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Einstein relation (kinetic theory)

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is frequently used for the inverse momentum relaxation time (time needed for the inertia momentum to become negligible compared to the random momenta) of the diffusive object. For spherical particles of radius
1951: 1436: 1105: 868: 305: 1867: 480: 238: 1652: 2729:{\displaystyle 0=\mathbf {J} _{\mathrm {drift} }+\mathbf {J} _{\mathrm {diffusion} }=-\mu \rho \nabla U-D\nabla \rho =\left(-\mu \rho -D{\frac {\mathrm {d} \rho }{\mathrm {d} U}}\right)\nabla U.} 2210: 1165: 1107:
This has been applied for many years to estimating the self-diffusion coefficient in liquids, and a version consistent with isomorph theory has been confirmed by computer simulations of the
635: 740: 3055: 1020: 547: 90: 2978: 1986: 2193:{\displaystyle \mathbf {J} _{\mathrm {drift} }(\mathbf {x} )=\mu (\mathbf {x} )F(\mathbf {x} )\rho (\mathbf {x} )=-\rho (\mathbf {x} )\mu (\mathbf {x} )\nabla U(\mathbf {x} ),} 971: 897: 1318: 2758: 1889: 1192: 2873: 2763: 1463: 1366: 576: 2497: 937: 2841: 2484: 2424: 1594: 1040: 3826: 2973: 2861: 2464: 2444: 2030: 2006: 1810: 1338: 1197: 789: 763: 683: 657: 505: 4130: 1668: 1495: 4155: 2319: 3741: 1988:
as a function of the position. After some time, equilibrium will be established: particles will pile up around the areas with lowest potential energy
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By replacing the diffusivities in the expressions of electric ionic mobilities of the cations and anions from the expressions of the
4200: 3234:"Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen" 1489: 4089: 696: 3944: 1818: 985: 3178:. Essay by Prof. R Home (with contributions from Prof B. McKellar and A./Prof D. Jamieson) dated 2005. Accessed 2017-04-28. 52: 2200:
i.e., the number of particles flowing past a given position equals the particle concentration times the average velocity.
4150: 3973: 3815: 3381: 1121: 170:. Note that the equation above describes the classical case and should be modified when quantum effects are relevant. 3834: 3711: 3323: 3949: 1478: 3219: 585: 3994: 167: 4241: 3804: 3676: 32: 3569: 2306:{\displaystyle \mathbf {J} _{\mathrm {diffusion} }(\mathbf {x} )=-D(\mathbf {x} )\nabla \rho (\mathbf {x} ),} 1046:
of the medium. Thus the Einstein–Smoluchowski relation results into the Stokes–Einstein–Sutherland relation
510: 3782: 3671: 3666: 2868: 2487: 2012:. At equilibrium, there is no net flow of particles: the tendency of particles to get pulled towards lower 1474: 3939: 3898: 3842: 3691: 3616: 3146: 1960: 3175: 3866: 3681: 100: 942: 873: 3774: 3721: 3701: 1345: 4246: 4219: 4170: 4165: 4145: 4135: 4095: 3790: 3646: 3562: 3125:{\displaystyle D=-\mu {\frac {\rho }{\frac {\mathrm {d} \rho }{\mathrm {d} U}}}=\mu k_{\text{B}}T,} 2041: 1288: 2741: 1872: 1170: 4175: 3398: 1662: 1108: 24: 3544: 1782:
The proof of the Einstein relation can be found in many references, for example see the work of
4107: 4015: 3987: 3890: 3749: 3352: 3313: 3190:"LXXV. A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin" 1441: 1351: 554: 4180: 4140: 3980: 3929: 3924: 3850: 3661: 3641: 3631: 3043:{\displaystyle {\frac {\mathrm {d} \rho }{\mathrm {d} U}}=-{\frac {1}{k_{\text{B}}T}}\rho .} 922: 4059: 4008: 4001: 3954: 3626: 3599: 3507: 3413: 3286: 3245: 3156: 2826: 2469: 2409: 1572: 1115: 1025: 159: 2036:, perfectly balances the tendency of particles to spread out due to diffusion, called the 8: 3397:
Costigliola, Lorenzo; Heyes, David M.; Schrøder, Thomas B.; Dyre, Jeppe C. (2019-01-14).
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Under this assumption, plugging this equation into the general Einstein relation gives:
1957:). Now assume that there are a large number of such particles, with local concentration 4022: 3906: 3882: 3726: 3609: 3604: 3523: 3497: 2958: 2846: 2449: 2429: 2015: 1991: 1813: 1795: 1482: 1323: 774: 748: 668: 642: 490: 149: 1596:
is the total density of available energy states, which gives the simplified relation:
4113: 3527: 3519: 3439: 3431: 3377: 3319: 2864: 2399:{\displaystyle \mathbf {J} _{\mathrm {drift} }+\mathbf {J} _{\mathrm {diffusion} }=0} 1341: 1282: 367: 318: 110: 4071: 4053: 3731: 3515: 3489: 3421: 3338:
Umberto Marini Bettolo Marconi, Andrea Puglisi, Lamberto Rondoni, Angelo Vulpiani,
3294: 3253: 3201: 2948:{\displaystyle \rho (\mathbf {x} )=Ae^{-{\frac {U(\mathbf {x} )}{k_{\text{B}}T}}},} 2313:
where the minus sign means that particles flow from higher to lower concentration.
1790: 4101: 4033: 3798: 3706: 3651: 3621: 3585: 3549: 3359: 2814:{\displaystyle D=-\mu {\frac {\rho }{\frac {\mathrm {d} \rho }{\mathrm {d} U}}}.} 912: 660: 246: 181: 44: 36: 4041: 2546:{\displaystyle \nabla \rho ={\frac {\mathrm {d} \rho }{\mathrm {d} U}}\nabla U.} 3858: 3636: 3275:"Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen" 1954: 979: 420: 416: 113: 3233: 3205: 4235: 4077: 4047: 3934: 3435: 3315:
Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology
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Now consider the equilibrium condition. First, there is no net flow, i.e.
1262:{\displaystyle D_{\text{r}}={\frac {k_{\text{B}}T}{8\pi \,\eta \,r^{3}}}.} 4190: 3874: 3696: 3399:"Revisiting the Stokes-Einstein relation without a hydrodynamic diameter" 3176:
World Year of Physics – William Sutherland at the University of Melbourne
4195: 2491: 2406:. Second, for non-interacting point particles, the equilibrium density 1783: 1759:{\displaystyle \Lambda _{e}={\frac {z_{i}^{2}F^{2}}{RT}}(D_{+}+D_{-}).} 3426: 1562:{\displaystyle p(\varphi )=N_{0}e^{\frac {q\varphi }{k_{\text{B}}T}},} 2009: 1269:
This is sometimes referred to as the Stokes–Einstein–Debye relation.
