574:
degenerate particles; however, adding heat does not increase the speed of most of the electrons, because they are stuck in fully occupied quantum states. Pressure is increased only by the mass of the particles, which increases the gravitational force pulling the particles closer together. Therefore, the phenomenon is the opposite of that normally found in matter where if the mass of the matter is increased, the object becomes bigger. In degenerate gas, when the mass is increased, the particles become spaced closer together due to gravity (and the pressure is increased), so the object becomes smaller. Degenerate gas can be compressed to very high densities, typical values being in the range of 10,000 kilograms per cubic centimeter.
2101:
461:
2113:
2185:
1657:
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occupy states of higher energy even at low temperatures. Degenerate gases strongly resist further compression because the electrons cannot move to already filled lower energy levels due to the Pauli exclusion principle. Since electrons cannot give up energy by moving to lower energy states, no thermal energy can be extracted. The momentum of the fermions in the fermion gas nevertheless generates pressure, termed "degeneracy pressure".
2149:
2173:
2125:
2161:
2137:
481:
that temperature has a negligible effect on the total pressure. The adjacent figure shows the thermal pressure (red line) and total pressure (blue line) in a Fermi gas, with the difference between the two being the degeneracy pressure. As the temperature falls, the density and the degeneracy pressure increase, until the degeneracy pressure contributes most of the total pressure.
704:. However, because protons are much more massive than electrons, the same momentum represents a much smaller velocity for protons than for electrons. As a result, in matter with approximately equal numbers of protons and electrons, proton degeneracy pressure is much smaller than electron degeneracy pressure, and proton degeneracy is usually modelled as a correction to the
530:
quantum states are filled up to the Fermi energy. Most stars are supported against their own gravitation by normal thermal gas pressure, while in white dwarf stars the supporting force comes from the degeneracy pressure of the electron gas in their interior. In neutron stars, the degenerate particles are neutrons.
671:
at a given energy. This phenomenon is compounded by the fact that the pressures within neutron stars are much higher than those in white dwarfs. The pressure increase is caused by the fact that the compactness of a neutron star causes gravitational forces to be much higher than in a less compact body
573:
of electrons are quite high and the rate of collision between electrons and other particles is quite low, therefore degenerate electrons can travel great distances at velocities that approach the speed of light. Instead of temperature, the pressure in a degenerate gas depends only on the speed of the
568:
are luminous not because they are generating energy but rather because they have trapped a large amount of heat which is gradually radiated away. Normal gas exerts higher pressure when it is heated and expands, but the pressure in a degenerate gas does not depend on the temperature. When gas becomes
773:
for neutron-degenerate objects. Whether quark-degenerate matter forms at all in these situations depends on the equations of state of both neutron-degenerate matter and quark-degenerate matter, both of which are poorly known. Quark stars are considered to be an intermediate category between neutron
159:
model. Examples include electrons in metals and in white dwarf stars and neutrons in neutron stars. The electrons are confined by
Coulomb attraction to positive ion cores; the neutrons are confined by gravitation attraction. The fermions, forced in to higher levels by the Pauli principle, exert
81:
remains non-zero even at absolute zero temperature. Adding particles or reducing the volume forces the particles into higher-energy quantum states. In this situation, a compression force is required, and is made manifest as a resisting pressure. The key feature is that this degeneracy pressure does
594:
and with realistic
Coulomb corrections, the corresponding mass limit is around 1.38 solar masses. The limit may also change with the chemical composition of the object, as it affects the ratio of mass to number of electrons present. The object's rotation, which counteracts the gravitational force,
529:
such as electrons, protons, and neutrons rather than molecules of ordinary matter. The electron gas in ordinary metals and in the interior of white dwarfs are two examples. Following the Pauli exclusion principle, there can be only one fermion occupying each quantum state. In a degenerate gas, all
552:
In an ordinary fermion gas in which thermal effects dominate, most of the available electron energy levels are unfilled and the electrons are free to move to these states. As particle density is increased, electrons progressively fill the lower energy states and additional electrons are forced to
505:
electrons alone as a degenerate gas, while the majority of the electrons are regarded as occupying bound quantum states. This solid state contrasts with degenerate matter that forms the body of a white dwarf, where most of the electrons would be treated as occupying free particle momentum states.
