are not possible. Later work restricted the scope of Watanabe and Oshikawa: strictly speaking, they showed that long-range order in both space and time is not possible in equilibrium, but breaking of time-translation symmetry alone is still possible.

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In 2019, physicists Valerii Kozin and Oleksandr Kyriienko proved that, in theory, a permanent quantum time crystal can exist as an isolated system if the system contains unusual long-range multiparticle interactions. The original "no-go" argument only holds in the presence of typical short-range

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structure in time. A time crystal is periodic in time in the same sense that the pendulum in a pendulum-driven clock is periodic in time. Unlike a pendulum, a time crystal "spontaneously" self-organizes into robust periodic motion (breaking a temporal symmetry).

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the frequency of the drive). However, once the perturbation or frequency of vibration grew too strong, the time crystal "melted" and lost this subharmonic oscillation, and it returned to the same state as before where it moved only with the induced frequency.

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Yoshii, Ryosuke; Takada, Satoshi; Tsuchiya, Shunji; Marmorini, Giacomo; Hayakawa, Hisao; Nitta, Muneto (2015). "Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions".

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Choi, Soonwon; Choi, Joonhee; Landig, Renate; Kucsko, Georg; Zhou, Hengyun; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman Y.; Demler, Eugene; Lukin, Mikhail D. (2017).

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Time crystals show a broken symmetry analogous to a discrete space-translation symmetry breaking. For example, the molecules of a liquid freezing on the surface of a crystal can align with the molecules of the crystal, but with a pattern

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In 2022, the Hamburg research team, supervised by Hans Keßler and Andreas Hemmerich, demonstrated, for the first time, a continuous dissipative time crystal exhibiting spontaneous breaking of continuous time-translation symmetry.

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oscillations were shown to be robust against perturbations of technical or fundamental character, such as quantum noise and, due to the openness of the system, fluctuations associated with dissipation. The system consisted of a

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and vice-versa in periodic cycles which are multiples of the laser's frequency. While the laser is necessary to maintain the necessary environmental conditions, no energy is absorbed from the laser, so the system remains in a

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Filippo Maria, Gambetta; Carollo, Federico; Marcuzzi, Matteo; Garrahan, Juan P.; Lesanovsky, Igor (8 January 2019). "Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems".

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Zhang, J.; Hess, P. W.; Kyprianidis, A.; Becker, P.; Lee, A.; Smith, J.; Pagano, G.; Potirniche, I.-D.; Potter, A. C.; Vishwanath, A.; Yao, N. Y.; Monroe, C. (2017). "Observation of a discrete time crystal".

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with long-range multispin interactions, and showed it broke continuous time-translational symmetry. Certain spin correlations in the system oscillate in time, despite the system being closed and in a

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and the time crystal was demonstrated to spontaneously break discrete time-translation symmetry by periodically switching between two atomic density patterns. In an earlier experiment in the group of

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Smith, J.; Lee, A.; Richerme, P.; Neyenhuis, B.; Hess, P. W.; Hauke, P.; Heyl, M.; Huse, D. A.; Monroe, C. (2016). "Many-body localization in a quantum simulator with programmable random disorder".

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Träger, Nick; Gruszecki, Paweł; Lisiecki, Filip; Groß, Felix; Förster, Johannes; Weigand, Markus; Głowiński, Hubert; Kuświk, Piotr; Dubowik, Janusz; Schütz, Gisela; Krawczyk, Maciej (2021-02-03).

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is that a translation in time has no effect on physical laws, i.e. that the laws of nature that apply today were the same in the past and will be the same in the future. This symmetry implies the

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and colleagues proposed a different way to create discrete time crystals in spin systems. These ideas were successful and independently realized by two experimental teams: a group led by

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In 2016, research groups at Princeton and at Santa Barbara independently suggested that periodically driven quantum spin systems could show similar behaviour. Also in 2016, Norman Yao at

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Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012). "Reply to Comment on "Space–Time Crystals of Trapped Ions"".

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Ordinary (non-time) crystals form through spontaneous symmetry breaking related to a spatial symmetry. Such processes can produce materials with interesting properties, such as

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Previously in June and November 2021 other teams had obtained virtual time crystals based on floquet systems under similar principles to those of the Google experiment, but on

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published a letter from the same group saying that for the first time they were able to observe interactions and the flow of constituent particles between two time crystals.

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Mi, Xiao; Ippoliti, Matteo; Quintana, Chris; Greene, Ami; Chen, Zijun; Gross, Jonathan; Arute, Frank; Arya, Kunal; Atalaya, Juan; Babbush, Ryan; Bardin, Joseph C. (2022).

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These characteristics makes discrete time crystals analogous to spatial crystals as described above and may be considered a novel type or phase of nonequilibrium matter.

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Autti, S.; Heikkinen, P. J.; Mäkinen, J. T.; Volovik, G. E.; Zavjalov, V. V.; Eltsov, V. B. (February 2021). "AC Josephson effect between two superfluid time crystals".

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Randall, J.; Bradley, C. E.; van der Gronden, F. V.; Galicia, A.; Abobeih, M. H.; Markham, M.; Twitchen, D. J.; Machado, F.; Yao, N. Y.; Taminiau, T. H. (2021-12-17).

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reported a dissipative time crystal akin to the system of July 2021 but all-optical, which allowed the scientist to operate it at room temperature. In this experiment

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and have repeated patterns in time even if the laws of the system are invariant by translation of time. The time crystals that are experimentally realized show

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is one in which the particles are in repetitive motion. The system cannot lose energy to the environment and come to rest because it is already in its quantum

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Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012a). "Space-Time Crystals of Trapped Ions".

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as well as space, the question arose in 2012 as to whether it is possible to break symmetry temporally, and thus create a "time crystal" that is resistant to

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Kyprianidis, A.; Machado, F.; Morong, W.; Becker, P.; Collins, K. S.; Else, D. V.; Feng, L.; Hess, P. W.; Nayak, C.; Pagano, G.; Yao, N. Y. (2021-06-11).

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predicted the behaviour of discrete time crystals in a periodically driven system with "an ultracold atomic cloud bouncing on an oscillating mirror".

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Iemini, Fernando; Russomanno, Angelo; Keeling, Jonathan; Schirò, Marco; Dalmonte, Marcello; Fazio, Rosario (16 July 2018). "Boundary time crystals".

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Wang, Y. H.; Steinberg, H.; Jarillo-Herrero, P.; Gedik, N. (2013). "Observation of Floquet-Bloch States on the Surface of a Topological Insulator".

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Khemani, Vedika; Moessner, Roderich; Sondhi, S. L. (2020). "Comment on 'Quantum Time Crystals from Hamiltonians with Long-Range Interactions'".

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We show that an ultracold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time-translation symmetry

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in space is broken and replaced by the lower discrete symmetry of the periodic crystal. As the laws of physics are symmetrical under continuous

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Volovik, G. E. (2013). "On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order".

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If a discrete time-translation symmetry is broken (which may be realized in periodically driven systems), then the system is referred to as a

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von Keyserlingk, C. W.; Khemani, Vedika; Sondhi, S. L. (2016). "Absolute stability and spatiotemporal long-range order in Floquet systems".

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the system exhibits spatial and temporal long-range order (unlike a local and intermittent order in a liquid near the surface of a crystal),

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Autti, S.; Eltsov, V. B.; Volovik, G. E. (May 2018). "Observation of a Time Quasicrystal and Its Transition to a Superfluid Time Crystal".

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Gong, Zongping; Hamazaki, Ryusuke; Ueda, Masahito (25 January 2018). "Discrete Time-Crystalline Order in Cavity and Circuit QED Systems".

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Many systems can show behaviors of spontaneous time-translation symmetry breaking but may not be discrete (or Floquet) time crystals:

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claimed to have created the world's first discrete time crystal. Using the ideas proposed by Yao et al., his team trapped a chain of

1932:. The main achievement of this work is a positive application of dissipation – actually helping to stabilise the system's dynamics. 8238: 7443: 4995: 4743:

https://www.msn.com/en-ca/news/technology/scientists-built-a-time-crystal-that-lasted-for-40-minutes-that-s-astonishing/ar-BB1iODrc

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Guo, Lingzhen; Marthaler, Michael; Schön, Gerd (2013). "Phase Space Crystals: A New Way to Create a Quasienergy Band Structure".

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reported that they had observed the formation of a time quasicrystal and its phase transition to a continuous time crystal in a

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Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich; Sondhi, S. L. (2016). "Phase Structure of Driven Quantum Systems".

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Kozin, Valerii K.; Kyriienko, Oleksandr (2019-11-20). "Quantum Time Crystals from Hamiltonians with Long-Range Interactions".

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Keßler, Hans; Kongkhambut, Phatthamon; Georges, Christoph; Mathey, Ludwig; Cosme, Jayson G.; Hemmerich, Andreas (2021-07-19).

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Lindner, Netanel H.; Refael, Gil; Galitski, Victor (2011). "Floquet topological insulator in semiconductor quantum wells".

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In June 2022, the observation of a continuous time crystal was reported by a team at the Institute of Laser Physics at the

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symmetric than the crystal: it breaks the initial symmetry. This broken symmetry exhibits three important characteristics:

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Kongkhambut, Phatthamon; Skulte, Jim; Mathey, Ludwig; Cosme, Jayson G.; Hemmerich, Andreas; Keßler, Hans (2022-08-05).

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it is the result of interactions between the constituents of the system, which align themselves relative to each other.

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Medenjak, Marko; Buča, Berislav; Jaksch, Dieter (2020-07-20). "Isolated Heisenberg magnet as a quantum time crystal".

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In March 2022, a new experiment studying time crystals on a quantum processor was performed by two physicists at the

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Dogra, Nishant; Landini, Manuele; Kroeger, Katrin; Hruby, Lorenz; Donner, Tobias; Esslinger, Tilman (2019-12-20).

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Nozières, Philippe (2013). "Time crystals: Can diamagnetic currents drive a charge density wave into rotation?".

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Several realizations of time crystals, which avoid the equilibrium no-go arguments, were later proposed. In 2014

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Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick (2016). "Symmetric Satellite Swarms and Choreographic Crystals".

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The "discrete" comes from the fact that their periodicity is a discrete, integer multiple of the driving period.

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was selected by a pair of laser beams. The lasers were pulsed, with the shape of the pulse controlled by an

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Khemani, Vedika; Moessner, Roderich; Sondhi, S. L. (23 October 2019). "A Brief History of Time Crystals".

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and physicists from multiple universities reported the observation of a discrete time crystal on Google's

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qubits using high frequency driving rather than many-body localization and then a collaboration between

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to capture the recurring periodic magnetization structure in the first known video record of such type.

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cooled to within one ten thousandth of a kelvin from absolute zero (0.0001 K). On August 17, 2020

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configuration of up and down spins and then stimulated with a laser to achieve a periodically driven "

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Shirley, Jon H. (1965). "Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time".

4258:"Self-Ordered Limit Cycles, Chaos, and Phase Slippage with a Superfluid inside an Optical Resonator" 1252:

Symmetries in nature lead directly to conservation laws, something which is precisely formulated by

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However, discrete (or Floquet) time crystals are unique in that they follow a strict definition of

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stationary over time, marginally satisfying the second law of thermodynamics by not decreasing.

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Normal process (N-process) and Umklapp process (U-process). While the N-process conserves total

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Iemini, F.; Russomanno, A.; Keeling, J.; Schirò, M.; Dalmonte, M.; Fazio, R. (2018-07-16).

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Sacha, Krzysztof (2015). "Modeling spontaneous breaking of time-translation symmetry".

6179:"Quantum simulations of a freely rotating ring of ultracold and identical bosonic ions" 6165: 6131: 6110: 6069: 6035: 6002: 5985: 5943: 5922: 5880: 5859: 5833: 5812: 5770: 5742: 5680: 5638: 5617: 5575: 5554: 5512: 5487: 5445: 5384: 5345: 5333: 5282: 5241: 5240:

Taheri, Hossein; Matsko, Andrey B.; Maleki, Lute; Sacha, Krzysztof (14 February 2022).

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Sacha, Krzysztof (2015). "Modeling spontaneous breaking of time-translation symmetry".

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Sacha, Krzysztof (2015). "Modeling spontaneous breaking of time-translation symmetry".

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in the Netherlands called Qutech created time crystals from nuclear spins in carbon-13

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In July 2021, a team led by Andreas Hemmerich at the Institute of Laser Physics at the

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it is a broken symmetry – the system shows oscillations with a period

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Wilczek, Frank (2013). "Superfluidity and Space–Time Translation Symmetry Breaking".

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Guo, Lingzhen; Liang, Pengfei (2020). "Condensed matter physics in time crystals".

5816: 5792: 5788: 5726: 5684: 5660: 5656: 5621: 5597: 5593: 5534: 5530: 5467: 5463: 5379: 5363: 5314: 5277: 5261: 5217:"New Breakthrough Could Bring Time Crystals Out of The Lab And Into The Real World" 5148: 5050: 4939: 4935: 4870: 4813: 4809: 4618: 4552: 4459: 4455: 4403: 4352: 4307: 4291: 4287: 4214: 4162: 4108: 4104: 4040: 4024: 3959: 3955: 3951: 3890: 3886: 3825: 3821: 3763: 3759: 3702: 3698: 3657: 3637: 3578: 3562: 3489: 3485: 3399: 3398:. Springer Series on Atomic, Optical, and Plasma Physics. Vol. 114. Springer. 3355: 3284: 3198: 3133: 3129: 2987: 2963: 2959: 2918: 2894: 2890: 2835: 2819: 2654: 2598: 2522: 2327: 2256: 2175: 1884: 1733: 1711: 1510: 1276: 1016: 328: 293: 288: 248: 218: 188: 148: 108: 9199: 5926: 3157: 1880:

response to the drive frequency is seen as a signature of time-crystalline order.