1043: 801: 343: 3274: 3189: 1891:. We assume that the particle would respond by moving with velocity 423:. Hence, the equation in the case of a charged particle is given as 3554: 3502: 3339: 2975:
is a constant related to the total number of particles. Therefore
808:, relevant for the electron mobility in normal metals like in the 3340:"Fluctuation-Dissipation: Response Theory in Statistical Physics" 1946:{\displaystyle v(\mathbf {x} )=\mu (\mathbf {x} )F(\mathbf {x} )} 245:, for diffusion of spherical particles through a liquid with low 173:
Two frequently used important special forms of the relation are:
47:. The more general form of the equation in the classical case is 20: 1431:{\displaystyle D={\frac {\mu _{q}p}{q{\frac {dp}{d\varphi }}}},} 361: 31:
is a previously unexpected connection revealed independently by
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is the electron temperature or ion temperature in plasma (K).
117: 3456: 3396: 3461:. New York (USA): Holt, Rineheart and Winston. p. 826. 1665:
of an electrolyte the Nernst–Einstein equation is derived:
1100:{\displaystyle D={\frac {k_{\text{B}}T}{6\pi \,\eta \,r}}.} 690: 2203:
The flow of particles due to the diffusion current is, by
863:{\displaystyle D={\frac {\mu _{q}\,E_{\mathrm {F} }}{q}},} 300:{\displaystyle D={\frac {k_{\text{B}}T}{6\pi \,\eta \,r}}} 2008:, but still will be spread out to some extent because of 791:
is electron temperature or ion temperature in plasma (V).
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Kubo, R. (1966). "The fluctuation-dissipation theorem".
2760:, it implies the general form of the Einstein relation: 3351:
Van Zeghbroeck, "Principles of Semiconductor Devices",
1862:{\displaystyle F(\mathbf {x} )=-\nabla U(\mathbf {x} )} 475:{\displaystyle D={\frac {\mu _{q}\,k_{\text{B}}T}{q}},} 3132:
which corresponds to the classical Einstein relation.
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The net flux of particles due to the drift current is
906: 233:{\displaystyle D={\frac {\mu _{q}\,k_{\text{B}}T}{q}}} 3827:
Die Grundlagen der Einsteinschen Relativitäts-Theorie
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for a proof of this relation). An example assuming a
1444: 1374: 1354: 1326: 1291: 1200: 1173: 1124: 1052: 1028: 988: 945: 925: 876: 818: 777: 751: 699: 671: 645: 588: 557: 513: 493: 429: 255: 190: 55: 3272: 2426:is solely a function of the local potential energy 3476:(in French). Paris (France): Ellipses. p. 78. 3187: 3124: 3042: 2967: 2947: 2855: 2835: 2813: 2752: 2728: 2545: 2478: 2458: 2438: 2418: 2398: 2305: 2192: 2024: 2000: 1980: 1945: 1883: 1861: 1804: 1758: 1646: 1588: 1561: 1457: 1430: 1360: 1332: 1312: 1261: 1186: 1159: 1099: 1034: 1014: 965: 931: 891: 862: 783: 757: 734: 677: 651: 629: 570: 541: 499: 474: 299: 232: 109:is the "mobility", or the ratio of the particle's 84: 3760:Investigations on the Theory of Brownian Movement 1160:{\displaystyle \zeta _{\text{r}}=8\pi \eta r^{3}} 4233: 3471: 3767:Relativity: The Special and the General Theory 2490:as discussed below.) That means, applying the 1470: 3570: 362:Electrical mobility equation (classical case) 3311: 3231: 1777: 630:{\displaystyle \mathrm {m^{2}V^{-1}s^{-1}} } 2738:As this expression holds at every position 1656: 1477:relation for the density of states and the 796:Electrical mobility equation (quantum case) 735:{\displaystyle D={\frac {\mu _{q}\,T}{Z}},} 3577: 3563: 1320:between the density of holes or electrons 3501: 3425: 3257: 1242: 1238: 1087: 1083: 1005: 1001: 838: 719: 449: 290: 286: 210: 65: 4201:Emergency Committee of Atomic Scientists 3486: 1167:, and the rotational diffusion constant 812:, Einstein relation should be modified: 415:is the ratio of the particle's terminal 352:is the radius of the spherical particle. 3457:Ashcroft, N. W.; Mermin, N. D. (1988). 3312:Dill, Ken A.; Bromberg, Sarina (2003). 1015:{\displaystyle \zeta =6\pi \,\eta \,r,} 919:is the inverse of the drag coefficient 385:is related to its generalized mobility 166:This equation is an early example of a 4234: 3945:Albert Einstein World Award of Science 3371: 2446:, i.e. if two locations have the same 542:{\displaystyle \mathrm {m^{2}s^{-1}} } 85:{\displaystyle D=\mu \,k_{\text{B}}T,} 3558: 3220:"Stokes–Einstein–Sutherland equation" 3584: 1981:{\displaystyle \rho (\mathbf {x} )} 907:Stokes–Einstein–Sutherland equation 693:, which is more common for plasma: 243:Stokes–Einstein–Sutherland equation 13: 3974:Albert Einstein: Creator and Rebel 3687:Einstein–Infeld–Hoffmann equations 3657:Einstein relation (kinetic theory) 3089: 3079: 2996: 2986: 2797: 2787: 2717: 2702: 2692: 2659: 2647: 2629: 2626: 2623: 2620: 2617: 2614: 2611: 2608: 2605: 2588: 2585: 2582: 2579: 2576: 2534: 2524: 2514: 2501: 2466:then they will also have the same 2384: 2381: 2378: 2375: 2372: 2369: 2366: 2363: 2360: 2343: 2340: 2337: 2334: 2331: 2283: 2246: 2243: 2240: 2237: 2234: 2231: 2228: 2225: 2222: 2170: 2074: 2071: 2068: 2065: 2062: 1842: 1673: 1481:, which is often used to describe 883: 845: 614: 601: 591: 526: 516: 14: 4258: 3835:The Einstein Theory of Relativity 3538: 4214: 4213: 3950:Einstein Prize for Laser Science 3318:. Garland Science. p. 327. 