480:
All matter experiences both normal thermal pressure and degeneracy pressure, but in commonly encountered gases, thermal pressure dominates so much that degeneracy pressure can be ignored. Likewise, degenerate matter still has normal thermal pressure; the degeneracy pressure dominates to the point
789:
and as the low temperature ground state limit for states of matter. The electron degeneracy pressure occurs in the ground state systems which are non-degenerate in energy levels. The term "degeneracy" derives from work on the specific heat of gases that pre-dates the use of the term in quantum
116:
were almost completely ionised and closely packed. Fowler described white dwarfs as composed of a gas of particles that became degenerate at low temperature; he also pointed out that ordinary atoms are broadly similar in regards to the filling of energy levels by fermions. Milne proposed that
656:, usually either as a result of a merger or by feeding off of a close binary partner. Above the Chandrasekhar limit, the gravitational pressure at the core exceeds the electron degeneracy pressure, and electrons begin to combine with protons to produce neutrons (via inverse
699:
Sufficiently dense matter containing protons experiences proton degeneracy pressure, in a manner similar to the electron degeneracy pressure in electron-degenerate matter: protons confined to a sufficiently small volume have a large uncertainty in their momentum due to the
151:. The Pauli principle allows only one fermion in each quantum state and the confinement ensures that energy of these states increases as they are filled. The lowest states fill up and fermions are forced to occupy high energy states even at low temperature.
484:
While degeneracy pressure usually dominates at extremely high densities, it is the ratio between degenerate pressure and thermal pressure which determines degeneracy. Given a sufficiently drastic increase in temperature (such as during a red giant star's
76:
prevents identical fermions from occupying the same quantum state. At lowest total energy (when the thermal energy of the particles is negligible), all the lowest energy quantum states are filled. This state is referred to as full degeneracy. This
589:
for objects with typical compositions expected for white dwarf stars (carbon and oxygen with two baryons per electron). This mass cut-off is appropriate only for a star supported by ideal electron degeneracy pressure under
Newtonian gravity; in
381:
492:
Degeneracy pressure contributes to the pressure of conventional solids, but these are not usually considered to be degenerate matter because a significant contribution to their pressure is provided by electrical repulsion of
533:
A fermion gas in which all quantum states below a given energy level are filled is called a fully degenerate fermion gas. The difference between this energy level and the lowest energy level is known as the Fermi energy.
154:
While the Pauli principle and Fermi-Dirac distribution applies to all matter, the interesting cases for degenerate matter involve systems of many fermions. These cases can be understood with the help of the
603:
that run out of fuel. During this shrinking, an electron-degenerate gas forms in the core, providing sufficient degeneracy pressure as it is compressed to resist further collapse. Above this mass limit, a
564:, largely helium and carbon nuclei, floating in a sea of electrons, which have been stripped from the nuclei. Degenerate gas is an almost perfect conductor of heat and does not obey ordinary gas laws.
451:
233:
664:). The result is an extremely compact star composed of "nuclear matter", which is predominantly a degenerate neutron gas with a small admixture of degenerate proton and electron gases.
916:
Andrew G. Truscott, Kevin E. Strecker, William I. McAlexander, Guthrie
Partridge, and Randall G. Hulet, "Observation of Fermi Pressure in a Gas of Trapped Atoms", Science, 2 March 2001
269:
630:, which are partially supported by the pressure from a degenerate neutron gas. Neutron stars are formed either directly from the supernova of stars with masses between 10 and 25
1321:
Hanle, Paul A. "The Coming of Age of Erwin Schrödinger: His
Quantum Statistics of Ideal Gases". Archive for History of Exact Sciences, vol. 17, no. 2, 1977, pp. 165â92. JSTOR,
82:
not depend on the temperature but only on the density of the fermions. Degeneracy pressure keeps dense stars in equilibrium, independent of the thermal structure of the star.