10082: 9992: 9938: 9838: 9711: 9564: 9301: 9194: 9189: 9117: 9112: 9079: 9006: 8642: 8580: 8270: 8265: 7936: 7891: 7557: 7474: 6859: 4323:"Dissipation-induced structural instability and chiral dynamics in a quantum gas" 2474: 2446: 2418: 2390: 2362: 2300:

Sacha, Krzysztof; Zakrzewski, Jakub (1 January 2018). "Time crystals: a review".

2011: 1920:

presented the first realization of a time crystal in an open system, a so-called

1864:

at Harvard also reported the creation of a driven time crystal. His group used a

1850: 1676: 1302: 1175: 1074: 875: 638: 588: 458: 213: 125: 4716:"Scientists Built a Time Crystal That Lasted for 40 Minutes. That's Astonishing" 3289: 3254: 3202: 2690:"Time Crystals Might Exist After All – And They Could Break Space-Time Symmetry" 1777:

longer, stating that it could last "at least a few hours, perhaps even longer".

10012: 9967: 9945: 9833: 9509: 9504: 9461: 9394: 9389: 9242: 8958: 8751: 8728: 8695: 8499: 8376: 7999: 7946: 7828: 7717: 7426: 6837:"The quasienergy of a quantum-mechanical system subjected to a periodic action" 6811: 6569: 6367: 6251: 6203: 6178: 5855: 5265: 4218: 4028: 3359: 3102:

Watanabe, Haruki; Oshikawa, Masaki (2015). "Absence of Quantum Time Crystals".

2823: 2331: 2179: 2090: 2078: 2046: 1952: 1929: 1925: 1729: 1660:) published several articles stating that space–time crystals were impossible. 1634: 1616: 1518: 1420:, is spontaneously broken to the lower discrete time-translation symmetry with 1321:

the system has a lower symmetry than the underlying arrangement of the crystal,

1180: 1159: 865: 720: 688: 668: 663: 618: 538: 473: 371: 258: 103: 20: 16:

Structure that repeats in time; a novel type or phase of non-equilibrium matter

8023: 7379: 7223: 6897: 6514: 6098: 5629:

Else, Dominic V.; Bauer, Bela; Nayak, Chetan (2016). "Floquet Time Crystals".

5192:"Physicists create discrete time crystals in a programmable quantum simulator" 4906:"Real-Space Observation of Magnon Interaction with Driven Space–Time Crystals" 4874: 3403: 10143: 10022: 9746: 9726: 9649: 9609: 9544: 9476: 9399: 9230: 8573: 8391: 8317: 7871: 7853: 7838: 7818: 7722: 7691: 7522: 7231: 7075: 7005: 6819: 6755: 6700: 6640: 6577: 6522: 6467: 6420: 6412: 6259: 6212: 6161: 6106: 6065: 5973: 5910: 5800: 5738: 5668: 5605: 5542: 5475: 5409:"'An ever-ticking clock': we made a 'time crystal' inside a quantum computer" 5375: 5273: 5160: 5062: 4630: 4564: 4467: 4364: 4226: 4036: 3574: 3497: 3367: 3210: 3141: 2971: 2902: 2831: 2666: 2187: 2050: 1861: 1790: 1699: 1668: 1630: 1619: 1306: 1234: 1230: 1171: 1047: 995: 968: 953: 943: 399: 380: 362: 263: 183: 9787: 6624: 5566:

Bruno, Patrick (2013b). "Comment on "Space-Time Crystals of Trapped Ions"".

5318: 5152: 5054: 4622: 4556: 4407: 4356: 593: 10047: 9771: 9644: 9639: 9634: 9599: 9549: 9247: 8793: 8718: 7808: 7630: 7435: 7083: 7013: 6950: 6933: 6763: 6708: 6648: 6375: 6328: 5981: 5918: 5808: 5676: 5613: 5550: 5483: 5393: 5367: 5334:"Realization of a discrete time crystal on 57 qubits of a quantum computer" 5291: 5168: 5070: 4947: 4882: 4821: 4638: 4572: 4475: 4372: 4299: 4234: 4167: 4142: 4116: 4054: 3971: 3898: 3833: 3771: 3710: 3649: 3592: 3505: 3149: 2979: 2910: 2849: 2339: 2057: 1806: 1766: 1522: 1167: 870: 613: 603: 573: 533: 528: 508: 353: 333: 9270: 1872:, which have strong dipole–dipole coupling and relatively long-lived spin 1585:, just like in spatial crystals. This is not the case for NMR spin echos. 9680: 9574: 9486: 9056: 9051: 8803: 8657: 8195: 7928: 7646: 7615: 7595: 7542: 2261: 2236: 2134: 2054: 2037: 1642: 1353: 1109: 1011: 990: 958: 948: 845: 698: 633: 608: 578: 523: 518: 450: 92: 8908: 6632: 3995:"Non-stationary coherent quantum many-body dynamics through dissipation" 3641: 3566: 3067: 10067: 10057: 9619: 9594: 9521: 9491: 9425: 9404: 9046: 8864: 8798: 8662: 7843: 7681: 7517: 6968: 6336:

Sacha, Krzysztof; Zakrzewski, Jakub (2018). "Time Crystals: a review".

4755:"Radical New Time Crystal Revealed That Lasts Millions of Times Longer" 3963: 2476:

Fundamentals of the Physics of Solids: Volume 1: Structure and Dynamics

2448:

Fundamentals of the Physics of Solids: Volume 1: Structure and Dynamics

1891: 1737: 1359:

The initial symmetry, which is the discrete time-translation symmetry (

973: 850: 543: 385: 178: 6459: 6310: 6057: 2739:"Google May Have Created an Unruly New State of Matter: Time Crystals" 2658: 2085: 1849:, have very close energy levels, separated by 12.642831 GHz. Ten 9918: 9107: 8647: 7901: 7727: 7512: 3454:

Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A. (2017).

1810: 1797:, confined by radio-frequency electromagnetic fields. One of the two 1794: 1529: 1104: 1057: 1052: 963: 598: 548: 421: 268: 168: 9354: 7408: 7304:"Physics team proposes a way to create an actual space-time crystal" 7067: 6997: 5500: 5116: 3792: 1853:

ions were placed in a line 0.025 mm long and coupled together.

1684: 1285: 9756: 9584: 9011: 8832: 8808: 8667: 8632: 6976:

Coleman, Piers (9 January 2013). "Quantum physics: Time crystals".

6552: 6442: 6350: 6293: 6277:"Anderson localization and Mott insulator phase in the time domain" 5885: 5838: 5643: 5350: 5135: 5037: 4922: 4857: 4796: 4539: 4503: 4442: 4339: 4274: 4091: 4011: 3938: 3873: 3808: 3746: 3685: 3624: 3549: 3472: 3271: 3238: 3185: 2932:

Shapere, Alfred; Wilczek, Frank (2012). "Classical Time Crystals".

2806: 2641: 2627:

Yao; Nayak (2018). "Time crystals in periodically driven systems".

2585: 2314: 1888: 1758: 1521:, and subharmonic response to a periodic driving force such as the 1226: 1006: 912: 860: 818: 784: 158: 7321:"Time crystals could behave almost like perpetual motion machines" 7250: 6794: 6730: 6607: 6497: 6234: 6136: 6040: 6007: 5948: 5775: 5580: 5517: 5450: 5094:"Creating Time Crystals Using New Quantum Computing Architectures" 3342: 3116: 2946: 2877: 2162: 1331: 9716: 9604: 9539: 9456: 9451: 9176: 8859: 8476: 7951: 7918: 7896: 7876: 3456:"Discrete Time Crystals: Rigidity, Criticality, and Realizations" 2015: 1865: 1563: 1203: 1187: 855: 806: 478: 463: 426: 417: 412: 7031:""Time Crystals" Could Be a Legitimate Form of Perpetual Motion" 4996:"Eternal Change for No Energy: A Time Crystal Finally Made Real" 4396:"Back to the future: The original time crystal makes a comeback" 3255:"Out-of-equilibrium phase diagram of long-range superconductors" 2715:"'Time Crystals' Could Be a Legitimate Form of Perpetual Motion" 2029:

and Brooklyn quantum processors observing a total of 57 qubits.

1612: 1577:

Moreover, the broken symmetry in time crystals is the result of

9325: 8836: 8332: 7886: 7881: 7487: 3060:"Notes from the Editors: The Aftermath of a Controversial Idea" 1936: 1906: 1290: 1094: 811: 431: 407: 138: 5018: 4692:"Physicists Create Continuous Time Crystal for the First Time" 4072: 3993:

Buča, Berislav; Tindall, Joseph; Jaksch, Dieter (2019-04-15).

1629:

The idea of a quantized time crystal was theorized in 2012 by

9334: 9320: 8105: 7861: 7482: 3919: 3670: 2567:

Else, D. W.; Monroe, C.; Nayak, C.; Yao, N. Y. (March 2020).

1809:

to avoid too much energy at the wrong optical frequency. The

1179:

terms of practical use, time crystals may one day be used as

1099: 436: 133: 7403: 4842: 4520: 8854: 8327: 8260: 7046:

Gibney, Elizabeth (2017). "The quest to crystallize time".

4903: 3253:

Uhrich, P.; Defenu, N.; Jafari, R.; Halimeh, J. C. (2020).

2006:

was used to direct lasers at a specific frequency inside a

1348:

one: they are periodically driven systems oscillating at a

801: 776: 3608: 2790:"Time-Crystalline Eigenstate Order on a Quantum Processor" 9330: 8471: 8456: 7492: 7338:"Physicist proves impossibility of quantum time crystals" 3252: 1667:-breaking, which ultimately led to the Watanabe–Oshikawa 1638: 143: 7195:"World's first time crystals cooked up using new recipe" 7135:"Time crystals enter the real world of condensed matter" 4320: 2787: 2762:"Physicists create time crystals with quantum computers" 7270:"Scientists Create A New Kind Of Matter: Time Crystals" 7179: 7101:"Death-defying time crystal could outlast the universe" 6934:"Focus: Turning a Quantum Computer into a Time Crystal" 5239: 4971:"World's first video recording of a space–time crystal" 1995:

on a diamond, attaining longer times but fewer qubits.

1710:. Both experiments were published in the same issue of 7251:

University of California, Berkeley (26 January 2017).

6537: 3857:"Dissipation Induced Nonstationarity in a Quantum Gas" 2281: 2279: 1663:

Subsequent work developed more precise definitions of

6176: 4496: 3231: 2062: 1975:

rather than quantum processors: first a group at the

1905:

described the creation of time crystal consisting of

1492: 1472: 1452: 1426: 1400: 1365: 1352:

of the frequency of the driving force. (According to

1270: 1170:. Time crystals were first proposed theoretically by 7253:"Physicists unveil new form of matter—time crystals" 8298: 7165:"'Choreographic crystals' have all the right moves" 5021:"Observation of a prethermal discrete time crystal" 2276: 41:

may be too technical for most readers to understand

7133:Hannaford, Peter; Sacha, Krzysztof (17 Mar 2020). 4781: 3170: 3020:"Perpetual Motion Test Could Amend Theory of Time" 2566: 2562: 2560: 2558: 2556: 2554: 2392:A Beautiful Question: Finding Nature's Deep Design 1562: – these oscillations generate no 1498: 1478: 1458: 1438: 1412: 1386: 7148:"Creating time crystals with a rotating ion ring" 4775: 3992: 3449: 3447: 1947:device. A chip of 20 qubits was used to obtain a 1652:In response to Wilczek and Zhang, Patrick Bruno ( 10141: 5242:"All-optical dissipative discrete time crystals" 4836: 4256:Piazza, Francesco; Ritsch, Helmut (2015-10-15). 4068: 4066: 4064: 3731: 3101: 2863:Wilczek, Frank (2012). "Quantum Time Crystals". 1293:momentum, the U-process changes phonon momentum. 8053: 7287:"Time crystals realize new order of space-time" 6080: 5407:Frey, Philipp; Rachel, Stephan (2 March 2022). 4769:"Physicists develop highly robust time crystal" 4730:"A Time Crystal Survived a Whopping 40 Minutes" 2731: 2622: 2620: 2551: 2299: 1332:Broken symmetry in discrete time crystals (DTC) 7372:"Time crystals might exist after all (Update)" 7132: 6834: 6025: 5870: 5092:S, Robert; ers; Berkeley, U. C. (2021-11-10). 4427: 3444: 3435: 2931: 2364:Conceptual Foundations of Quantum Field Theory 2287:"Physicists Create World's First Time Crystal" 2208: 1309:, however, is conserved in a perfect crystal. 9817: 9803: 9286: 8924: 8039: 7451: 6961:"Focus: New Crystal Type is Always in Motion" 6778: 5691: 5332:Frey, Philipp; Rachel, Stephan (2022-03-04). 5307:"Physicists produce biggest time crystal yet" 4664:"Researchers observe continuous time crystal" 4141:Gong, Zongping; Ueda, Masahito (2021-07-19). 4061: 3855:Buča, Berislav; Jaksch, Dieter (2019-12-23). 3315: 3308:harvp error: no target: CITEREFWilczek2013b ( 2783: 2781: 1131: 754: 7465: 7212:"Can matter cycle through shapes eternally?" 6427: 6335: 5435: 5091: 4975:Max Planck Institute for Intelligent Systems 4387: 4255: 3604: 3602: 2759: 2617: 1903:Max Planck Institute for Intelligent Systems 1344:time-translation symmetry breaking, not the 1241: 1190:in nature is a manifestation of spontaneous 9300: 7293:. Christian Science Monitor. Archived from 6592: 5628: 4075:"Observation of a Dissipative Time Crystal" 3529: 3525: 3523: 3439: 2219: 1868:crystal doped with a high concentration of 1785:In October 2016, Christopher Monroe at the 1545:discrete time-translation symmetry breaking 9810: 9796: 9293: 9279: 8931: 8917: 8046: 8032: 7541: 7458: 7444: 5996: 5933: 5823: 5760: 5406: 5331: 4599:"Unleashing spontaneity in a time crystal" 4523:"Observation of a continuous time crystal" 3854: 3453: 3085: 3005: 3001: 2778: 2712: 2124: 1935:In November 2021, a collaboration between 1138: 1124: 761: 747: 91: 8938: 7192: 7180:Joint Quantum Institute (22 March 2011). 7118:"Curious Crystal Dances for Its Symmetry" 6949: 6793: 6729: 6606: 6551: 6496: 6441: 6349: 6318: 6292: 6233: 6202: 6135: 6039: 6006: 5947: 5884: 5837: 5774: 5720: 5642: 5579: 5516: 5449: 5383: 5349: 5281: 5134: 5036: 4993: 4921: 4856: 4795: 4538: 4502: 4441: 4338: 4273: 4166: 4090: 4044: 4010: 3937: 3872: 3807: 3745: 3684: 3623: 3599: 3582: 3548: 3471: 3341: 3288: 3270: 3237: 3184: 3115: 3017: 2945: 2876: 2839: 2805: 2640: 2584: 2573:Annual Review of Condensed Matter Physics 2367:. Cambridge: Cambridge University Press. 2313: 2260: 2230: 2228: 2161: 2120: 2118: 1757:. Kozin and Kyriienko instead analyzed a 69:Learn how and when to remove this message 53:, without removing the technical details. 7162: 7098: 6663: 6177:Robicheaux, F.; Niffenegger, K. (2015). 6121: 6081:Mendonça, J. T.; Dodonov, V. V. (2014). 5189: 4968: 4140: 3520: 3304: 3225: 3081: 2626: 2603:10.1146/annurev-conmatphys-031119-050658 2420:Introduction to Condensed Matter Physics 2234: 1611: 1284: 1213:. A discrete time crystal never reaches 8564:Continuous-variable quantum information 7193:Ouellette, Jennifer (31 January 2017). 7115: 6975: 6715: 6482: 6390: 5692:Grifoni, Milena; Hänggi, Peter (1998). 4689: 4596: 3095: 3089: 2862: 2416: 2388: 1654:European Synchrotron Radiation Facility 10142: 10008:Atomic, molecular, and optical physics 7267: 7209: 7171:. Institute of Physics. 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American Physical Society: 5. 2096: 2084: 2072: 1744:fields that decay as quickly as 783: 728: 727: 714: 30: 10129:Timeline of physics discoveries 7370:Zyga, Lisa (9 September 2016). 7319:Zyga, Lisa (20 February 2012). 7201:. New Scientist. Archived from 7107:. New Scientist. Archived from 7029:Cowen, Ron (27 February 2012). 6959:Ball, Philip (8 January 2016). 5400: 5325: 5298: 5233: 5208: 5183: 5110: 5085: 5012: 4987: 4962: 4897: 4761: 4747: 4736: 4722: 4708: 4668:www.cui-advanced.uni-hamburg.de 4490: 4421: 4314: 4249: 4195:"Quantum time crystals open up" 4193:Ball, Philip (September 2021). 4143:"Time Crystals in Open Systems" 3913: 3848: 3786: 3725: 3664: 3428: 3321: 3297: 3246: 3164: 3074: 3051: 3034: 3011: 2994: 2925: 2856: 2753: 2706: 2681: 2466: 2438: 2423:. singapore: World Scientific. 2410: 2389:Wilczek, Frank (16 July 2015). 1813:electron states in that setup, 10165:Non-equilibrium thermodynamics 6748:10.1103/PhysRevLett.111.250402 6693:10.1103/PhysRevLett.110.118902 6338:Reports on Progress in Physics 5966:10.1103/PhysRevLett.109.163001 5903:10.1103/PhysRevLett.116.250401 5793:10.1103/PhysRevLett.111.205303 5661:10.1103/PhysRevLett.117.090402 5598:10.1103/PhysRevLett.111.029301 5535:10.1103/PhysRevLett.110.118901 5468:10.1103/PhysRevLett.116.015503 4940:10.1103/PhysRevLett.126.057201 4814:10.1103/PhysRevLett.120.215301 4460:10.1103/PhysRevLett.123.210602 4292:10.1103/PhysRevLett.115.163601 4109:10.1103/PhysRevLett.127.043602 3956:10.1103/PhysRevLett.121.035301 3891:10.1103/PhysRevLett.123.260401 3826:10.1103/PhysRevLett.122.015701 3764:10.1103/PhysRevLett.120.040404 3703:10.1103/PhysRevLett.121.035301 3490:10.1103/PhysRevLett.118.030401 3134:10.1103/PhysRevLett.114.251603 2964:10.1103/PhysRevLett.109.160402 2895:10.1103/PhysRevLett.109.160401 2501:Ball, Philip (July 17, 2018). 2382: 2361:Cao, Tian Yu (25 March 2004). 2354: 2302:Reports on Progress in Physics 2293: 2237:"How to Create a Time Crystal" 2213: 2202: 2141: 1780: 1515:oscillating chemical reactions 1369: 1: 9742:Macroscopic quantum phenomena 8559:Adiabatic quantum computation 7568:Spontaneous symmetry breaking 7336:Zyga, Lisa (22 August 2013). 6967:. APS Physics. Archived from 5731:10.1016/S0370-1573(98)00022-2 3066:. APS Physics. Archived from 2133:. APS Physics. Archived from 2127:"Viewpoint: Crystals of Time" 2109: 2060:between which it oscillated. 1993:nitrogen-vacancy (NV) centers 1540:nonlinear dynamical systems. 1281:spontaneous symmetry breaking 1069:Ultimate fate of the universe 9752:Order and disorder (physics) 8954:Principle of maximum entropy 8610:Topological quantum computer 2503:"In search of time crystals" 2018:at subharmonic frequencies. 1336:Time crystals seem to break 7: 10093:Quantum information science 8888:Quantum information science 8055:Quantum information science 7378:. Science X. Archived from 7361:. Science X. Archived from 7327:. Science X. Archived from 7310:. Science X. Archived from 7259:. Science X. Archived from 7154:. Science X. 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(1967). 6812:10.1103/PhysRevB.92.224512 6570:10.1103/PhysRevB.94.085112 6252:10.1103/PhysRevA.91.033617 6204:10.1103/PhysRevA.91.063618 5694:"Driven quantum tunneling" 5305:Cho, Adrian (2022-03-02). 5266:10.1038/s41467-022-28462-x 4219:10.1038/s41563-021-01090-4 4029:10.1038/s41467-019-09757-y 3360:10.1103/PhysRevA.91.033617 2824:10.1038/s41586-021-04257-w 2180:10.1103/PhysRevA.91.033617 1979:obtained time crystals on 1966:protected eigenstate order 1624:University of Paris-Saclay 1607: 1534:parametric down-conversion 1274: 1245: 1220: 304:Spin gapless semiconductor 18: 10101: 10038: 9966: 9882: 9854: 9826: 9704: 9658: 9530: 9444: 9418: 9362: 9351: 9313: 9213: 9175: 9140: 9095: 9037: 8976: 8965: 8946: 8878: 8821: 8784: 8750: 8727: 8694: 8685: 8618: 8547: 8485: 8445: 8412:Quantum Fourier transform 8357: 8308:Post-quantum cryptography 8251:Entanglement distillation 8224: 8133: 8061: 7965: 7927: 7852: 7796: 7756: 7705: 7697:Density functional theory 7672:electronic band structure 7639: 7588: 7581: 7550: 7539: 7473: 7344:. Space X. Archived from 7224:10.1038/nature.2013.13657 6898:10.1007/978-3-030-52523-1 6886:Sacha, Krzysztof (2020). 6515:10.1134/S0021364013210133 6275:Sacha, Krzysztof (2015). 6099:10.1007/s10946-014-9404-9 4875:10.1038/s41563-020-0780-y 3404:10.1007/978-3-030-52523-1 3392:Sacha, Krzysztof (2020). 2713:Cowen, Ron (2017-02-02). 2527:10.1088/2058-7058/31/7/32 2395:. Penguin Books Limited. 1724:. The researchers used a 1665:time-translation symmetry 1387:{\displaystyle t\to t+nT} 1338:time-translation symmetry 1261:time-translation symmetry 1248:Time-translation symmetry 1242:Time-translation symmetry 244:Electronic band structure 10155:Condensed matter physics 10030:Condensed matter physics 9777:Thermo-dielectric effect 9676:Enthalpy of vaporization 9370:Bose–Einstein condensate 9238:Condensed matter physics 9221:Statistical field theory 8898:Quantum mechanics topics 8593:Quantum machine learning 8569:One-way quantum computer 8422:Quantum phase estimation 8323:Quantum key distribution 8256:Monogamy of entanglement 7867:Bogoliubov quasiparticle 7611:Quantum spin Hall effect 7503:Bose–Einstein condensate 7467:Condensed matter physics 6924: 6878: 6664:Wilczek, Frank (2013a). 6413:10.1103/PhysRev.138.B979 6368:10.1088/1361-6633/aa8b38 5856:10.1088/1367-2630/ab9d54 5499:Bruno, Patrick (2013a). 