2915: 2884: 2746: 2599: 2570: 2354: 2325: 2293: 2276: 2256: 2216: 2180: 2163: 2149: 2129: 2115: 2101: 2084: 2056: 1971: 1936: 1922: 1905: 1877: 1852: 1829: 1488:materials, one can compute (see 1471:§ Proof of the general case 1272: 966:{\displaystyle \gamma =\zeta /m} 892:{\displaystyle E_{\mathrm {F} }} 356: 168:fluctuation-dissipation relation 3995:Einstein: His Life and Universe 3480: 3465: 3450: 3406:The Journal of Chemical Physics 3390: 689:If the temperature is given in 3617:Mass–energy equivalence (E=mc) 3365: 3345: 3332: 3305: 3266: 3225: 3212: 3181: 3169: 2919: 2911: 2888: 2880: 2297: 2289: 2280: 2272: 2260: 2252: 2184: 2176: 2167: 2159: 2153: 2145: 2133: 2125: 2119: 2111: 2105: 2097: 2088: 2080: 1975: 1967: 1940: 1932: 1926: 1918: 1909: 1901: 1856: 1848: 1833: 1825: 1750: 1724: 1508: 1502: 1307: 1301: 1285:, i.e. a relation of the form 507:is the diffusion coefficient ( 178:Einstein–Smoluchowski equation 1: 3545:Einstein relation calculators 3273:von Smoluchowski, M. (1906). 3162: 1789:Suppose some fixed, external 1313:{\displaystyle p=p(\varphi )} 3474:Composants Ă  semiconducteurs 3376:. Springer. pp. 20–28. 2869:Maxwell-Boltzmann statistics 2753:{\displaystyle \mathbf {x} } 2488:Maxwell-Boltzmann statistics 1884:{\displaystyle \mathbf {x} } 1479:Maxwell–Boltzmann statistics 1187:{\displaystyle D_{\text{r}}} 7: 3940:Albert Einstein Peace Prize 3717:Unsuccessful investigations 3188:Sutherland William (1905). 3147:Conductivity (electrolytic) 3135: 2555:Therefore, at equilibrium: 1368:, the Einstein relation is 16:Equation in Brownian motion 10: 4263: 3867:Picasso at the Lapin Agile 3805:Russell–Einstein Manifesto 3677:Bose–Einstein correlations 3520:10.1088/0034-4885/29/1/306 43:in 1906 in their works on 4209: 4123: 4032: 3963: 3917: 3814: 3775:The Meaning of Relativity 3740: 3592: 3472:Bonnaud, Olivier (2006). 3206:10.1080/14786440509463331 1778:Proof of the general case 1346:electrochemical potential 663:of particle (C, coulombs) 4166:Albert Einstein Archives 4096:Bernhard Caesar Einstein 3843:Relics: Einstein's Brain 3791:The Evolution of Physics 3672:Bose–Einstein statistics 3667:Bose–Einstein condensate 3647:Einstein field equations 3299:10.1002/andp.19063261405 3259:10.1002/andp.19053220806 2042:drift-diffusion equation 1657:Nernst–Einstein equation 1458:{\displaystyle \mu _{q}} 1361:{\displaystyle \varphi } 571:{\displaystyle \mu _{q}} 336:of the charged particle; 4176:Einstein Papers Project 3692:Einstein–de Haas effect 2867:can be modeled through 1663:equivalent conductivity 25:kinetic theory of gases 4108:Thomas Martin Einstein 4016:Introducing Relativity 3988:Einstein for Beginners 3891:Einstein and Eddington 3682:Einstein–Cartan theory 3194:Philosophical Magazine 3126: 3044: 2969: 2949: 2857: 2837: 2815: 2754: 2730: 2547: 2480: 2460: 2440: 2420: 2400: 2307: 2194: 2026: 2002: 1982: 1947: 1885: 1863: 1806: 1760: 1648: 1590: 1563: 1459: 1432: 1362: 1340:and the corresponding 1334: 1314: 1263: 1188: 1161: 1101: 1036: 1016: 967: 933: 932:{\displaystyle \zeta } 893: 864: 785: 769:of particle (unitless) 759: 736: 679: 653: 631: 572: 543: 501: 476: 301: 234: 86: 4242:Statistical mechanics 4181:Einstein refrigerator 4171:Einstein's Blackboard 4050:(second wife; cousin) 3981:Einstein and Religion 3930:Albert Einstein Medal 3925:Albert Einstein Award 3783:The World as I See It 3722:Wave–particle duality 3702:Bohr–Einstein debates 3662:Cosmological constant 3642:Equivalence principle 3632:Einstein coefficients 3374:Gas Discharge Physics 3372:Raizer, Yuri (2001). 3232:Einstein, A. (1905). 