758:. The equations of state for the various proposed forms of quark-degenerate matter vary widely, and are usually also poorly defined, due to the difficulty of modelling
68:, an ensemble of non-interacting fermions. In a quantum mechanical description, particles limited to a finite volume may take only a discrete set of energies, called
1339:
765:
Quark-degenerate matter may occur in the cores of neutron stars, depending on the equations of state of neutron-degenerate matter. It may also occur in hypothetical
855:
applied Fermi's model to the puzzle of the stability of white dwarf stars. This approach was extended to relativistic models by later studies and with the work of
667:
Neutrons in a degenerate neutron gas are spaced much more closely than electrons in an electron-degenerate gas because the more massive neutron has a much shorter
1132:
Rotondo, Michael; Rueda, Jorge A.; Ruffini, Remo; Xue, She-Sheng (2011). "Relativistic
Feynman-Metropolis-Teller theory for white dwarfs in general relativity".
821:, the effect at low temperatures came to be called "gas degeneracy". A fully degenerate gas has no volume dependence on pressure when temperature approaches
266:
temperature. At relatively low densities, the pressure of a fully degenerate gas can be derived by treating the system as an ideal Fermi gas, in this way
556:
Under high densities, matter becomes a degenerate gas when all electrons are stripped from their parent atoms. The core of a star, once hydrogen burning
262:
is the volume, the pressure exerted by degenerate matter depends only weakly on its temperature. In particular, the pressure remains nonzero even at
569:
super-compressed, particles position right up against each other to produce degenerate gas that behaves more like a solid. In degenerate gases the
387:
is the mass of the individual particles making up the gas. At very high densities, where most of the particles are forced into quantum states with
1428:
394:
1594:
1415:
An english translation of the original work of Enrico Fermi on the quantization of the monoatomic ideal gas, is given in this paper
770:
680:
185:
1540:
1071:
1526:
805:
at very low temperature as "degeneration"; he attributed this to quantum effects. In subsequent work in various papers on
388:
1386:
730:
is expected to occur. Several variations of this hypothesis have been proposed that represent quark-degenerate states.
85:
A degenerate mass whose fermions have velocities close to the speed of light (particle kinetic energy larger than its
2205:
1102:
836:
developed a semi-classical model for electrons in a metal. The model treated the electrons as a gas. Later in 1927,
2100:
1861:
1931:
1856:
1587:
1035:
984:
848:
model for metals. Sommerfeld called the low temperature region with quantum effects a "wholly degenerate gas".
2043:
1871:
672:
with similar mass. The result is a star with a diameter on the order of a thousandth that of a white dwarf.
2053:
1926:
1671:
872:
582:
543:
24:
2091:
856:
2220:
2210:
1580:
144:
73:
34:
457:
is another proportionality constant depending on the properties of the particles making up the gas.
100:, stellar objects composed of degenerate matter, was originally developed in a joint effort between
2078:
1977:
1607:
786:
164:
20:
1567:
1972:
747:
1475:
2215:
1997:
1987:
1737:
1732:
1238:
Annala, Eemeli; Gorda, Tyler; Kurkela, Aleksi; NÀttilÀ, Joonas; Vuorinen, Aleksi (2020-06-01).