3922:"Boundary Time Crystals" 2569:"Discrete Time Crystals" 2332:10.1088/1361-6633/aa8b38 2053:phase localizing at two 2043:Bose–Einstein condensate 2025:, this time using IBM's 1922:dissipative time crystal 1883:In May 2018, a group in 1870:nitrogen-vacancy centers 1726:Bose–Einstein condensate 1297:Common crystals exhibit 1152:condensed matter physics 154:Bose–Einstein condensate 85:Condensed matter physics 9671:Enthalpy of sublimation 9096:Mathematical approaches 9085:Lennard-Jones potential 9001:thermodynamic potential 8505:Randomized benchmarking 8367:Amplitude amplification 7141:. Institute of Physics. 6718:Physical Review Letters 6673:Physical Review Letters 6625:10.1126/science.1239834 5936:Physical Review Letters 5873:Physical Review Letters 5763:Physical Review Letters 5631:Physical Review Letters 5568:Physical Review Letters 5505:Physical Review Letters 5438:Physical Review Letters 5319:10.1126/science.adb1790 5153:10.1126/science.abk0603 5055:10.1126/science.abg8102 4910:Physical Review Letters 4784:Physical Review Letters 4623:10.1126/science.add2015 4557:10.1126/science.abo3382 4430:Physical Review Letters 4408:10.1126/science.aba3793 4357:10.1126/science.aaw4465 4262:Physical Review Letters 4079:Physical Review Letters 3926:Physical Review Letters 3861:Physical Review Letters 3460:Physical Review Letters 3104:Physical Review Letters 2934:Physical Review Letters 2865:Physical Review Letters 2023:University of Melbourne 1803:acousto-optic modulator 1681:Jagiellonian University 1656:) and Masaki Oshikawa ( 1555:than the driving force, 1181:quantum computer memory 10114:Nobel Prize in Physics 9976:Relativistic mechanics 9686:Latent internal energy 9436:Color-glass condensate 9132:conformal field theory 8605:Quantum Turing machine 8598:quantum neural network 8345:Quantum secret sharing 7399:University of Maryland 7210:Powell, Devin (2013). 7122:scientificamerican.com 7035:scientificamerican.com 6951:10.1103/Physics.14.131 5826:New Journal of Physics 5368:10.1126/sciadv.abm7652 4168:10.1103/Physics.14.104 1977:University of Maryland 1959:spins are flipped for 1949:many-body localization 1909:and probed them under 1787:University of Maryland 1708:University of Maryland 1626: 1598:laws of thermodynamics 1579:many-body interactions 1500: 1480: 1460: 1440: 1439:{\displaystyle n>1} 1414: 1388: 1294: 1265:conservation of energy 1196:translational symmetry 10180:Statistical mechanics 10119:Philosophy of physics 9496:Magnetically ordered 9047:Ferromagnetism models 8940:Statistical mechanics 8677:Entanglement-assisted 8638:quantum convolutional 8313:Quantum coin flipping 8278:Quantum teleportation 8239:entanglement-assisted 8069:DiVincenzo's criteria 7743:Topological insulator 7677:Anderson localization 7382:on 11 September 2016. 5246:Nature Communications 3999:Nature Communications 3436:Khemani et al. (2016) 2209:Khemani et al. (2016) 2034:University of Hamburg 1918:University of Hamburg 1722:University of Hamburg 1615: 1501: 1481: 1461: 1441: 1415: 1389: 1288: 1211:discrete time crystal 299:Topological insulator 10078:Mathematical physics 9375:Fermionic condensate 8488:processor benchmarks 8417:Quantum optimization 8300:Quantum cryptography 8111:physical vs. logical 7621:Aharonov–Bohm effect 7508:Fermionic condensate 7274:popularmechanics.com 6944:. APS Physics: 131. 3316:Yoshii et al. (2015) 3000:See Li et al. ( 2262:10.1103/Physics.10.5 1645:, a nanoengineer at 1569:the system exhibits 1490: 1486:the driving period, 1470: 1450: 1424: 1398: 1363: 1200:translations in time 317:Electronic phenomena 164:Fermionic condensate 10053:Atmospheric physics 9892:Classical mechanics 9820:branches of physics 9590:Chemical ionization 9482:Programmable matter 9472:Quantum spin liquid 9340:Supercritical fluid 9226:elementary particle 8991:partition functions 8201:Quantum speed limit 8096:Quantum programming 8091:Quantum information 8012:Physics WikiProject 7687:tight binding model 7667:Fermi liquid theory 7652:Free electron model 7601:Quantum Hall effect 7582:Electrons in solids 7348:on 3 February 2017. 7331:on 3 February 2017. 7297:on 2 February 2017. 7280:on 3 February 2017. 7263:on 28 January 2017. 7246:on 3 February 2017. 7205:on 1 February 2017. 7175:on 3 February 2017. 7128:on 3 February 2017. 7111:on 2 February 2017. 7060:2017Natur.543..164G 7041:on 2 February 2017. 6990:2013Natur.493..166C 6971:on 3 February 2017. 6856:1967JETP...24.1006Z 6844:Soviet Physics JETP 6804:2015PhRvB..92v4512Y 6740:2013PhRvL.111y0402W 6685:2013PhRvL.110k8902W 6617:2013Sci...342..453W 6562:2016PhRvB..94h5112V 6507:2013JETPL..98..491V 6452:2016NatPh..12..907S 6405:1965PhRv..138..979S 6360:2018RPPh...81a6401S 6303:2015NatSR...510787S 6244:2015PhRvA..91c3617S 6195:2015PhRvA..91f3618R 6146:2013EL....10357008N 6050:2011NatPh...7..490L 6017:2012arXiv1212.6959L 5958:2012PhRvL.109p3001L 5895:2016PhRvL.116y0401K 5848:2020NJPh...22g5003G 5785:2013PhRvL.111t5303G 5713:1998PhR...304..229G 5653:2016PhRvL.117i0402E 5590:2013PhRvL.111b9301B 5527:2013PhRvL.110k8901B 5460:2016PhRvL.116a5503B 5360:2022SciA....8M7652F 5258:2022NatCo..13..848T 5145:2021Sci...374.1474R 5129:(6574): 1474–1478. 5047:2021Sci...372.1192K 5031:(6547): 1192–1196. 4932:2021PhRvL.126e7201T 4867:2021NatMa..20..171A 4806:2018PhRvL.120u5301A 4718:. 24 February 2024. 4615:2022Sci...377..576L 4549:2022Sci...377..670K 4452:2019PhRvL.123u0602K 4349:2019Sci...366.1496D 4333:(6472): 1496–1499. 4284:2015PhRvL.115p3601P 4211:2021NatMa..20.1172B 4159:2021PhyOJ..14..104G 4101:2021PhRvL.127d3602K 4021:2019NatCo..10.1730B 3948:2018PhRvL.121c5301I 3883:2019PhRvL.123z0401B 3818:2019PhRvL.122a5701G 3756:2018PhRvL.120d0404G 3695:2018PhRvL.121c5301I 3642:10.1038/nature21413 3634:2017Natur.543..217Z 3567:10.1038/nature21426 3559:2017Natur.543..221C 3482:2017PhRvL.118c0401Y 3352:2015PhRvA..91c3617S 3281:2020PhRvB.101x5148U 3195:2020PhRvB.102d1117M 3126:2015PhRvL.114y1603W 3070:on 2 February 2017. 3030:on 2 February 2017. 2956:2012PhRvL.109p0402S 2887:2012PhRvL.109p0401W 2816:2022Natur.601..531M 2741:. Popular Mechanics 2719:Scientific American 2651:2018PhT....71i..40Y 2595:2020ARCMP..11..467E 2519:2018PhyW...31g..29B 2324:2018RPPh...81a6401S 2253:2017PhyOJ..10....5R 2172:2015PhRvA..91c3617S 2137:on 2 February 2017. 1955:" system where all 1767:ground energy state 1702:and a group led by 1658:University of Tokyo 1523:Faraday instability 1519:aerodynamic flutter 1413:{\displaystyle n=1} 1215:thermal equilibrium 1164:lowest-energy state 1162:of particles whose 324:Quantum Hall effect 10170:Physical paradoxes 10109:History of physics 9737:Leidenfrost effect 9666:Enthalpy of fusion 9431:Quark–gluon plasma 9253:information theory 9160:correlation length 9155:Critical exponents 9142:Critical phenomena 9123:stochastic process 9103:Boltzmann equation 8996:equations of state 8850:Forest/Rigetti QCS 8586:quantum logic gate 8372:Bernstein–Vazirani 8359:Quantum algorithms 8234:Classical capacity 8118:Quantum processors 8101:Quantum simulation 7573:Critical phenomena 7413:Harvard University 7395:Christopher Monroe 6281:Scientific Reports 4757:. 5 February 2024. 4732:. 6 February 2024. 3440:Else et al. (2016) 3024:quantamagazine.org 2220:Else et al. (2016) 1973:quantum simulators 1941:Sycamore processor 1704:Christopher Monroe 1627: 1583:collective process 1560:crypto-equilibrium 1496: 1476: 1456: 1436: 1410: 1384: 1295: 1259:The basic idea of 1063:Radiometric dating 721:Physics portal 10175:Quantum mechanics 10137: 10136: 10124:Physics education 10073:Materials science 10040:Interdisciplinary 9998:Quantum mechanics 9785: 9784: 9767:Superheated vapor 9762:Superconductivity 9732:Equation of state 9580:Flash evaporation 9532:Phase transitions 9517:String-net liquid 9410:Photonic molecule 9380:Degenerate matter 9268: 9267: 9258:Boltzmann machine 9128:mean-field theory 9029:Maxwell relations 8906: 8905: 8817: 8816: 8714:Linear optical QC 8495:Quantum supremacy 8449:complexity theory 8402:Quantum annealing 8353: 8352: 8290:Superdense coding 8079:Quantum computing 8021: 8020: 7907:Exciton-polariton 7792: 7791: 7764:Thermoelectricity 7314:on 15 April 2013. 7054:(7644): 164–166. 6984:(7431): 166–167. 6907:978-3-030-52522-4 6782:Physical Review B 6601:(6157): 453–457. 6540:Physical Review B 6460:10.1038/nphys3783 6399:(4B): B979–B987. 6311:10.1038/srep10787 6222:Physical Review A 6183:Physical Review A 6058:10.1038/nphys1926 5429:Academic articles 4609:(6606): 576–577. 4533:(6606): 670–673. 3802:(15701): 015701. 3740:(40404): 040404. 3679:(35301): 035301. 3618:(7644): 217–220. 3543:(7644): 221–225. 3413:978-3-030-52522-4 3330:Physical Review A 3259:Physical Review B 3173:Physical Review B 3086:Yao et al. (2017) 2800:(7894): 531–536. 2659:10.1063/PT.3.4020 2486:978-3-540-72600-5 2458:978-3-540-72600-5 2430:978-981-238-711-0 2402:978-1-84614-702-9 2374:978-0-521-60272-3 2150:Physical Review A 2004:injection locking 1945:quantum computing 1669:"no-go" statement 1637:and professor at 1558:the system is in 1499:{\displaystyle n} 1479:{\displaystyle T} 1459:{\displaystyle t} 1303:Umklapp processes 1254:Noether's theorem 1192:symmetry breaking 1186:The existence of 1148: 1147: 771: 770: 469:Granular material 237:Electronic phases 79: 78: 71: 10192: 10063:Chemical physics 10003:Particle physics 9929:Classical optics 9812: 9805: 9798: 9789: 9788: 9722:Compressed fluid 9357: 9302:States of matter 9295: 9288: 9281: 9272: 9271: 9150:Phase transition 8971: 8970: 8933: 8926: 8919: 8910: 8909: 8896: 8895: 8886: 8885: 8692: 8691: 8622:error correction 8551:computing models 8517:Relaxation times 8407:Quantum counting 8296: 8295: 8244:quantum capacity 8191:No-teleportation 8176:No-communication 8048: 8041: 8034: 8025: 8024: 8009: 8008: 7997: 7985: 7984: 7973: 7972: 7912:Phonon polariton 7804:Amorphous magnet 7784:Electrostriction 7779:Flexoelectricity 7774:Ferroelectricity 7769:Piezoelectricity 7626:Josephson effect 7606:Spin Hall effect 7586: 7585: 7563:Phase transition 7545: 7528:Luttinger liquid 7475:States of matter 7460: 7453: 7446: 7437: 7436: 7383: 7366: 7349: 7332: 7315: 7298: 7281: 7264: 7247: 7242:. Archived from 7206: 7199:newscientist.com 7189: 7176: 7169:physicsworld.com 7159: 7142: 7139:physicsworld.com 7129: 7112: 7105:newscientist.com 7095: 7042: 7025: 6972: 6955: 6953: 6919: 6873: 6871: 6870: 6864: 6858:. Archived from 6850:(5): 1006–1008. 