3127: 3045: 2970: 2950: 2858: 2838: 2836:{\displaystyle \rho } 2823:The relation between 2816: 2755: 2731: 2548: 2481: 2479:{\displaystyle \rho } 2461: 2441: 2421: 2419:{\displaystyle \rho } 2401: 2308: 2195: 2027: 2003: 1983: 1948: 1886: 1864: 1807: 1761: 1649: 1591: 1589:{\displaystyle N_{0}} 1564: 1460: 1433: 1363: 1335: 1315: 1264: 1189: 1162: 1102: 1037: 1035:{\displaystyle \eta } 1017: 968: 939:. A damping constant 934: 894: 865: 786: 760: 737: 680: 654: 632: 573: 544: 502: 477: 302: 235: 101:diffusion coefficient 87: 4060:Hans Albert Einstein 4009:I Am Albert Einstein 3955:Einstein Prize (APS) 3627:Photoelectric effect 3600:Theory of relativity 3157:Ion transport number 3056: 2979: 2959: 2874: 2847: 2827: 2764: 2742: 2559: 2498: 2470: 2450: 2430: 2410: 2320: 2211: 2051: 2016: 1992: 1961: 1895: 1873: 1819: 1796: 1669: 1600: 1573: 1496: 1475:parabolic dispersion 1442: 1372: 1352: 1324: 1289: 1198: 1171: 1122: 1116:rotational diffusion 1050: 1026: 986: 943: 923: 911:In the limit of low 874: 816: 775: 749: 697: 669: 643: 586: 555: 511: 491: 427: 366:For a particle with 253: 188: 160:absolute temperature 53: 3712:Thought experiments 3512:1966RPPh...29..255K 3459:Solid State Physics 3418:2019JChPh.150b1101C 3291:1906AnP...326..756V 3250:1905AnP...322..549E 3142:Smoluchowski factor 2865:classical particles 1702: 1467:electrical mobility 810:free electron model 580:electrical mobility 375:electrical mobility 334:electrical mobility 180:, for diffusion of 41:Marian Smoluchowski 23:(specifically, the 4161:Things named after 4023:Subtle is the Lord 3846:(1994 documentary) 3838:(1923 documentary) 3830:(1922 documentary) 3727:Gravitational wave 3610:General relativity 3605:Special relativity 3358:2021-05-06 at the 3279:Annalen der Physik 3238:Annalen der Physik 3122: 3040: 2965: 2945: 2853: 2833: 2811: 2750: 2726: 2543: 2476: 2456: 2436: 2416: 2396: 2303: 2190: 2022: 1998: 1978: 1943: 1881: 1859: 1814:conservative force 1802: 1756: 1688: 1644: 1586: 1559: 1455: 1428: 1358: 1330: 1310: 1281:with an arbitrary 1259: 1184: 1157: 1118:, the friction is 1097: 1032: 1012: 963: 929: 889: 860: 781: 755: 732: 675: 649: 627: 568: 539: 497: 472: 297: 230: 150:Boltzmann constant 82: 33:William Sutherland 4229: 4228: 4131:Awards and honors 4114:Siegbert Einstein 4002:Einstein's Cosmos 3427:10.1063/1.5080662 3113: 3098: 3097: 3032: 3025: 3004: 2968:{\displaystyle A} 2938: 2931: 2856:{\displaystyle U} 2806: 2805: 2710: 2532: 2459:{\displaystyle U} 2439:{\displaystyle U} 2038:diffusion current 2025:{\displaystyle U} 2001:{\displaystyle U} 1805:{\displaystyle U} 1722: 1639: 1629: 1553: 1546: 1490:density of states 1423: 1420: 1342:quasi Fermi level 1333:{\displaystyle p} 1283:density of states 1254: 1224: 1208: 1181: 1132: 1092: 1069: 855: 784:{\displaystyle T} 758:{\displaystyle Z} 727: 678:{\displaystyle T} 652:{\displaystyle q} 500:{\displaystyle D} 467: 457: 368:electrical charge 319:electrical charge 295: 272: 228: 218: 73: 29:Einstein relation 4254: 4217: 4216: 4116:(distant cousin) 4110:(great-grandson) 4072:Hermann Einstein 4054:Lieserl Einstein 3732:Tea leaf paradox 3579: 3572: 3565: 3556: 3555: 3532: 3531: 3505: 3490:Rep. Prog. Phys. 3484: 3478: 3477: 3469: 3463: 3462: 3454: 3448: 3447: 3429: 3403: 3394: 3388: 3387: 3369: 3363: 3349: 3343: 3336: 3330: 3329: 3309: 3303: 3302: 3270: 3264: 3263: 3261: 3229: 3223: 3216: 3210: 3209: 3185: 3179: 3173: 3131: 3129: 3128: 3123: 3115: 3114: 3111: 3099: 3096: 3092: 3086: 3082: 3076: 3072: 3049: 3047: 3046: 3041: 3033: 3031: 3027: 3026: 3023: 3013: 3005: 3003: 2999: 2993: 2989: 2983: 2974: 2972: 2971: 2966: 2954: 2952: 2951: 2946: 2941: 2940: 2939: 2937: 2933: 2932: 2929: 2922: 2918: 2906: 2887: 2862: 2860: 2859: 2854: 2842: 2840: 2839: 2834: 2820: 2818: 2817: 2812: 2807: 2804: 2800: 2794: 2790: 2784: 2780: 2759: 2757: 2756: 2751: 2749: 2735: 2733: 2732: 2727: 2716: 2712: 2711: 2709: 2705: 2699: 2695: 2689: 2634: 2633: 2632: 2602: 2593: 2592: 2591: 2573: 2552: 2550: 2549: 2544: 2533: 2531: 2527: 2521: 2517: 2511: 2485: 2483: 2482: 2477: 2465: 2463: 2462: 2457: 2445: 2443: 2442: 2437: 2425: 2423: 2422: 2417: 2405: 2403: 2402: 2397: 2389: 2388: 2387: 2357: 2348: 2347: 2346: 2328: 2312: 2310: 2309: 2304: 2296: 2279: 2259: 2251: 2250: 2249: 2219: 2199: 2197: 2196: 2191: 2183: 2166: 2152: 2132: 2118: 2104: 2087: 2079: 2078: 2077: 2059: 2031: 2029: 2028: 2023: 2007: 2005: 2004: 1999: 1987: 1985: 1984: 1979: 1974: 1952: 1950: 1949: 1944: 1939: 1925: 1908: 1890: 1888: 1887: 1882: 1880: 1868: 1866: 1865: 1860: 1855: 1832: 1811: 1809: 1808: 1803: 1791:potential energy 1765: 1763: 1762: 1757: 1749: 1748: 1736: 1735: 1723: 1721: 1713: 1712: 1711: 1701: 1696: 1686: 1681: 1680: 1653: 1651: 1650: 1645: 1640: 1635: 1631: 1630: 1627: 1620: 1618: 1617: 1595: 1593: 1592: 1587: 1585: 1584: 1568: 1566: 1565: 1560: 1555: 1554: 1552: 1548: 1547: 1544: 1537: 1529: 1523: 1522: 1464: 1462: 1461: 1456: 1454: 1453: 1437: 1435: 1434: 1429: 1424: 1422: 1421: 1419: 1411: 1403: 1397: 1393: 1392: 1382: 1367: 1365: 1364: 1359: 1339: 1337: 1336: 1331: 1319: 1317: 1316: 1311: 1268: 1266: 1265: 1260: 1255: 1253: 1252: 1251: 1230: 1226: 1225: 1222: 1215: 