841:
806:
130:
54:
163:
The allocation or distribution of fermions into quantum states ranked by energy is called the
1298:
1027:
1020:
701:
376:{\displaystyle P={\frac {(3\pi ^{2})^{2/3}\hbar ^{2}}{5m}}\left({\frac {N}{V}}\right)^{5/3},}
1916:
1676:
1354:
1261:
1204:
1151:
939:
502:
927:
818:
8:
2177:
1891:
1783:
1773:
1686:
1641:
1114:
878:
860:
646:
595:
also changes the limit for any particular object. Celestial objects below this limit are
578:
498:
148:
1358:
1265:
1208:
1155:
943:
750:
materials are degenerate gases of quarks in which quarks pair up in a manner similar to
2165:
2153:
2038:
1967:
1801:
1503:
1456:
1404:
1378:
1251:
1220:
1194:
1167:
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759:
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591:
247:
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1992:
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1536:
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1224:
1171:
1098:
1077:
1067:
1041:
1031:
990:
980:
957:
884:
844:
to this electron gas model, computing the specific heat of metals; the result became
837:
782:
514:
19:
This article is about a state of matter. For multiple states with equal energy, see
2129:
2117:
2023:
1646:
1532:
1487:
1440:
1429:"Propaganda in Science: Sommerfeld and the Spread of the Electron Theory of Metals"
1362:
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1212:
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947:
833:
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101:
86:
2013:
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852:
810:
38:
460:
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1811:
1806:
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1163:
794:
755:
731:
570:
557:
510:
494:
1274:
1239:
1081:
2199:
2048:
2028:
1951:
1911:
1846:
1778:
1701:
1499:
1452:
1374:
1283:
1011:
994:
961:
952:
822:
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735:
684:
676:
465:
263:
140:
69:
1568:
Lecture 17: Stellar
Evolution. Discusses degenerate gases in models of stars
1403:
Zannoni, Alberto (1999). "On the
Quantization of the Monoatomic Ideal Gas".
585:
cannot support the object against collapse. The limit is approximately 1.44
2141:
2073:
1946:
1941:
1936:
1901:
1851:
1768:
1335:
829:
721:
627:
621:
605:
486:
118:
109:
105:
50:
42:
1572:
1045:
905:
577:
There is an upper limit to the mass of an electron-degenerate object, the
1982:
1876:
1788:
1409:
1062:
Taylor, John Robert; Zafiratos, Chris D.; Dubson, Michael Andrew (2004).
751:
688:
668:
642:
596:
565:
547:
180:
46:
1460:
509:
Exotic examples of degenerate matter include neutron degenerate matter,
1921:
1896:
1823:
1793:
1727:
1706:
1366:
1322:
1097:
section 15.3 â R Kippenhahn & A. Weigert, 1990, 3rd printing 1994.
814:
766:
743:
727:
717:
657:
638:
609:
586:
117:
degenerate matter is found in most of the nuclei of stars, not only in
2184:
167:. Degenerate matter exhibits the results of Fermi-Dirac distribution.
1444:
845:
802:
675:
The properties of neutron matter set an upper limit to the mass of a
626:
Neutron degeneracy is analogous to electron degeneracy and exists in
469:
176:
156:
65:
58:
1656:
2058:
1886:
1256:
739:
526:
473:
1199:
1146:
489:), matter can become non-degenerate without reducing its density.
2018:
1906:
1841:
1758:
1753:
726:
At densities greater than those supported by neutron degeneracy,
136:
135:
Degenerate matter exhibits quantum mechanical properties when a
1627:
734:
is a degenerate gas of quarks that is often assumed to contain
501:
of metals derives their physical properties by considering the
497:
and the screening of nuclei from each other by electrons. The
113:
1636:
1622:
560:
reactions stops, becomes a collection of positively charged
1057:
1055:
600:
254:
is the number of particles (typically atoms or molecules),
2136:
1433:
Historical
Studies in the Physical and Biological Sciences
1240:"Evidence for quark-matter cores in massive neutron stars"
608:(primarily supported by neutron degeneracy pressure) or a
1632:
1237:
1066:(2 ed.). Upper Saddle River, NJ: Pearson Education.
561:
1185:
Potekhin, A. Y. (2011). "The
Physics of Neutron Stars".