6841: 6831: 6797: 6775: 6733: 6712: 6670: 6660: 6610: 6589: 6555: 6534: 6500: 6479: 6445: 6424: 6387: 6353: 6332: 6322: 6296: 6271: 6237: 6216: 6206: 6173: 6139: 6118: 6077: 6043: 6020: 6010: 5993: 5951: 5930: 5888: 5867: 5841: 5820: 5778: 5757: 5755: 5749:. Archived from 5724: 5707:(5–6): 229–354. 5698: 5688: 5646: 5625: 5583: 5562: 5520: 5495: 5453: 5423: 5422: 5420: 5419: 5413:The Conversation 5404: 5398: 5397: 5387: 5353: 5338:Science Advances 5329: 5323: 5322: 5302: 5296: 5295: 5285: 5237: 5231: 5230: 5228: 5227: 5212: 5206: 5205: 5203: 5202: 5187: 5181: 5180: 5138: 5114: 5108: 5107: 5105: 5104: 5089: 5083: 5082: 5040: 5016: 5010: 5009: 5007: 5006: 4991: 4985: 4984: 4982: 4981: 4966: 4960: 4959: 4925: 4901: 4895: 4894: 4860: 4845:Nature Materials 4840: 4834: 4833: 4799: 4779: 4773: 4772: 4765: 4759: 4758: 4751: 4745: 4740: 4734: 4733: 4726: 4720: 4719: 4712: 4706: 4705: 4703: 4702: 4687: 4678: 4677: 4675: 4674: 4660: 4651: 4650: 4594: 4585: 4584: 4542: 4518: 4509: 4508: 4506: 4494: 4488: 4487: 4445: 4425: 4419: 4418: 4416: 4414: 4391: 4385: 4384: 4342: 4318: 4312: 4311: 4277: 4253: 4247: 4246: 4199:Nature Materials 4190: 4181: 4180: 4170: 4138: 4129: 4128: 4094: 4070: 4059: 4058: 4048: 4014: 3990: 3984: 3983: 3941: 3917: 3911: 3910: 3876: 3852: 3846: 3845: 3811: 3790: 3784: 3783: 3749: 3729: 3723: 3722: 3688: 3668: 3662: 3661: 3627: 3606: 3597: 3596: 3586: 3552: 3527: 3518: 3517: 3475: 3451: 3442: 3432: 3426: 3425: 3389: 3383: 3382: 3345: 3325: 3319: 3313: 3301: 3295: 3294: 3292: 3274: 3250: 3244: 3243: 3241: 3229: 3223: 3222: 3188: 3168: 3162: 3161: 3119: 3099: 3093: 3088:, p. 1 and 3078: 3072: 3071: 3055: 3049: 3038: 3032: 3031: 3015: 3009: 2998: 2992: 2991: 2949: 2929: 2923: 2922: 2880: 2860: 2854: 2853: 2843: 2809: 2785: 2776: 2775: 2773: 2772: 2757: 2751: 2750: 2748: 2746: 2735: 2729: 2728: 2726: 2725: 2710: 2704: 2703: 2701: 2700: 2685: 2679: 2678: 2644: 2624: 2615: 2614: 2588: 2564: 2549: 2548: 2543: 2541: 2498: 2492: 2491:See p. 191. 2490: 2470: 2464: 2463:See p. 193. 2462: 2442: 2436: 2434: 2414: 2408: 2406: 2386: 2380: 2379:See p. 151. 2378: 2358: 2352: 2351: 2317: 2297: 2291: 2290: 2283: 2274: 2273: 2271: 2269: 2264: 2232: 2223: 2217: 2211: 2206: 2200: 2199: 2165: 2145: 2139: 2138: 2122: 2101: 2100: 2089: 2088: 2077: 2076: 2068: 1896:Nature Materials 1885:Aalto University 1848: 1833: 1756: 1749: 1734:Tilman Esslinger 1571:long-range order 1511:convection cells 1505: 1503: 1502: 1497: 1485: 1483: 1482: 1477: 1465: 1463: 1462: 1457: 1445: 1443: 1442: 1437: 1419: 1417: 1416: 1411: 1393: 1391: 1390: 1385: 1277:Crystal symmetry 1140: 1133: 1126: 1070: 954:Day of Judgement 787: 773: 772: 763: 756: 749: 736: 731: 730: 723: 719: 718: 329:Spin Hall effect 219:Phase transition 189:Luttinger liquid 126:States of matter 109:Phase transition 95: 81: 80: 74: 67: 63: 60: 54: 34: 33: 26: 10200: 10199: 10195: 10194: 10193: 10191: 10190: 10189: 10185:2012 in science 10160:Crystallography 10140: 10139: 10138: 10133: 10097: 10083:Medical physics 10034: 9993:Nuclear physics 9962: 9956:Non-equilibrium 9878: 9850: 9822: 9816: 9786: 9781: 9712:Baryonic matter 9700: 9654: 9625:Saturated fluid 9565:Crystallization 9526: 9500:Antiferromagnet 9440: 9414: 9358: 9349: 9309: 9299: 9269: 9264: 9209: 9171: 9136: 9118:BBGKY hierarchy 9113:Vlasov equation 9091: 9080:depletion force 9073:Particles with 9033: 8972: 8968: 8963: 8942: 8937: 8907: 8902: 8874: 8824: 8813: 8786:Superconducting 8780: 8746: 8737:Neutral atom QC 8729:Ultracold atoms 8723: 8688:implementations 8687: 8681: 8621: 8614: 8581:Quantum circuit 8549: 8543: 8537: 8527: 8487: 8481: 8448: 8441: 8397:Hidden subgroup 8349: 8338:other protocols 8294: 8271:quantum network 8266:Quantum channel 8226: 8220: 8166:No-broadcasting 8156:Gottesman–Knill 8129: 8057: 8052: 8022: 8017: 7961: 7942:Granular matter 7937:Amorphous solid 7923: 7848: 7834:Antiferromagnet 7824:Superparamagnet 7797:Magnetic phases 7788: 7752: 7701: 7662:Bloch's theorem 7635: 7577: 7558:Order parameter 7551:Phase phenomena 7546: 7537: 7469: 7464: 7427:Krzysztof Sacha 7391: 7386: 7365:on 9 July 2015. 7158:on 4 July 2013. 7068:10.1038/543164a 6998:10.1038/493166a 6965:physics.aps.org 6927: 6922: 6908: 6881: 6876: 6868: 6866: 6862: 6839: 6668: 6666:"Wilczek Reply" 6436:(10): 907–911. 6393:Physical Review 5753: 5701:Physics Reports 5696: 5431: 5426: 5417: 5415: 5405: 5401: 5344:(9): eabm7652. 5330: 5326: 5303: 5299: 5238: 5234: 5225: 5223: 5213: 5209: 5200: 5198: 5188: 5184: 5115: 5111: 5102: 5100: 5090: 5086: 5017: 5013: 5004: 5002: 5000:Quanta Magazine 4992: 4988: 4979: 4977: 4967: 4963: 4902: 4898: 4841: 4837: 4780: 4776: 4767: 4766: 4762: 4753: 4752: 4748: 4741: 4737: 4728: 4727: 4723: 4714: 4713: 4709: 4700: 4698: 4688: 4681: 4672: 4670: 4662: 4661: 4654: 4595: 4588: 4519: 4512: 4495: 4491: 4426: 4422: 4412: 4410: 4392: 4388: 4319: 4315: 4254: 4250: 4191: 4184: 4139: 4132: 4071: 4062: 3991: 3987: 3918: 3914: 3853: 3849: 3796:Phys. Rev. Lett 3791: 3787: 3734:Phys. Rev. Lett 3730: 3726: 3673:Phys. Rev. Lett 3669: 3665: 3607: 3600: 3528: 3521: 3452: 3445: 3433: 3429: 3414: 3390: 3386: 3326: 3322: 3307: 3305:Wilczek (2013b) 3302: 3298: 3251: 3247: 3230: 3226: 3169: 3165: 3100: 3096: 3082:Nozières (2013) 3079: 3075: 3064:physics.aps.org 3056: 3052: 3039: 3035: 3016: 3012: 2999: 2995: 2930: 2926: 2861: 2857: 2786: 2779: 2770: 2768: 2758: 2754: 2744: 2742: 2737: 2736: 2732: 2723: 2721: 2711: 2707: 2698: 2696: 2686: 2682: 2625: 2618: 2565: 2552: 2539: 2537: 2499: 2495: 2487: 2471: 2467: 2459: 2443: 2439: 2435:See p. 18. 2431: 2415: 2411: 2403: 2387: 2383: 2375: 2359: 2355: 2298: 2294: 2285: 2284: 2277: 2267: 2265: 2233: 2226: 2218: 2214: 2207: 2203: 2146: 2142: 2131:physics.aps.org 2123: 2116: 2112: 2107: 2095: 2083: 2071: 2063: 1926:ultracold atoms 1846: 1835: 1830: 1820: 1819: 1783: 1751: 1745: 1716:in March 2017. 1677:Krzysztof Sacha 1610: 1594: 1491: 1488: 1487: 1471: 1468: 1467: 1451: 1448: 1447: 1425: 1422: 1421: 1399: 1396: 1395: 1364: 1361: 1360: 1334: 1283: 1275:Main articles: 1273: 1250: 1244: 1223: 1144: 1115: 1114: 1090: 1089: 1080: 1079: 1075:Time in physics 1068: 1043: 1042: 1041: 1022: 1021: 1002: 1001: 1000: 979: 978: 939: 938: 937: 918: 917: 893: 892: 881: 880: 841: 840: 839:Fields of study 831: 830: 797: 796: 767: 726: 713: 712: 705: 704: 703: 493: 485: 484: 483: 459:Amorphous solid 453: 443: 442: 441: 420: 402: 392: 391: 390: 379: 377:Antiferromagnet 370: 368:Superparamagnet 361: 348: 347:Magnetic phases 340: 339: 338: 318: 310: 309: 308: 238: 230: 229: 228: 214:Order parameter 208: 207:Phase phenomena 200: 199: 198: 128: 118: 75: 64: 58: 55: 47:help improve it 44: 35: 31: 24: 17: 12: 11: 5: 10198: 10188: 10187: 10182: 10177: 10172: 10167: 10162: 10157: 10152: 10135: 10134: 10132: 10131: 10126: 10121: 10116: 10111: 10105: 10103: 10099: 10098: 10096: 10095: 10090: 10085: 10080: 10075: 10070: 10065: 10060: 10055: 10050: 10044: 10042: 10036: 10035: 10033: 10032: 10027: 10026: 10025: 10020: 10015: 10005: 10000: 9995: 9990: 9989: 9988: 9983: 9972: 9970: 9964: 9963: 9961: 9960: 9959: 9958: 9953: 9946:Thermodynamics 9943: 9942: 9941: 9936: 9926: 9921: 9916: 9915: 9914: 9909: 9904: 9899: 9888: 9886: 9880: 9879: 9877: 9876: 9875: 9874: 9864: 9858: 9856: 9852: 9851: 9849: 9848: 9847: 9846: 9836: 9830: 9828: 9824: 9823: 9815: 9814: 9807: 9800: 9792: 9783: 9782: 9780: 9779: 9774: 9769: 9764: 9759: 9754: 9749: 9744: 9739: 9734: 9729: 9724: 9719: 9714: 9708: 9706: 9702: 9701: 9699: 9698: 9693: 9691:Trouton's rule 9688: 9683: 9678: 9673: 9668: 9662: 9660: 9656: 9655: 9653: 9652: 9647: 9642: 9637: 9632: 9627: 9622: 9617: 9612: 9607: 9602: 9597: 9592: 9587: 9582: 9577: 9572: 9567: 9562: 9560:Critical point 9557: 9552: 9547: 9542: 9536: 9534: 9528: 9527: 9525: 9524: 9519: 9514: 9513: 9512: 9507: 9502: 9494: 9489: 9484: 9479: 9474: 9469: 9464: 9462:Liquid crystal 9459: 9454: 9448: 9446: 9442: 9441: 9439: 9438: 9433: 9428: 9422: 9420: 9416: 9415: 9413: 9412: 9407: 9402: 9397: 9395:Strange matter 9392: 9390:Rydberg matter 9387: 9382: 9377: 9372: 9366: 9364: 9360: 9359: 9352: 9350: 9348: 9347: 9342: 9337: 9328: 9323: 9317: 9315: 9311: 9310: 9298: 9297: 9290: 9283: 9275: 9266: 9265: 9263: 9262: 9261: 9260: 9255: 9250: 9243:Complex system 9240: 9235: 9234: 9233: 9228: 9217: 9215: 9211: 9210: 9208: 9207: 9202: 9197: 9192: 9187: 9181: 9179: 9173: 9172: 9170: 9169: 9168: 9167: 9162: 9152: 9146: 9144: 9138: 9137: 9135: 9134: 9125: 9120: 9115: 9110: 9105: 9099: 9097: 9093: 9092: 9090: 9089: 9088: 9087: 9082: 9071: 9070: 9069: 9064: 9059: 9054: 9043: 9041: 9035: 9034: 9032: 9031: 9026: 9025: 9024: 9019: 9014: 9009: 8998: 8993: 8988: 8982: 8980: 8974: 8973: 8966: 8964: 8962: 8961: 8959:ergodic theory 8956: 8950: 8948: 8944: 8943: 8936: 8935: 8928: 8921: 8913: 8904: 8903: 8901: 8900: 8890: 8879: 8876: 8875: 8873: 8872: 8870:many others... 