1210: 1209: 1206: 1193: 1191: 1190: 1185: 1183: 1182: 1179: 1166: 1164: 1163: 1158: 1156: 1155: 1134: 1133: 1130: 1106: 1104: 1103: 1098: 1093: 1091: 1075: 1071: 1070: 1067: 1060: 1041: 1039: 1038: 1033: 1021: 1019: 1018: 1013: 972: 970: 969: 964: 959: 938: 936: 935: 930: 898: 896: 895: 890: 888: 887: 886: 869: 867: 866: 861: 856: 851: 850: 849: 848: 837: 836: 826: 800:For the case of 790: 788: 787: 782: 764: 762: 761: 756: 741: 739: 738: 733: 728: 723: 718: 717: 707: 684: 682: 681: 676: 658: 656: 655: 650: 636: 634: 633: 628: 626: 625: 624: 612: 611: 599: 598: 577: 575: 574: 569: 567: 566: 548: 546: 545: 540: 538: 537: 536: 524: 523: 506: 504: 503: 498: 481: 479: 478: 473: 468: 463: 459: 458: 455: 448: 447: 437: 414: 406:. The parameter 405: 389:by the equation 388: 384: 372: 351: 341: 331: 316: 306: 304: 303: 298: 296: 294: 278: 274: 273: 270: 263: 239: 237: 236: 231: 229: 224: 220: 219: 216: 209: 208: 198: 157: 147: 136: 108: 98: 91: 89: 88: 83: 75: 74: 71: 39:in 1905, and by 4262: 4261: 4257: 4256: 4255: 4253: 4252: 4251: 4247:Albert Einstein 4232: 4231: 4230: 4225: 4205: 4156:Religious views 4151:Political views 4119: 4104:(granddaughter) 4102:Evelyn Einstein 4090:Robert Einstein 4084:Eduard Einstein 4028: 3965: 3959: 3913: 3883:Einstein's Gift 3817: 3810: 3751:Annus mirabilis 3736: 3707:Teleparallelism 3652:Einstein radius 3622:Brownian motion 3588: 3586:Albert Einstein 3583: 3550:ion diffusivity 3541: 3536: 3535: 3485: 3481: 3470: 3466: 3455: 3451: 3401: 3395: 3391: 3384: 3370: 3366: 3360:Wayback Machine 3350: 3346: 3337: 3333: 3326: 3310: 3306: 3285:(14): 756–780. 3271: 3267: 3230: 3226: 3217: 3213: 3200:(54): 781–785. 3186: 3182: 3174: 3170: 3165: 3138: 3110: 3106: 3088: 3087: 3078: 3077: 3071: 3057: 3054: 3053: 3022: 3018: 3017: 3012: 2995: 2994: 2985: 2984: 2982: 2980: 2977: 2976: 2960: 2957: 2956: 2928: 2924: 2923: 2914: 2907: 2905: 2901: 2897: 2883: 2875: 2872: 2871: 2848: 2845: 2844: 2828: 2825: 2824: 2796: 2795: 2786: 2785: 2779: 2765: 2762: 2761: 2745: 2743: 2740: 2739: 2701: 2700: 2691: 2690: 2688: 2672: 2668: 2604: 2603: 2598: 2597: 2575: 2574: 2569: 2568: 2560: 2557: 2556: 2523: 2522: 2513: 2512: 2510: 2499: 2496: 2495: 2471: 2468: 2467: 2451: 2448: 2447: 2431: 2428: 2427: 2411: 2408: 2407: 2359: 2358: 2353: 2352: 2330: 2329: 2324: 2323: 2321: 2318: 2317: 2292: 2275: 2255: 2221: 2220: 2215: 2214: 2212: 2209: 2208: 2179: 2162: 2148: 2128: 2114: 2100: 2083: 2061: 2060: 2055: 2054: 2052: 2049: 2048: 2017: 2014: 2013: 1993: 1990: 1989: 1970: 1962: 1959: 1958: 1935: 1921: 1904: 1896: 1893: 1892: 1876: 1874: 1871: 1870: 1851: 1828: 1820: 1817: 1816: 1797: 1794: 1793: 1780: 1744: 1740: 1731: 1727: 1714: 1707: 1703: 1697: 1692: 1687: 1685: 1676: 1672: 1670: 1667: 1666: 1659: 1626: 1622: 1621: 1619: 1613: 1609: 1601: 1598: 1597: 1580: 1576: 1574: 1571: 1570: 1543: 1539: 1538: 1530: 1528: 1524: 1518: 1514: 1497: 1494: 1493: 1449: 1445: 1443: 1440: 1439: 1412: 1404: 1402: 1398: 1388: 1384: 1383: 1381: 1373: 1370: 1369: 1353: 1350: 1349: 1325: 1322: 1321: 1290: 1287: 1286: 1275: 1247: 1243: 1231: 1221: 1217: 1216: 1214: 1205: 1201: 1199: 1196: 1195: 1178: 1174: 1172: 1169: 1168: 1151: 1147: 1129: 1125: 1123: 1120: 1119: 1114:In the case of 1076: 1066: 1062: 1061: 1059: 1051: 1048: 1047: 1027: 1024: 1023: 987: 984: 983: 955: 944: 941: 940: 924: 921: 920: 915:, the mobility 913:Reynolds number 909: 882: 881: 877: 875: 872: 871: 844: 843: 839: 832: 828: 827: 825: 817: 814: 813: 798: 776: 773: 772: 750: 747: 746: 713: 709: 708: 706: 698: 695: 694: 670: 667: 666: 661:electric charge 644: 641: 640: 617: 613: 604: 600: 594: 590: 589: 587: 584: 583: 562: 558: 556: 553: 552: 529: 525: 519: 515: 514: 512: 509: 508: 492: 489: 488: 454: 450: 443: 439: 438: 436: 428: 425: 424: 412: 407: 399: 390: 386: 382: 377: 370: 364: 359: 349: 342:is the dynamic 339: 329: 324: 314: 279: 269: 265: 264: 262: 254: 251: 250: 247:Reynolds number 215: 211: 204: 200: 199: 197: 189: 186: 185: 155: 146: 140: 131: 121: 106: 96: 70: 66: 54: 51: 50: 45:Brownian motion 37:Albert Einstein 17: 12: 11: 5: 4260: 4250: 4249: 4244: 4227: 4226: 4224: 4223: 4210: 4207: 4206: 4204: 4203: 4198: 4193: 4188: 4183: 4178: 4173: 4168: 4163: 4158: 4153: 4148: 4143: 4138: 4133: 4127: 4125: 4121: 4120: 4118: 4117: 4111: 4105: 4099: 4093: 4087: 4081: 4075: 4069: 4063: 4057: 4051: 4045: 4038: 4036: 4030: 4029: 4027: 4026: 4019: 4012: 4005: 3998: 3991: 3984: 3977: 3969: 3967: 3961: 3960: 3958: 3957: 3952: 3947: 3942: 3937: 3932: 3927: 3921: 3919: 3915: 3914: 3912: 3911: 3903: 3895: 3894:(2008 TV film) 3887: 3879: 3871: 3863: 3859:Young Einstein 3855: 3851:Insignificance 3847: 3839: 3831: 3822: 3820: 3812: 3811: 3809: 3808: 3802: 3799:Why Socialism? 