1178:
1052:
599:
stars, formed by the gradual shrinking of the cores of
1131:
977:
A History of Astronomy : from 1890 to the Present
53:, where thermal pressure alone is not enough to avoid
2089:
1061:
446:{\displaystyle P=K\left({\frac {N}{V}}\right)^{4/3},}
397:
272:
188:
143:. These properties result from a combination of the
1019:
445:
375:
227:
64:Degenerate matter is usually modelled as an ideal
1026:. New York: Holt, Rinehart and Winston. pp.
932:Monthly Notices of the Royal Astronomical Society
2197:
1473:
1006:
1004:
1524:
1340:"Zur Quantelung des idealen einatomigen Gases"
769:, formed by the collapse of objects above the
1588:
1010:
1001:
228:{\displaystyle P=k_{\rm {B}}{\frac {NT}{V}},}
898:
112:. Eddington had suggested that the atoms in
1602:
1064:Modern physics for scientists and engineers
1595:
1581:
45:to refer to dense stellar objects such as
1408:
1273:
1255:
1198:
1145:
951:
910:
160:pressure preventing further compression.
57:. The term also applies to metals in the
1184:
785:uses the word 'degenerate' in two ways:
459:
179:, whose pressure is proportional to its
41:at low temperature. The term is used in
1474:Koester, D; Chanmugam, G (1990-07-01).
1402:
906:http://apod.nasa.gov/apod/ap100228.html
525:Degenerate gases are gases composed of
2198:
1426:
974:
925:
537:
170:
16:Type of dense exotic matter in physics
1576:
1334:
771:TolmanâOppenheimerâVolkoff mass limit
615:
1323:http://www.jstor.org/stable/41133485
1296:
881: â Theoretical model in physics
694:
464:Pressure vs temperature curves of a
711:
520:
13:
1231:
645:acquiring a mass in excess of the
201:
14:
2232:
1561:
887:â High-pressure phase of hydrogen
2183:
2171:
2159:
2147:
2135:
2123:
2111:
2099:
1655:
840:applied the Pauli principle via
702:Heisenberg uncertainty principle
681:TolmanâOppenheimerâVolkoff limit
476:), for a given particle density.
1525:Cohen-Tanoudji, Claude (2011).
1467:
1420:
1396:
1328:
1315:
1290:
1095:Stellar Structure and Evolution
797:described the reduction of the
708:of electron-degenerate matter.
1480:Reports on Progress in Physics
1476:"Physics of white dwarf stars"
1427:Eckert, Michael (1987-01-01).
1217:10.3367/UFNe.0180.201012c.1279
1125:
1107:
1088:
968:
919:
299:
282:
139:system temperature approaches
91:relativistic degenerate matter
1:
2044:Macroscopic quantum phenomena
1518:
2054:Order and disorder (physics)
975:David., Leverington (1995).
926:Fowler, R. H. (1926-12-10).
891:
683:, which is analogous to the
583:electron degeneracy pressure
544:Electron degeneracy pressure
7:
1297:Cain, Fraser (2016-07-25).
979:. London: Springer London.
866:
391:, the pressure is given by
10:
2237:
1528:Advances in Atomic Physics
1492:10.1088/0034-4885/53/7/001
1164:10.1103/PhysRevD.84.084007
857:Subrahmanyan Chandrasekhar
777:
715:
619:
541:
128:
124:
18:
2006:
1960:
1832:
1746:
1720:
1664:
1653:
1615:
1275:10.1038/s41567-020-0914-9
738:in addition to the usual
468:and quantum ideal gases (
145:Pauli exclusion principle
74:Pauli exclusion principle
35:Pauli exclusion principle
2206:Concepts in astrophysics
2079:Thermo-dielectric effect
1978:Enthalpy of vaporization
1672:BoseâEinstein condensate
1325:. Accessed 27 July 2023.