8867: 8862: 8857: 8852: 8843: 8829: 8827: 8819: 8818: 8815: 8814: 8812: 8811: 8806: 8801: 8796: 8790: 8788: 8782: 8781: 8779: 8778: 8773: 8768: 8763: 8757: 8755: 8748: 8747: 8745: 8744: 8742:Trapped-ion QC 8739: 8733: 8731: 8725: 8724: 8722: 8721: 8716: 8711: 8706: 8700: 8698: 8696:Quantum optics 8689: 8683: 8682: 8680: 8679: 8674: 8673: 8672: 8665: 8660: 8655: 8650: 8645: 8640: 8635: 8626: 8624: 8616: 8615: 8613: 8612: 8607: 8602: 8601: 8600: 8590: 8589: 8588: 8578: 8577: 8576: 8566: 8561: 8555: 8553: 8545: 8544: 8542: 8541: 8540: 8539: 8535: 8529: 8525: 8514: 8513: 8512: 8502: 8500:Quantum volume 8497: 8491: 8489: 8483: 8482: 8480: 8479: 8474: 8469: 8464: 8459: 8453: 8451: 8443: 8442: 8440: 8439: 8434: 8429: 8424: 8419: 8414: 8409: 8404: 8399: 8394: 8389: 8384: 8379: 8377:Boson sampling 8374: 8369: 8363: 8361: 8355: 8354: 8351: 8350: 8348: 8347: 8342: 8341: 8340: 8335: 8330: 8320: 8315: 8310: 8304: 8302: 8293: 8292: 8287: 8286: 8285: 8275: 8274: 8273: 8263: 8258: 8253: 8248: 8247: 8246: 8241: 8230: 8228: 8222: 8221: 8219: 8218: 8213: 8211:Solovay–Kitaev 8208: 8203: 8198: 8193: 8188: 8183: 8178: 8173: 8168: 8163: 8158: 8153: 8148: 8143: 8137: 8135: 8131: 8130: 8128: 8127: 8126: 8125: 8115: 8114: 8113: 8103: 8098: 8093: 8088: 8087: 8086: 8076: 8071: 8065: 8063: 8059: 8058: 8051: 8050: 8043: 8036: 8028: 8019: 8018: 8016: 8015: 8003: 8000:Physics Portal 7991: 7979: 7966: 7963: 7962: 7960: 7959: 7954: 7949: 7947:Liquid crystal 7944: 7939: 7933: 7931: 7925: 7924: 7922: 7921: 7916: 7915: 7914: 7909: 7899: 7894: 7889: 7884: 7879: 7874: 7869: 7864: 7858: 7856: 7854:Quasiparticles 7850: 7849: 7847: 7846: 7841: 7836: 7831: 7826: 7821: 7816: 7814:Superdiamagnet 7811: 7806: 7800: 7798: 7794: 7793: 7790: 7789: 7787: 7786: 7781: 7776: 7771: 7766: 7760: 7758: 7754: 7753: 7751: 7750: 7745: 7740: 7738:Superconductor 7735: 7730: 7725: 7720: 7718:Mott insulator 7715: 7709: 7707: 7703: 7702: 7700: 7699: 7694: 7689: 7684: 7679: 7674: 7669: 7664: 7659: 7654: 7649: 7643: 7641: 7637: 7636: 7634: 7633: 7628: 7623: 7618: 7613: 7608: 7603: 7598: 7592: 7590: 7583: 7579: 7578: 7576: 7575: 7570: 7565: 7560: 7554: 7552: 7548: 7547: 7540: 7538: 7536: 7535: 7530: 7525: 7520: 7515: 7510: 7505: 7500: 7495: 7490: 7485: 7479: 7477: 7471: 7470: 7463: 7462: 7455: 7448: 7440: 7434: 7433: 7424: 7415: 7406: 7401: 7390: 7389:External links 7387: 7385: 7384: 7367: 7350: 7333: 7316: 7299: 7282: 7265: 7248: 7207: 7190: 7177: 7160: 7143: 7130: 7113: 7096: 7043: 7026: 6973: 6956: 6928: 6926: 6923: 6921: 6920: 6906: 6882: 6880: 6877: 6875: 6874: 6832: 6788:(22): 224512. 6776: 6724:(25): 250402. 6713: 6679:(11): 118902. 6661: 6590: 6535: 6491:(8): 491–495. 6480: 6430:Nature Physics 6425: 6388: 6333: 6272: 6217: 6174: 6119: 6078: 6034:(6): 490–495. 6028:Nature Physics 6022: 6021: 5994: 5942:(16): 163001. 5931: 5879:(25): 250401. 5868: 5821: 5769:(20): 205303. 5758: 5756:on 2017-02-11. 5722:10.1.1.65.9479 5689: 5626: 5563: 5511:(11): 118901. 5496: 5432: 5430: 5427: 5425: 5424: 5399: 5324: 5297: 5232: 5207: 5182: 5109: 5084: 5011: 4986: 4961: 4896: 4851:(2): 171–174. 4835: 4790:(21): 215301. 4774: 4760: 4746: 4735: 4721: 4707: 4679: 4652: 4586: 4510: 4489: 4436:(21): 210602. 4420: 4386: 4313: 4268:(16): 163601. 4248: 4182: 4130: 4060: 3985: 3912: 3867:(26): 260401. 3847: 3785: 3724: 3663: 3598: 3519: 3443: 3427: 3412: 3384: 3320: 3296: 3265:(24): 245148. 3245: 3224: 3163: 3110:(25): 251603. 3094: 3090:Volovik (2013) 3073: 3050: 3033: 3010: 2993: 2940:(16): 160402. 2924: 2871:(16): 160401. 2855: 2777: 2752: 2730: 2705: 2680: 2616: 2550: 2493: 2485: 2465: 2457: 2437: 2429: 2409: 2401: 2381: 2373: 2353: 2292: 2275: 2224: 2212: 2201: 2140: 2113: 2111: 2108: 2106: 2105: 2093: 2081: 2047:optical cavity 2008:microresonator 1930:optical cavity 1928:coupled to an 1860:Also in 2016, 1851:Doppler-cooled 1844: 1828: 1817: 1782: 1779: 1730:optical cavity 1635:Nobel laureate 1617:Nobel laureate 1609: 1606: 1593: 1592:Thermodynamics 1590: 1575: 1574: 1567: 1556: 1538:period-doubled 1495: 1475: 1455: 1435: 1432: 1429: 1409: 1406: 1403: 1383: 1380: 1377: 1374: 1371: 1368: 1333: 1330: 1329: 1328: 1325: 1322: 1272: 1269: 1246:Main article: 1243: 1240: 1222: 1219: 1160:quantum system 1146: 1145: 1143: 1142: 1135: 1128: 1120: 1117: 1116: 1113: 1112: 1107: 1102: 1097: 1091: 1088:Related topics 1087: 1086: 1085: 1082: 1081: 1078: 1077: 1072: 1065: 1060: 1055: 1050: 1044: 1040: 1039: 1034: 1030: 1029: 1028: 1027: 1024: 1023: 1020: 1019: 1014: 1009: 1003: 999: 998: 993: 987: 986: 985: 984: 981: 980: 977: 976: 971: 966: 961: 956: 951: 946: 940: 936: 935: 932: 926: 925: 924: 923: 920: 919: 916: 915: 910: 905: 900: 894: 888: 887: 886: 883: 882: 879: 878: 873: 868: 863: 858: 853: 848: 842: 838: 837: 836: 833: 832: 829: 828: 827: 826: 815: 814: 809: 804: 798: 795:Major concepts 794: 793: 792: 789: 788: 780: 779: 769: 768: 766: 765: 758: 751: 743: 740: 739: 738: 737: 724: 707: 706: 702: 701: 696: 691: 686: 681: 676: 671: 666: 661: 656: 651: 646: 641: 636: 631: 626: 621: 616: 611: 606: 601: 596: 591: 586: 581: 576: 571: 566: 561: 556: 551: 546: 541: 536: 531: 526: 521: 516: 511: 506: 501: 495: 494: 491: 490: 487: 486: 482: 481: 476: 474:Liquid crystal 471: 466: 461: 455: 454: 449: 448: 445: 444: 440: 439: 434: 429: 424: 415: 410: 404: 403: 400:Quasiparticles 398: 397: 394: 393: 389: 388: 383: 374: 365: 359:Superdiamagnet 356: 350: 349: 346: 345: 342: 341: 337: 336: 331: 326: 320: 319: 316: 315: 312: 311: 307: 306: 301: 296: 291: 286: 284:Thermoelectric 281: 279:Superconductor 276: 271: 266: 261: 259:Mott insulator 256: 251: 246: 240: 239: 236: 235: 232: 231: 227: 226: 221: 216: 210: 209: 206: 205: 202: 201: 197: 196: 191: 186: 181: 176: 171: 166: 161: 156: 151: 146: 141: 136: 130: 129: 124: 123: 120: 119: 117: 116: 111: 106: 100: 97: 96: 88: 87: 77: 76: 38: 36: 29: 21:timing crystal 15: 9: 6: 4: 3: 2: 10197: 10186: 10183: 10181: 10178: 10176: 10173: 10171: 10168: 10166: 10163: 10161: 10158: 10156: 10153: 10151: 10148: 10147: 10145: 10130: 10127: 10125: 10122: 10120: 10117: 10115: 10112: 10110: 10107: 10106: 10104: 10100: 10094: 10091: 10089: 10088:Ocean physics 10086: 10084: 10081: 10079: 10076: 10074: 10071: 10069: 10066: 10064: 10061: 10059: 10056: 10054: 10051: 10049: 10046: 10045: 10043: 10041: 10037: 10031: 10028: 10024: 10023:Modern optics 10021: 10019: 10016: 10014: 10011: 10010: 10009: 10006: 10004: 10001: 9999: 9996: 9994: 9991: 9987: 9984: 9982: 9979: 9978: 9977: 9974: 9973: 9971: 9969: 9965: 9957: 9954: 9952: 9949: 9948: 9947: 9944: 9940: 9937: 9935: 9932: 9931: 9930: 9927: 9925: 9922: 9920: 9917: 9913: 9910: 9908: 9905: 9903: 9900: 9898: 9895: 9894: 9893: 9890: 9889: 9887: 9885: 9881: 9873: 9872:Computational 9870: 9869: 9868: 9865: 9863: 9860: 9859: 9857: 9853: 9845: 9842: 9841: 9840: 9837: 9835: 9832: 9831: 9829: 9825: 9821: 9813: 9808: 9806: 9801: 9799: 9794: 9793: 9790: 9778: 9775: 9773: 9770: 9768: 9765: 9763: 9760: 9758: 9755: 9753: 9750: 9748: 9747:Mpemba effect 9745: 9743: 9740: 9738: 9735: 9733: 9730: 9728: 9727:Cooling curve 9725: 9723: 9720: 9718: 9715: 9713: 9710: 9709: 9707: 9703: 9697: 9694: 9692: 9689: 9687: 9684: 9682: 9679: 9677: 9674: 9672: 9669: 9667: 9664: 9663: 9661: 9657: 9651: 9650:Vitrification 9648: 9646: 9643: 9641: 9638: 9636: 9633: 9631: 9628: 9626: 9623: 9621: 9618: 9616: 9615:Recombination 9613: 9611: 9610:Melting point 9608: 9606: 9603: 9601: 9598: 9596: 9593: 9591: 9588: 9586: 9583: 9581: 9578: 9576: 9573: 9571: 9568: 9566: 9563: 9561: 9558: 9556: 9555:Critical line 9553: 9551: 9548: 9546: 9545:Boiling point 9543: 9541: 9538: 9537: 9535: 9533: 9529: 9523: 9520: 9518: 9515: 9511: 9508: 9506: 9503: 9501: 9498: 9497: 9495: 9493: 9490: 9488: 9485: 9483: 9480: 9478: 9477:Exotic matter 9475: 9473: 9470: 9468: 9465: 9463: 9460: 9458: 9455: 9453: 9450: 9449: 9447: 9443: 9437: 9434: 9432: 9429: 9427: 9424: 9423: 9421: 9417: 9411: 9408: 9406: 9403: 9401: 9398: 9396: 9393: 9391: 9388: 9386: 9383: 9381: 9378: 9376: 9373: 9371: 9368: 9367: 9365: 9361: 9356: 9346: 9343: 9341: 9338: 9336: 9332: 9329: 9327: 9324: 9322: 9319: 9318: 9316: 9312: 9307: 9303: 9296: 9291: 9289: 9284: 9282: 9277: 9276: 9273: 9259: 9256: 9254: 9251: 9249: 9246: 9245: 9244: 9241: 9239: 9236: 9232: 9231:superfluidity 9229: 9227: 9224: 9223: 9222: 9219: 9218: 9216: 9212: 9206: 9203: 9201: 9198: 9196: 9193: 9191: 9188: 9186: 9183: 9182: 9180: 9178: 9174: 9166: 9163: 9161: 9158: 9157: 9156: 9153: 9151: 9148: 9147: 9145: 9143: 9139: 9133: 9129: 9126: 9124: 9121: 9119: 9116: 9114: 9111: 9109: 9106: 9104: 9101: 9100: 9098: 9094: 9086: 9083: 9081: 9078: 9077: 9076: 9072: 9068: 9065: 9063: 9060: 9058: 9055: 9053: 9050: 9049: 9048: 9045: 9044: 9042: 9040: 9036: 9030: 9027: 9023: 9020: 9018: 9015: 9013: 9010: 9008: 9005: 9004: 9002: 8999: 8997: 8994: 8992: 8989: 8987: 8984: 8983: 8981: 8979: 8975: 8960: 8957: 8955: 8952: 8951: 8949: 8945: 8941: 8934: 8929: 8927: 8922: 8920: 8915: 8914: 8911: 8899: 8891: 8889: 8881: 8880: 8877: 8871: 8868: 8866: 8863: 8861: 8858: 8856: 8853: 8851: 8847: 8844: 8842: 8838: 8834: 8831: 8830: 8828: 8826: 8820: 8810: 8807: 8805: 8802: 8800: 8797: 8795: 8792: 8791: 8789: 8787: 8783: 8777: 8774: 8772: 8769: 8767: 8766:Spin qubit QC 8764: 8762: 8759: 8758: 8756: 8753: 8749: 8743: 8740: 8738: 8735: 8734: 8732: 8730: 8726: 8720: 8717: 8715: 8712: 8710: 8707: 8705: 8702: 8701: 8699: 8697: 8693: 8690: 8684: 8678: 8675: 8671: 8670: 8666: 8664: 8661: 8659: 8656: 8654: 8651: 8649: 8646: 8644: 8641: 8639: 8636: 8634: 8631: 8630: 8628: 8627: 8625: 8623: 8617: 8611: 8608: 8606: 8603: 8599: 8596: 8595: 8594: 8591: 8587: 8584: 8583: 8582: 8579: 8575: 8574:cluster state 8572: 8571: 8570: 8567: 8565: 8562: 8560: 8557: 8556: 8554: 8552: 8546: 8538: 8534: 8530: 8528: 8524: 8520: 8519: 8518: 8515: 8511: 8508: 8507: 8506: 8503: 