3795: 3787: 3779: 3771: 3763: 3756: 3746: 3744: 3738: 3737: 3735: 3734: 3729: 3724: 3719: 3714: 3709: 3704: 3699: 3694: 3689: 3684: 3679: 3674: 3669: 3664: 3659: 3654: 3649: 3644: 3639: 3637:Einstein solid 3634: 3629: 3624: 3619: 3614: 3613: 3612: 3607: 3596: 3594: 3590: 3589: 3582: 3581: 3574: 3567: 3559: 3553: 3552: 3547: 3540: 3539:External links 3537: 3534: 3533: 3496:(1): 255–284. 3479: 3464: 3449: 3389: 3383:978-3540194620 3382: 3364: 3344: 3331: 3324: 3304: 3265: 3244:(8): 549–560. 3224: 3211: 3180: 3167: 3166: 3164: 3161: 3160: 3159: 3154: 3149: 3144: 3137: 3134: 3121: 3118: 3109: 3105: 3102: 3095: 3091: 3085: 3081: 3075: 3070: 3067: 3064: 3061: 3039: 3036: 3030: 3021: 3016: 3011: 3008: 3002: 2998: 2992: 2988: 2964: 2944: 2936: 2927: 2921: 2917: 2913: 2910: 2904: 2900: 2896: 2893: 2890: 2886: 2882: 2879: 2852: 2832: 2810: 2803: 2799: 2793: 2789: 2783: 2778: 2775: 2772: 2769: 2748: 2725: 2722: 2719: 2715: 2708: 2704: 2698: 2694: 2687: 2684: 2681: 2678: 2675: 2671: 2667: 2664: 2661: 2658: 2655: 2652: 2649: 2646: 2643: 2640: 2637: 2631: 2628: 2625: 2622: 2619: 2616: 2613: 2610: 2607: 2601: 2596: 2590: 2587: 2584: 2581: 2578: 2572: 2567: 2564: 2542: 2539: 2536: 2530: 2526: 2520: 2516: 2509: 2506: 2503: 2475: 2455: 2435: 2415: 2395: 2392: 2386: 2383: 2380: 2377: 2374: 2371: 2368: 2365: 2362: 2356: 2351: 2345: 2342: 2339: 2336: 2333: 2327: 2302: 2299: 2295: 2291: 2288: 2285: 2282: 2278: 2274: 2271: 2268: 2265: 2262: 2258: 2254: 2248: 2245: 2242: 2239: 2236: 2233: 2230: 2227: 2224: 2218: 2189: 2186: 2182: 2178: 2175: 2172: 2169: 2165: 2161: 2158: 2155: 2151: 2147: 2144: 2141: 2138: 2135: 2131: 2127: 2124: 2121: 2117: 2113: 2110: 2107: 2103: 2099: 2096: 2093: 2090: 2086: 2082: 2076: 2073: 2070: 2067: 2064: 2058: 2021: 1997: 1977: 1973: 1969: 1966: 1955:Drag (physics) 1942: 1938: 1934: 1931: 1928: 1924: 1920: 1917: 1914: 1911: 1907: 1903: 1900: 1879: 1858: 1854: 1850: 1847: 1844: 1841: 1838: 1835: 1831: 1827: 1824: 1801: 1779: 1776: 1755: 1752: 1747: 1743: 1739: 1734: 1730: 1726: 1720: 1717: 1710: 1706: 1700: 1695: 1691: 1684: 1679: 1675: 1658: 1655: 1643: 1638: 1634: 1625: 1616: 1612: 1608: 1605: 1583: 1579: 1558: 1551: 1542: 1536: 1533: 1527: 1521: 1517: 1513: 1510: 1507: 1504: 1501: 1452: 1448: 1427: 1418: 1415: 1410: 1407: 1401: 1396: 1391: 1387: 1380: 1377: 1357: 1329: 1309: 1306: 1303: 1300: 1297: 1294: 1274: 1271: 1258: 1250: 1246: 1241: 1237: 1234: 1229: 1220: 1213: 1204: 1177: 1154: 1150: 1146: 1143: 1140: 1137: 1128: 1096: 1090: 1086: 1082: 1079: 1074: 1065: 1058: 1055: 1031: 1011: 1008: 1004: 1000: 997: 994: 991: 962: 958: 954: 951: 948: 928: 908: 905: 885: 880: 859: 854: 847: 842: 835: 831: 824: 821: 797: 794: 793: 792: 780: 770: 754: 731: 726: 722: 716: 712: 705: 702: 687: 686: 674: 664: 648: 638: 623: 620: 616: 610: 607: 603: 597: 593: 565: 561: 550: 535: 532: 528: 522: 518: 496: 471: 466: 462: 453: 446: 442: 435: 432: 421:electric field 419:to an applied 417:drift velocity 410: 397: 380: 363: 360: 358: 355: 354: 353: 347: 337: 327: 322: 321:of a particle; 308: 307: 293: 289: 285: 282: 277: 268: 261: 258: 240: 227: 223: 214: 207: 203: 196: 193: 164: 163: 153: 144: 138: 129: 116:to an applied 114:drift velocity 104: 81: 78: 69: 64: 61: 58: 15: 9: 6: 4: 3: 2: 4259: 4248: 4245: 4243: 4240: 4239: 4237: 4222: 4221: 4212: 4211: 4208: 4202: 4199: 4197: 4194: 4192: 4189: 4187: 4184: 4182: 4179: 4177: 4174: 4172: 4169: 4167: 4164: 4162: 4159: 4157: 4154: 4152: 4149: 4147: 4144: 4142: 4139: 4137: 4134: 4132: 4129: 4128: 4126: 4122: 4115: 4112: 4109: 4106: 4103: 4100: 4097: 4094: 4091: 4088: 4085: 4082: 4079: 4078:Maja Einstein 4076: 4073: 4070: 4067: 4064: 4061: 4058: 4055: 4052: 4049: 4048:Elsa Einstein 4046: 4043: 4040: 4039: 4037: 4035: 4031: 4025: 4024: 4020: 4018: 4017: 4013: 4011: 4010: 4006: 4004: 4003: 3999: 3997: 3996: 3992: 3990: 3989: 3985: 3983: 3982: 3978: 3976: 3975: 3971: 3970: 3968: 3962: 3956: 3953: 3951: 3948: 3946: 3943: 3941: 3938: 3936: 3935:Kalinga Prize 3933: 3931: 3928: 3926: 3923: 3922: 3920: 3916: 3909: 3908: 3904: 3902:(2017 series) 3901: 3900: 3896: 3893: 3892: 3888: 3885: 3884: 3880: 3877: 3876: 3872: 3869: 3868: 3864: 3861: 3860: 3856: 3853: 3852: 3848: 3845: 3844: 3840: 3837: 3836: 3832: 3829: 3828: 3824: 3823: 3821: 3819: 3813: 3806: 3803: 3800: 3796: 3793: 3792: 3788: 3785: 3784: 3780: 3777: 3776: 3772: 3769: 3768: 3764: 3761: 3757: 3754: 3752: 3748: 3747: 3745: 3743: 3739: 3733: 3730: 3728: 3725: 3723: 3720: 3718: 3715: 3713: 3710: 3708: 3705: 3703: 3700: 3698: 3695: 3693: 3690: 3688: 3685: 3683: 3680: 3678: 3675: 3673: 3670: 3668: 3665: 3663: 3660: 3658: 3655: 3653: 3650: 3648: 3645: 3643: 3640: 3638: 3635: 3633: 3630: 3628: 3625: 3623: 3620: 3618: 3615: 3611: 3608: 3606: 3603: 3602: 3601: 3598: 3597: 3595: 3591: 3587: 3580: 3575: 3573: 3568: 3566: 3561: 3560: 3557: 3551: 3548: 3546: 3543: 3542: 3529: 3525: 3521: 3517: 3513: 3509: 3504: 3499: 3495: 3492: 3491: 3483: 3475: 3468: 3460: 3453: 3445: 3441: 3437: 3433: 3428: 3423: 3419: 3415: 3412:(2): 021101. 