8501: 8498: 8496: 8493: 8492: 8490: 8484: 8478: 8475: 8473: 8470: 8468: 8465: 8463: 8460: 8458: 8455: 8454: 8452: 8450: 8444: 8438: 8435: 8433: 8430: 8428: 8425: 8423: 8420: 8418: 8415: 8413: 8410: 8408: 8405: 8403: 8400: 8398: 8395: 8393: 8390: 8388: 8385: 8383: 8382:Deutsch–Jozsa 8380: 8378: 8375: 8373: 8370: 8368: 8365: 8364: 8362: 8360: 8356: 8346: 8343: 8339: 8336: 8334: 8331: 8329: 8326: 8325: 8324: 8321: 8319: 8318:Quantum money 8316: 8314: 8311: 8309: 8306: 8305: 8303: 8301: 8297: 8291: 8288: 8284: 8281: 8280: 8279: 8276: 8272: 8269: 8268: 8267: 8264: 8262: 8259: 8257: 8254: 8252: 8249: 8245: 8242: 8240: 8237: 8236: 8235: 8232: 8231: 8229: 8227:communication 8223: 8217: 8214: 8212: 8209: 8207: 8204: 8202: 8199: 8197: 8194: 8192: 8189: 8187: 8184: 8182: 8179: 8177: 8174: 8172: 8169: 8167: 8164: 8162: 8159: 8157: 8154: 8152: 8149: 8147: 8144: 8142: 8139: 8138: 8136: 8132: 8124: 8121: 8120: 8119: 8116: 8112: 8109: 8108: 8107: 8104: 8102: 8099: 8097: 8094: 8092: 8089: 8085: 8082: 8081: 8080: 8077: 8075: 8072: 8070: 8067: 8066: 8064: 8060: 8056: 8049: 8044: 8042: 8037: 8035: 8030: 8029: 8026: 8014: 8013: 8004: 8002: 8001: 7996: 7992: 7990: 7989: 7980: 7978: 7977: 7968: 7967: 7964: 7958: 7955: 7953: 7950: 7948: 7945: 7943: 7940: 7938: 7935: 7934: 7932: 7930: 7926: 7920: 7917: 7913: 7910: 7908: 7905: 7904: 7903: 7900: 7898: 7895: 7893: 7890: 7888: 7885: 7883: 7880: 7878: 7875: 7873: 7870: 7868: 7865: 7863: 7860: 7859: 7857: 7855: 7851: 7845: 7842: 7840: 7837: 7835: 7832: 7830: 7827: 7825: 7822: 7820: 7817: 7815: 7812: 7810: 7807: 7805: 7802: 7801: 7799: 7795: 7785: 7782: 7780: 7777: 7775: 7772: 7770: 7767: 7765: 7762: 7761: 7759: 7755: 7749: 7746: 7744: 7741: 7739: 7736: 7734: 7731: 7729: 7726: 7724: 7723:Semiconductor 7721: 7719: 7716: 7714: 7711: 7710: 7708: 7704: 7698: 7695: 7693: 7692:Hubbard model 7690: 7688: 7685: 7683: 7680: 7678: 7675: 7673: 7670: 7668: 7665: 7663: 7660: 7658: 7655: 7653: 7650: 7648: 7645: 7644: 7642: 7638: 7632: 7629: 7627: 7624: 7622: 7619: 7617: 7614: 7612: 7609: 7607: 7604: 7602: 7599: 7597: 7594: 7593: 7591: 7587: 7584: 7580: 7574: 7571: 7569: 7566: 7564: 7561: 7559: 7556: 7555: 7553: 7549: 7544: 7534: 7531: 7529: 7526: 7524: 7521: 7519: 7516: 7514: 7511: 7509: 7506: 7504: 7501: 7499: 7496: 7494: 7491: 7489: 7486: 7484: 7481: 7480: 7478: 7476: 7472: 7468: 7461: 7456: 7454: 7449: 7447: 7442: 7441: 7438: 7432: 7428: 7425: 7423: 7419: 7416: 7414: 7410: 7407: 7405: 7404:Frank Wilczek 7402: 7400: 7396: 7393: 7392: 7381: 7377: 7373: 7368: 7364: 7360: 7356: 7351: 7347: 7343: 7339: 7334: 7330: 7326: 7322: 7317: 7313: 7309: 7305: 7300: 7296: 7292: 7291:csmonitor.com 7288: 7283: 7279: 7275: 7271: 7266: 7262: 7258: 7254: 7249: 7245: 7241: 7237: 7233: 7229: 7225: 7221: 7217: 7213: 7208: 7204: 7200: 7196: 7191: 7187: 7183: 7178: 7174: 7170: 7166: 7161: 7157: 7153: 7149: 7144: 7140: 7136: 7131: 7127: 7123: 7119: 7114: 7110: 7106: 7102: 7097: 7093: 7089: 7085: 7081: 7077: 7073: 7069: 7065: 7061: 7057: 7053: 7049: 7044: 7040: 7036: 7032: 7027: 7023: 7019: 7015: 7011: 7007: 7003: 6999: 6995: 6991: 6987: 6983: 6979: 6974: 6970: 6966: 6962: 6957: 6952: 6947: 6943: 6939: 6935: 6930: 6929: 6917: 6913: 6909: 6903: 6899: 6895: 6891: 6890: 6889:Time Crystals 6884: 6883: 6865:on 2017-02-11 6861: 6857: 6853: 6849: 6845: 6838: 6833: 6829: 6825: 6821: 6817: 6813: 6809: 6805: 6801: 6796: 6791: 6787: 6783: 6777: 6773: 6769: 6765: 6761: 6757: 6753: 6749: 6745: 6741: 6737: 6732: 6727: 6723: 6719: 6714: 6710: 6706: 6702: 6698: 6694: 6690: 6686: 6682: 6678: 6674: 6667: 6662: 6658: 6654: 6650: 6646: 6642: 6638: 6634: 6630: 6626: 6622: 6618: 6614: 6609: 6604: 6600: 6596: 6591: 6587: 6583: 6579: 6575: 6571: 6567: 6563: 6559: 6554: 6549: 6546:(8): 085112. 6545: 6541: 6536: 6532: 6528: 6524: 6520: 6516: 6512: 6508: 6504: 6499: 6494: 6490: 6486: 6481: 6477: 6473: 6469: 6465: 6461: 6457: 6453: 6449: 6444: 6439: 6435: 6431: 6426: 6422: 6418: 6414: 6410: 6406: 6402: 6398: 6394: 6389: 6385: 6381: 6377: 6373: 6369: 6365: 6361: 6357: 6352: 6347: 6344:(1): 016401. 6343: 6339: 6334: 6330: 6326: 6321: 6316: 6312: 6308: 6304: 6300: 6295: 6290: 6286: 6282: 6278: 6273: 6269: 6265: 6261: 6257: 6253: 6249: 6245: 6241: 6236: 6231: 6228:(3): 033617. 6227: 6223: 6218: 6214: 6210: 6205: 6200: 6196: 6192: 6189:(6): 063618. 6188: 6184: 6180: 6175: 6171: 6167: 6163: 6159: 6155: 6151: 6147: 6143: 6138: 6133: 6129: 6125: 6120: 6116: 6112: 6108: 6104: 6100: 6096: 6093:(1): 93–100. 6092: 6088: 6084: 6079: 6075: 6071: 6067: 6063: 6059: 6055: 6051: 6047: 6042: 6037: 6033: 6029: 6024: 6023: 6018: 6014: 6009: 6004: 6000: 5995: 5991: 5987: 5983: 5979: 5975: 5971: 5967: 5963: 5959: 5955: 5950: 5945: 5941: 5937: 5932: 5928: 5924: 5920: 5916: 5912: 5908: 5904: 5900: 5896: 5892: 5887: 5882: 5878: 5874: 5869: 5865: 5861: 5857: 5853: 5849: 5845: 5840: 5835: 5832:(7): 075003. 5831: 5827: 5822: 5818: 5814: 5810: 5806: 5802: 5798: 5794: 5790: 5786: 5782: 5777: 5772: 5768: 5764: 5759: 5752: 5748: 5744: 5740: 5736: 5732: 5728: 5723: 5718: 5714: 5710: 5706: 5702: 5695: 5690: 5686: 5682: 5678: 5674: 5670: 5666: 5662: 5658: 5654: 5650: 5645: 5640: 5637:(9): 090402. 5636: 5632: 5627: 5623: 5619: 5615: 5611: 5607: 5603: 5599: 5595: 5591: 5587: 5582: 5577: 5574:(2): 029301. 5573: 5569: 5564: 5560: 5556: 5552: 5548: 5544: 5540: 5536: 5532: 5528: 5524: 5519: 5514: 5510: 5506: 5502: 5497: 5493: 5489: 5485: 5481: 5477: 5473: 5469: 5465: 5461: 5457: 5452: 5447: 5444:(1): 015503. 5443: 5439: 5434: 5433: 5414: 5410: 5403: 5395: 5391: 5386: 5381: 5377: 5373: 5369: 5365: 5361: 5357: 5352: 5347: 5343: 5339: 5335: 5328: 5320: 5316: 5312: 5308: 5301: 5293: 5289: 5284: 5279: 5275: 5271: 5267: 5263: 5259: 5255: 5251: 5247: 5243: 5236: 5222: 5218: 5211: 5197: 5196:Physics World 5193: 5186: 5178: 5174: 5170: 5166: 5162: 5158: 5154: 5150: 5146: 5142: 5137: 5132: 5128: 5124: 5120: 5113: 5099: 5095: 5088: 5080: 5076: 5072: 5068: 5064: 5060: 5056: 5052: 5048: 5044: 5039: 5034: 5030: 5026: 5022: 5015: 5001: 4997: 4990: 4976: 4972: 4965: 4957: 4953: 4949: 4945: 4941: 4937: 4933: 4929: 4924: 4919: 4916:(5): 057201. 4915: 4911: 4907: 4900: 4892: 4888: 4884: 4880: 4876: 4872: 4868: 4864: 4859: 4854: 4850: 4846: 4839: 4831: 4827: 4823: 4819: 4815: 4811: 4807: 4803: 4798: 4793: 4789: 4785: 4778: 4770: 4764: 4756: 4750: 4744: 4739: 4731: 4725: 4717: 4711: 4697: 4693: 4686: 4684: 4669: 4665: 4659: 4657: 4648: 4644: 4640: 4636: 4632: 4628: 4624: 4620: 4616: 4612: 4608: 4604: 4600: 4593: 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3839: 3835: 3831: 3827: 3823: 3819: 3815: 3810: 3805: 3801: 3797: 3789: 3781: 3777: 3773: 3769: 3765: 3761: 3757: 3753: 3748: 3743: 3739: 3735: 3728: 3720: 3716: 3712: 3708: 3704: 3700: 3696: 3692: 3687: 3682: 3678: 3674: 3667: 3659: 3655: 3651: 3647: 3643: 3639: 3635: 3631: 3626: 3621: 3617: 3613: 3605: 3603: 3594: 3590: 3585: 3580: 3576: 3572: 3568: 3564: 3560: 3556: 3551: 3546: 3542: 3538: 3534: 3526: 3524: 3515: 3511: 3507: 3503: 3499: 3495: 3491: 3487: 3483: 3479: 3474: 3469: 3466:(3): 030401. 3465: 3461: 3457: 3450: 3448: 3441: 3437: 3431: 3423: 3419: 3415: 3409: 3405: 3401: 3397: 3396: 3395:Time Crystals 3388: 3381: 3377: 3373: 3369: 3365: 3361: 3357: 3353: 3349: 3344: 3339: 3336:(3): 033617. 3335: 3331: 3324: 3317: 3311: 3306: 3300: 3291: 3286: 3282: 3278: 3273: 3268: 3264: 3260: 3256: 3249: 3240: 3235: 3228: 3220: 3216: 3212: 3208: 3204: 3200: 3196: 3192: 3187: 3182: 3179:(4): 041117. 3178: 3174: 3167: 3159: 3155: 3151: 3147: 3143: 3139: 3135: 3131: 3127: 3123: 3118: 3113: 3109: 3105: 3098: 3091: 3087: 3083: 3077: 3069: 3065: 3061: 3054: 3047: 3046:Bruno (2013b) 3043: 3042:Bruno (2013a) 3037: 3029: 3025: 3021: 3014: 3007: 3003: 2997: 2989: 2985: 2981: 2977: 2973: 2969: 2965: 2961: 2957: 2953: 2948: 2943: 2939: 2935: 2928: 2920: 2916: 2912: 2908: 2904: 2900: 2896: 2892: 2888: 2884: 2879: 2874: 2870: 2866: 2859: 2851: 2847: 2842: 2837: 2833: 2829: 2825: 2821: 2817: 2813: 2808: 2803: 2799: 2795: 2791: 2784: 2782: 2767: 2763: 2756: 2740: 2734: 2720: 2716: 2709: 2695: 2691: 2684: 2676: 2672: 2668: 2664: 2660: 2656: 2652: 2648: 2643: 2638: 2634: 2630: 2629:Physics Today 2623: 2621: 2612: 2608: 2604: 2600: 2596: 2592: 2587: 2582: 2578: 2574: 2570: 2563: 2561: 2559: 2557: 2555: 2547: 2536: 2532: 2528: 2524: 2520: 2516: 2512: 2508: 2507:Physics World 2504: 2497: 2488: 2482: 2478: 2477: 2469: 2460: 2454: 2450: 2449: 2441: 2432: 2426: 2422: 2421: 2413: 2404: 2398: 2394: 2393: 2385: 2376: 2370: 2366: 2365: 2357: 2349: 2345: 2341: 2337: 2333: 2329: 2325: 2321: 2316: 2311: 2308:(1): 016401. 2307: 2303: 2296: 2288: 2282: 2280: 2263: 2258: 2254: 2250: 2246: 2242: 2238: 2231: 2229: 2221: 2216: 2210: 2205: 2197: 2193: 2189: 2185: 2181: 2177: 2173: 2169: 2164: 2159: 2156:(3): 033617. 2155: 2151: 2144: 2136: 2132: 2128: 2121: 2119: 2114: 2104: 2099: 2094: 2092: 2087: 2082: 2080: 2075: 2070: 2069: 2066: 2061: 2059: 2058:ground states 2056: 2052: 2048: 2044: 2039: 2035: 2030: 2028: 2024: 2019: 2017: 2013: 2009: 2005: 2001: 1996: 1994: 1990: 1986: 1982: 1978: 1974: 1969: 1967: 1962: 1958: 1954: 1950: 1946: 1942: 1938: 1933: 1931: 1927: 1923: 1919: 1914: 1912: 1908: 1904: 1899: 1897: 1893: 1890: 1886: 1881: 1879: 1875: 1871: 1867: 1863: 1862:Mikhail Lukin 1858: 1854: 1852: 1843: 1839: 1831: 1824: 1816: 1812: 1808: 1804: 1800: 1796: 1792: 1788: 1778: 1774: 1770: 1768: 1764: 1760: 1754: 1748: 1741: 1739: 1735: 1731: 1727: 1723: 1717: 1715: 1714: 1709: 1705: 1701: 1700:Mikhail Lukin 1697: 1693: 1688: 1686: 1682: 1678: 1673: 1670: 1666: 1661: 1659: 1655: 1650: 1648: 1644: 1640: 1636: 1632: 1631:Frank Wilczek 1625: 1621: 1620:Frank Wilczek 1618: 1614: 1605: 1601: 1599: 1589: 1586: 1584: 1580: 1572: 1568: 1565: 1561: 1557: 1554: 1550: 1549: 1548: 1546: 1541: 1539: 1535: 1531: 1528: 1524: 1520: 1516: 1512: 1507: 1493: 1473: 1453: 1433: 1430: 1427: 1407: 1404: 1401: 1381: 1378: 1375: 1372: 1366: 1357: 1355: 1351: 1347: 1343: 1339: 1326: 1323: 1320: 1319: 1318: 1316: 1310: 1308: 1307:Quasimomentum 1304: 1300: 1292: 1287: 1282: 1278: 1268: 1266: 1262: 1257: 1255: 1249: 1239: 1236: 1235:ferromagnetic 1232: 1231:salt crystals 1228: 1218: 1216: 1212: 1207: 1205: 1201: 1197: 1193: 1189: 1184: 1182: 1177: 1174:in 2012 as a 1173: 1172:Frank Wilczek 1169: 1165: 1161: 1157: 1153: 1141: 1136: 1134: 1129: 1127: 1122: 1121: 1119: 1118: 1111: 1108: 1106: 1103: 1101: 1098: 1096: 1093: 1092: 1084: 1083: 1076: 1073: 1071: 1066: 1064: 1061: 1059: 1056: 1054: 1051: 1049: 1048:Chronobiology 1046: 1045: 1038: 1035: 1032: 1031: 1026: 1025: 1018: 1015: 1013: 1010: 1008: 1005: 1004: 997: 994: 992: 989: 988: 983: 982: 975: 972: 970: 969:Reincarnation 967: 965: 962: 960: 957: 955: 952: 950: 947: 945: 942: 941: 933: 931: 928: 927: 922: 921: 914: 911: 909: 906: 904: 901: 899: 896: 895: 891: 885: 884: 877: 874: 872: 869: 867: 864: 862: 859: 857: 854: 852: 849: 847: 844: 843: 835: 834: 825: 822: 821: 820: 817: 816: 813: 810: 808: 805: 803: 800: 799: 791: 790: 786: 782: 781: 778: 775: 774: 764: 759: 757: 752: 750: 745: 744: 742: 741: 735: 725: 722: 717: 711: 710: 709: 708: 700: 697: 695: 692: 690: 687: 685: 682: 680: 677: 675: 672: 670: 667: 665: 662: 660: 657: 655: 652: 650: 647: 645: 642: 640: 637: 635: 632: 630: 627: 625: 622: 620: 617: 615: 612: 610: 607: 605: 602: 600: 597: 595: 592: 590: 587: 585: 582: 580: 577: 575: 572: 570: 567: 565: 562: 560: 557: 555: 552: 550: 547: 545: 542: 540: 537: 535: 532: 530: 527: 525: 522: 520: 517: 515: 512: 510: 507: 505: 502: 500: 499:Van der Waals 497: 496: 489: 488: 480: 477: 475: 472: 470: 467: 465: 462: 460: 457: 456: 452: 447: 446: 438: 435: 433: 430: 428: 425: 423: 419: 416: 414: 411: 409: 406: 405: 401: 396: 395: 387: 384: 382: 378: 375: 373: 369: 366: 364: 360: 357: 355: 352: 351: 344: 343: 335: 332: 330: 327: 325: 322: 321: 314: 313: 305: 302: 300: 297: 295: 294:Ferroelectric 292: 290: 289:Piezoelectric 287: 285: 282: 280: 277: 275: 272: 270: 267: 265: 264:Semiconductor 262: 260: 257: 255: 252: 250: 247: 245: 242: 241: 234: 233: 225: 222: 220: 217: 215: 212: 211: 204: 203: 195: 192: 190: 187: 185: 184:Superfluidity 182: 180: 177: 175: 172: 170: 167: 165: 162: 160: 157: 155: 152: 150: 147: 145: 142: 140: 137: 135: 132: 131: 127: 122: 121: 115: 112: 110: 107: 105: 102: 101: 99: 98: 94: 90: 89: 86: 83: 82: 73: 70: 62: 52: 48: 42: 39:This article 37: 28: 27: 22: 10048:Astrophysics 9862:Experimental 9772:Superheating 9645:Vaporization 9640:Triple point 9635:Supercooling 9600:Lambda point 9550:Condensation 9467:Time crystal 9466: 9445:Other states 9385:Quantum Hall 9214:Applications 9165:size scaling 8794:Charge qubit 8719:KLM protocol 8668: 8532: 8522: 8216:Purification 8146:Eastin–Knill 8010: 7998: 7986: 7974: 7892:Pines' demon 7631:Kondo effect 7533:Time crystal 7532: 7380:the original 7375: 7363:the original 7358: 7346:the original 7341: 7329:the original 7324: 7312:the original 7307: 7295:the original 7290: 7278:the original 7273: 7261:the original 7256: 7244:the original 7215: 7203:the original 7198: 7185: 7173:the original 7168: 7156:the original 7151: 7138: 7126:the original 7121: 7109:the original 7104: 7051: 7047: 7039:the original 7034: 6981: 6977: 6969:the original 6964: 6941: 6937: 6888: 6867:. Retrieved 6860:the original 6847: 6843: 6785: 6781: 6721: 6717: 6676: 6672: 6633:1721.1/88434 6598: 6594: 6543: 6539: 6488: 6485:JETP Letters 6484: 6433: 6429: 6396: 6392: 6341: 6337: 6284: 6280: 6225: 6221: 6186: 6182: 6130:(5): 57008. 6127: 6123: 6090: 6086: 6031: 6027: 5998: 5939: 5935: 5876: 5872: 5829: 5825: 5766: 5762: 5751:the original 5704: 5700: 5634: 5630: 5571: 5567: 5508: 5504: 5441: 5437: 5416:. Retrieved 5412: 5402: 5341: 5337: 5327: 5310: 5300: 5249: 5245: 5235: 5224:. Retrieved 5221:ScienceAlert 5220: 5210: 5199:. Retrieved 5195: 5185: 5126: 5122: 5112: 5101:. Retrieved 5098:SciTechDaily 5097: 5087: 5028: 5024: 5014: 5003:. Retrieved 4999: 4989: 4978:. Retrieved 4974: 4964: 4913: 4909: 4899: 4848: 4844: 4838: 4787: 4783: 4777: 4763: 4749: 4738: 4724: 4710: 4699:. Retrieved 4696:SciTechDaily 4695: 4671:. Retrieved 4667: 4606: 4602: 4530: 4526: 4492: 4433: 4429: 4423: 4411:. Retrieved 4399: 4389: 4330: 4326: 4316: 4265: 4261: 4251: 4202: 4198: 4150: 4146: 4082: 4078: 4002: 3998: 3988: 3929: 3925: 3915: 3864: 3860: 3850: 3799: 3795: 3788: 3737: 3733: 3727: 3676: 3672: 3666: 3615: 3611: 3540: 3536: 3463: 3459: 3430: 3394: 3387: 3379: 3333: 3329: 3323: 3299: 3262: 3258: 3248: 3227: 3176: 3172: 3166: 3107: 3103: 3097: 3076: 3068:the original 3063: 3053: 3036: 3028:the original 3023: 3013: 2996: 2937: 2933: 2927: 2868: 2864: 2858: 2797: 2793: 2769:. Retrieved 2765: 2755: 2743:. Retrieved 2733: 2722:. Retrieved 2718: 2708: 2697:. Retrieved 2694:ScienceAlert 2693: 2683: 2635:(9): 40–47. 2632: 2628: 2576: 2572: 2545: 2540:September 6, 2538:. Retrieved 2510: 2506: 2496: 2479:. Springer. 2475: 2468: 2451:. Springer. 2447: 2440: 2419: 2412: 2391: 2384: 2363: 2356: 2305: 2301: 2295: 2266:. Retrieved 2244: 2240: 2215: 2204: 2153: 2149: 2143: 2135:the original 2130: 2051:superradiant 2031: 2020: 2012:lattice trap 2000:UC Riverside 1997: 1981:trapped-ions 1970: 1960: 1956: 1934: 1921: 1915: 1900: 1895: 1882: 1859: 1855: 1841: 1837: 1826: 1822: 1814: 1807:Tukey window 1805:, using the 1784: 1775: 1771: 1752: 1746: 1742: 1718: 1712: 1689: 1674: 1662: 1651: 1628: 1602: 1595: 1587: 1582: 1576: 1570: 1559: 1552: 1544: 1542: 1508: 1506:an integer. 1358: 1349: 1345: 1341: 1335: 1314: 1311: 1298: 1296: 1260: 1258: 1251: 1224: 1210: 1208: 1185: 1168:ground state 1156:time crystal 1155: 1149: 871:Paleontology 824:of the world 629:von Klitzing 334:Kondo effect 194:Time crystal 193: 174:Fermi liquid 65: 56: 40: 9951:Statistical 9867:Theoretical 9844:Engineering 9681:Latent heat 9630:Sublimation 9575:Evaporation 9510:Ferromagnet 9505:Ferrimagnet 9487:Dark matter 9419:High energy 9205:von Neumann 9075:force field 9067:percolation 8825:programming 8804:Phase qubit 8709:Circuit QED 8181:No-deleting 8123:cloud-based 7929:Soft matter 7829:Ferromagnet 7647:Drude model 7616:Berry phase 7596:Hall effect 7409:Lukin Group 7186:jqi.umd.edu 5999:Unpublished 4205:(9): 1172. 4005:(1): 1730. 3964:10023/14492 2688:Crew, Bec. 2579:: 467–499. 2103:Mathematics 2038:limit cycle 2010:creating a 1878:subharmonic 1799:spin states 1781:Experiments 1763:Hamiltonian 1643:Xiang Zhang 1641:. In 2013, 1354:Philip Ball 1110:Time travel 1017:Hexadecimal 991:Measurement 959:Immortality 846:Archaeology 451:Soft matter 372:Ferromagnet 10144:Categories 10068:Geophysics 10058:Biophysics 9902:Analytical 9855:Approaches 9696:Volatility 9659:Quantities 9620:Regelation 9595:Ionization 9570:Deposition 9522:Superglass 9492:Antimatter 9426:QCD matter 9405:Supersolid 9400:Superfluid 9363:Low energy 9062:Heisenberg 8865:libquantum 8799:Flux qubit 8704:Cavity QED 8653:Bacon–Shor 8643:stabilizer 8171:No-cloning 7844:Spin glass 7839:Metamagnet 7819:Paramagnet 7706:Conduction 7682:BCS theory 7523:Superfluid 7518:Supersolid 7418:Norman Yao 6869:2017-02-08 6553:1605.00639 6443:1508.07026 6351:1704.03735 6294:1502.02507 5886:1508.03344 5839:2005.03138 5644:1603.08001 5418:2022-03-08 5351:2105.06632 5252:(1): 848. 5226:2022-03-11 5201:2021-12-27 5136:2107.00736 5103:2021-12-27 5038:2102.01695 5005:2021-07-30 4980:2021-08-07 4923:1911.13192 4858:2003.06313 4797:1712.06877 4701:2022-08-07 4673:2022-08-07 4540:2202.06980 4504:2001.11037 4443:1907.07215 4340:1901.05974 4275:1507.08644 4092:2012.08885 4012:1804.06744 3939:1708.05014 3874:1905.12880 3809:1807.10161 3747:1708.01472 3686:1708.05014 3625:1609.08684 3550:1610.08057 3473:1608.02589 3272:1910.10715 3239:1910.10745 3186:1905.08266 2807:2107.13571 2771:2021-12-03 2724:2023-07-22 2699:2017-09-21 2642:1811.06657 2586:1905.13232 2407:See Ch. 3. 2315:1704.03735 2110:References 1892:superfluid 1793:ions in a 1761:many-body 1738:ETH Zurich 1530:spin echos 1346:continuous 1176:time-based 1037:Naturalism 974:Kalachakra 903:Eternalism 898:Presentism 890:Philosophy 876:Futurology 851:Chronology 594:Louis Néel 584:Schrieffer 492:Scientists 386:Spin glass 381:Metamagnet 363:Paramagnet 179:Supersolid 59:March 2024 10018:Molecular 9919:Acoustics 9912:Continuum 9907:Celestial 9897:Newtonian 9884:Classical 9827:Divisions 9185:Boltzmann 9108:H-theorem 8986:Ensembles 8771:NV center 8206:Threshold 8186:No-hiding 8151:Gleason's 7902:Polariton 7809:Diamagnet 7757:Couplings 7733:Conductor 7728:Semimetal 7713:Insulator 7589:Phenomena 7513:Fermi gas 7240:181223762 7232:1476-4687 7076:0028-0836 7022:205075903 7006:0028-0836 6916:240770955 6828:118348062 6820:1098-0121 6795:1404.3519 6756:0031-9007 6731:1308.5949 6701:0031-9007 6641:0036-8075 6608:1310.7563 6586:118699328 6578:2469-9950 6531:119100114 6523:0021-3640 6498:1309.1845 6468:1745-2473 6421:0031-899X 6287:: 10787. 6268:118627872 6260:2469-9934 6235:1410.3638 6213:2469-9926 6170:118662499 6162:0295-5075 6137:1306.6229 6115:122631523 6107:1071-2836 6066:1745-2473 6041:1008.1792 6008:1212.6959 5974:0031-9007 5949:1206.4772 5911:0031-9007 5864:218538401 5801:0031-9007 5776:1305.1800 5747:120738031 5739:0370-1573 5717:CiteSeerX 5669:0031-9007 5606:0031-9007 5581:1211.4792 5543:0031-9007 5518:1210.4128 5476:0031-9007 5451:1407.5876 5376:2375-2548 5274:2041-1723 5177:235727352 5161:0036-8075 5079:231786633 5063:0036-8075 4956:208512720 4891:212717702 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