3411: 3407: 3400: 3393: 3385: 3379: 3375: 3368: 3361: 3357: 3354: 3348: 3341: 3335: 3327: 3325:9780815320517 3321: 3317: 3316: 3308: 3300: 3296: 3292: 3288: 3284: 3281:(in German). 3280: 3276: 3269: 3260: 3255: 3251: 3247: 3243: 3240:(in German). 3239: 3235: 3228: 3221: 3215: 3207: 3203: 3199: 3195: 3191: 3184: 3177: 3172: 3168: 3158: 3155: 3153: 3152:Stokes radius 3150: 3148: 3145: 3143: 3140: 3139: 3133: 3119: 3116: 3107: 3103: 3100: 3093: 3083: 3073: 3068: 3065: 3062: 3059: 3050: 3037: 3034: 3028: 3019: 3014: 3009: 3006: 3000: 2990: 2962: 2942: 2934: 2925: 2908: 2902: 2898: 2894: 2891: 2877: 2870: 2866: 2850: 2830: 2821: 2808: 2801: 2791: 2781: 2776: 2773: 2770: 2767: 2736: 2723: 2720: 2713: 2706: 2696: 2685: 2682: 2679: 2676: 2673: 2669: 2665: 2662: 2656: 2653: 2650: 2644: 2641: 2638: 2635: 2594: 2565: 2562: 2553: 2540: 2537: 2528: 2518: 2507: 2504: 2493: 2489: 2473: 2453: 2433: 2413: 2393: 2390: 2349: 2314: 2300: 2286: 2269: 2266: 2263: 2206: 2201: 2187: 2173: 2156: 2142: 2139: 2136: 2122: 2108: 2094: 2091: 2045: 2043: 2039: 2035: 2034:drift current 2032:, called the 2019: 2011: 1995: 1964: 1956: 1929: 1915: 1912: 1898: 1845: 1839: 1836: 1822: 1815: 1799: 1792: 1787: 1785: 1775: 1773: 1769: 1753: 1745: 1741: 1737: 1732: 1728: 1718: 1715: 1708: 1704: 1698: 1693: 1689: 1682: 1677: 1664: 1654: 1641: 1636: 1632: 1623: 1614: 1610: 1606: 1603: 1581: 1577: 1556: 1549: 1540: 1534: 1531: 1525: 1519: 1515: 1511: 1505: 1499: 1491: 1487: 1486:semiconductor 1484: 1480: 1476: 1472: 1468: 1450: 1446: 1425: 1416: 1413: 1408: 1405: 1399: 1394: 1389: 1385: 1378: 1375: 1355: 1347: 1343: 1327: 1304: 1298: 1295: 1292: 1284: 1280: 1279:semiconductor 1273:Semiconductor 1270: 1256: 1248: 1244: 1239: 1235: 1232: 1227: 1218: 1211: 1202: 1175: 1152: 1148: 1144: 1141: 1138: 1135: 1126: 1117: 1112: 1110: 1109:Lennard-Jones 1094: 1088: 1084: 1080: 1077: 1072: 1063: 1056: 1053: 1045: 1029: 1009: 1006: 1002: 998: 995: 992: 989: 981: 977: 960: 956: 952: 949: 946: 926: 918: 914: 904: 902: 878: 857: 852: 840: 833: 829: 822: 819: 811: 807: 803: 778: 771: 768: 767:charge number 752: 745: 744: 743: 729: 724: 720: 714: 710: 703: 700: 692: 672: 665: 662: 646: 639: 621: 618: 608: 605: 595: 581: 563: 559: 551: 533: 530: 520: 494: 487: 486: 485: 482: 469: 464: 460: 451: 444: 440: 433: 430: 422: 418: 413: 404: 400: 393: 383: 376: 369: 357:Special cases 348: 345: 338: 335: 330: 323: 320: 313: 312: 311: 291: 287: 283: 280: 275: 266: 259: 256: 248: 244: 241: 225: 221: 212: 205: 201: 194: 191: 183: 179: 176: 175: 174: 171: 169: 161: 154: 151: 143: 139: 135: 128: 124: 119: 115: 112: 105: 102: 95: 94: 93: 79: 76: 67: 62: 59: 56: 48: 46: 42: 38: 34: 30: 26: 22: 4218: 4186:Einsteinhaus 4066:Pauline Koch 4044:(first wife) 4042:Mileva Marić 4021: 4014: 4007: 4000: 3993: 3986: 3979: 3972: 3905: 3897: 3889: 3881: 3873: 3865: 3857: 3849: 3841: 3833: 3825: 3789: 3781: 3773: 3765: 3750: 3656: 3493: 3488: 3482: 3473: 3467: 3458: 3452: 3409: 3405: 3392: 3373: 3367: 3347: 3334: 3314: 3307: 3282: 3278: 3268: 3241: 3237: 3227: 3214: 3197: 3196:. Series 6. 3193: 3183: 3171: 3051: 2822: 2737: 2554: 2315: 2202: 2046: 2037: 2033: 1812:generates a 1788: 1781: 1772:gas constant 1767: 1660: 1276: 1113: 975: 916: 910: 901:Fermi energy 806:Fermi liquid 799: 688: 483: 408: 402: 395: 391: 378: 365: 325: 309: 242: 177: 172: 165: 141: 133: 126: 122: 49: 28: 18: 4191:Einsteinium 3964:Books about 3910:(2023 film) 3907:Oppenheimer 3886:(2003 play) 3878:(1994 film) 3870:(1993 play) 3862:(1988 film) 3854:(1985 film) 3697:EPR paradox 3353:Chapter 2.7 3218:P. Hänggi, 980:Stokes' law 184:particles: 4236:Categories 4196:Max Talmey 4098:(grandson) 4056:(daughter) 3816:In popular 3163:References 2492:chain rule 2486:(e.g. see 2205:Fick's law 1784:Ryogo Kubo 3528:250892844 3503:0710.4394 3436:0021-9606 3104:μ 3084:ρ 3074:ρ 3069:μ 3066:− 3035:ρ 3010:− 2991:ρ 2903:− 2878:ρ 2831:ρ 2792:ρ 2782:ρ 2777:μ 2774:− 2718:∇ 2697:ρ 2683:− 2680:ρ 2677:μ 2674:− 2663:ρ 2660:∇ 2654:− 2648:∇ 2645:ρ 2642:μ 2639:− 2535:∇ 2519:ρ 2505:ρ 2502:∇ 2474:ρ 2414:ρ 2287:ρ 2284:∇ 2267:− 2171:∇ 2157:μ 2143:ρ 2140:− 2123:ρ 2095:μ 2010:diffusion 1965:ρ 1916:μ 1843:∇ 1840:− 1746:− 1674:Λ 1611:μ 1535:φ 1506:φ 1483:inorganic 1447:μ 1417:φ 1386:μ 1356:φ 1305:φ 1240:η 1236:π 1145:η 1142:π 1127:ζ 1111:system. 1085:η 1081:π 1044:viscosity 1030:η 1003:η 999:π 990:ζ 953:ζ 947:γ 927:ζ 830:μ 802:Fermi gas 711:μ 619:− 606:− 560:μ 531:− 441:μ 344:viscosity 288:η 284:π 202:μ 63:μ 35:in 1904, 4220:Category 4146:Memorial 4092:(cousin) 4080:(sister) 4074:(father) 4068:(mother) 3966:Einstein 3801:" (1949) 3762:" (1905) 3444:30646717 3356:Archived 3136:See also 111:terminal 4124:Related 3818:culture 3593:Physics 3508:Bibcode 3414:Bibcode 3287:Bibcode 3246:Bibcode 1770:is the 1465:is the 1042:is the 765:is the 659:is the 578:is the 332:is the 317:is the 182:charged 158:is the 148:is the 99:is the 27:), the 21:physics 4034:Family 3918:Prizes 3899:Genius 3807:(1955) 3794:(1938) 3786:(1934) 3778:(1922) 3770:(1916) 3755:(1905) 3753:papers 3526:  3442:  3434:  3380:  3322:  2955:where 1569:where 1438:where 1022:where 982:gives 870:where 742:where 484:where 373:, its 92:where 4141:House 4136:Brain 4086:(son) 4062:(son) 3742:Works 3524:S2CID 3498:arXiv 3402:(PDF) 2040:(see 1953:(see 1766:were 1469:(see 1277:In a 804:or a 691:volts 310:Here 118:force 3875:I.Q. 3440:PMID 3432:ISSN 3378:ISBN 3320:ISBN 2863:for 2843:and 1344:(or 3516:doi 3422:doi 3410:150 3295:doi 3283:326 3254:doi 3242:322 3202:doi 2044:). 1492:): 1194:is 899:is 19:In 4238:: 3522:. 3514:. 3506:. 3494:29 3438:. 3430:. 3420:. 3408:. 3404:. 3293:. 3277:. 3252:. 3236:. 3192:. 2494:, 2207:, 1786:. 1774:. 1348:) 978:, 903:. 637:). 549:). 394:= 249:: 125:= 120:, 3797:" 3758:" 3578:e 3571:t 3564:v 3530:. 3518:: 3510:: 3500:: 3446:. 3424:: 3416:: 3386:. 3362:. 3342:. 3328:. 3301:. 3297:: 3289:: 3262:. 3256:: 3248:: 3222:. 3208:. 3204:: 3198:9 3120:, 3117:T 3112:B 3108:k 3101:= 3094:U 3090:d 3080:d 3063:= 3060:D 3038:. 3029:T 3024:B 3020:k 3015:1 3007:= 3001:U 2997:d 2987:d 2963:A 2943:, 2935:T 2930:B 2926:k 2920:) 2916:x 2912:( 2909:U 2899:e 2895:A 2892:= 2889:) 2885:x 2881:( 2851:U 2809:. 2802:U 2798:d 2788:d 2771:= 2768:D 2747:x 2724:. 2721:U 2714:) 2707:U 2703:d 2693:d 2686:D 2670:( 2666:= 2657:D 2651:U 2636:= 2630:n 2627:o 2624:i 2621:s 2618:u 2615:f 2612:f 2609:i 2606:d 2600:J 2595:+ 2589:t 2586:f 2583:i 2580:r 2577:d 2571:J 2566:= 2563:0 2541:. 2538:U 2529:U 2525:d 2515:d 2508:= 2454:U 2434:U 2394:0 2391:= 2385:n 2382:o 2379:i 2376:s 2373:u 2370:f 2367:f 2364:i 2361:d 2355:J 2350:+ 2344:t 2341:f 2338:i 2335:r 2332:d 2326:J 2301:, 2298:) 2294:x 2290:( 2281:) 2277:x 2273:( 2270:D 2264:= 2261:) 2257:x 2253:( 2247:n 2244:o 2241:i 2238:s 2235:u 2232:f 2229:f 2226:i 2223:d 2217:J 2188:, 2185:) 2181:x 2177:( 2174:U 2168:) 2164:x 2160:( 2154:) 2150:x 2146:( 2137:= 2134:) 2130:x 2126:( 2120:) 2116:x 2112:( 2109:F 2106:) 2102:x 2098:( 2092:= 2089:) 2085:x 2081:( 2075:t 2072:f 2069:i 2066:r 2063:d 2057:J 2020:U 1996:U 1976:) 1972:x 1968:( 1941:) 1937:x 1933:( 1930:F 1927:) 1923:x 1919:( 1913:= 1910:) 1906:x 1902:( 1899:v 1878:x 1857:) 1853:x 1849:( 1846:U 1837:= 1834:) 1830:x 1826:( 1823:F 1800:U 1768:R 1754:. 1751:) 1742:D 1738:+ 1733:+ 1729:D 1725:( 1719:T 1716:R 1709:2 1705:F 1699:2 1694:i 1690:z 1683:= 1678:e 1642:. 1637:q 1633:T 1628:B 1624:k 1615:q 1607:= 1604:D 1582:0 1578:N 1557:, 1550:T 1545:B 1541:k 1532:q 1526:e 1520:0 1516:N 1512:= 1509:) 1503:( 1500:p 1451:q 1426:, 1414:d 1409:p 1406:d 1400:q 1395:p 1390:q 1379:= 1376:D 1328:p 1308:) 1302:( 1299:p 1296:= 1293:p 1257:. 1249:3 1245:r 1233:8 1228:T 1223:B 1219:k 1212:= 1207:r 1203:D 1180:r 1176:D 1153:3 1149:r 1139:8 1136:= 1131:r 1095:. 1089:r 1078:6 1073:T 1068:B 1064:k 1057:= 1054:D 1010:, 1007:r 996:6 993:= 976:r 961:m 957:/ 950:= 917:ÎĽ 884:F 879:E 858:, 853:q 846:F 841:E 834:q 823:= 820:D 779:T 753:Z 730:, 725:Z 721:T 715:q 704:= 701:D 673:T 647:q 622:1 615:s 609:1 602:V 596:2 592:m 582:( 564:q 534:1 527:s 521:2 517:m 495:D 470:, 465:q 461:T 456:B 452:k 445:q 434:= 431:D 411:q 409:ÎĽ 403:q 401:/ 398:q 396:ÎĽ 392:ÎĽ 387:ÎĽ 381:q 379:ÎĽ 371:q 350:r 346:; 340:η 328:q 326:ÎĽ 315:q 292:r 281:6 276:T 271:B 267:k 260:= 257:D 226:q 222:T 217:B 213:k 206:q 195:= 192:D 162:. 156:T 152:; 145:B 142:k 137:; 134:F 132:/ 130:d 127:v 123:ÎĽ 107:ÎĽ 103:; 97:D 80:, 77:T 72:B 68:k 60:= 57:D

Index

physics
kinetic theory of gases
William Sutherland
Albert Einstein
Marian Smoluchowski
Brownian motion
diffusion coefficient
terminal
drift velocity
force
Boltzmann constant
absolute temperature
fluctuation-dissipation relation
charged
Reynolds number
electrical charge
electrical mobility
viscosity
electrical charge
electrical mobility
drift velocity
electric field
electrical mobility
electric charge
volts
charge number
Fermi gas
Fermi liquid
free electron model
Fermi energy

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