1119:Encyclopaedia Britannica
875:â Degenerate bosonic gas
873:BoseâEinstein condensate
861:model for star stability
787:degenerate energy levels
517:and white dwarf matter.
165:Fermi-Dirac distribution
21:Degenerate energy levels
1973:Enthalpy of sublimation
1299:"What are Quark Stars?"
774:stars and black holes.
612:may be formed instead.
37:significantly alters a
1988:Latent internal energy
1738:Color-glass condensate
1347:Zeitschrift fĂŒr Physik
953:10.1093/mnras/87.2.114
842:Fermi-Dirac statistics
807:quantum thermodynamics
477:
447:
377:
229:
131:Fermi-Dirac statistics
55:gravitational collapse
23:. For other uses, see
1798:Magnetically ordered
1115:"Chandrasekhar limit"
463:
448:
389:relativistic energies
378:
258:is temperature, and
230:
1677:Fermionic condensate
859:became the accepted
748:Color superconductor
395:
270:
186:
1892:Chemical ionization
1784:Programmable matter
1774:Quantum spin liquid
1642:Supercritical fluid
1359:1926ZPhy...36..902F
1266:2020NatPh..16..907A
1209:2010PhyU...53.1235Y
1156:2011PhRvD..84h4007R
1022:Solid state physics
944:1926MNRAS..87..114F
879:Fermi liquid theory
647:Chandrasekhar limit
616:Neutron degeneracy
579:Chandrasekhar limit
538:Electron degeneracy
499:free electron model
466:classical ideal gas
175:Unlike a classical
171:Degeneracy pressure
149:quantum confinement
79:degeneracy pressure
2039:Leidenfrost effect
1968:Enthalpy of fusion
1733:Quarkâgluon plasma
1367:10.1007/BF01400221
1353:(11â12): 902â912.
706:equations of state
592:general relativity
478:
443:
373:
248:Boltzmann constant
225:
2087:
2086:
2069:Superheated vapor
2064:Superconductivity
2034:Equation of state
1882:Flash evaporation
1834:Phase transitions
1819:String-net liquid
1712:Photonic molecule
1682:Degenerate matter
1542:978-981-277-496-5
1193:(12): 1235â1256.
1134:Physical Review D
1073:978-0-13-805715-2
1016:Mermin, N. David.
1012:Neil W., Ashcroft
928:"On Dense Matter"
885:Metallic hydrogen
838:Arnold Sommerfeld
819:Erwin Schrödinger
783:Quantum mechanics
695:Proton degeneracy
515:metallic hydrogen
420:
350:
335:
220:
31:Degenerate matter
2228:
2221:Phases of matter
2211:Degenerate stars
2188:
2187:
2176:
2175:
2174:
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2162:
2152:
2151:
2150:
2140:
2139:
2128:
2127:
2126:
2116:
2115:
2114:
2104:
2103:
2095:
2024:Compressed fluid
1659:
1604:States of matter
1597:
1590:
1583:
1574:
1573:
1557:
1555:
1554:
1545:. Archived from
1533:World Scientific
1512:
1511:
1471:
1465:
1464:
1445:10.2307/27757582
1424:
1418:
1417:
1412:
1410:cond-mat/9912229
1400:
1394:
1393:
1391:
1385:. Archived from
1344:
1332:
1326:
1319:
1313:
1312:
1310:
1309:
1294:
1288:
1287:
1277:
1259:
1235:
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1175:
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1123:
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1111:
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1085:
1059:
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1049:
1025:
1008:
999:
998:
972:
966:
965:
955:
923:
917:
914:
908:
902:
834:Llewellyn Thomas
712:Quark degeneracy
662:electron capture
571:kinetic energies
521:Degenerate gases
452:
450:
449:
444:
439:
438:
434:
425:
421:
413:
382:
380:
379:
374:
369:
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343:
336:
334:
326:
325:
324:
315:
314:
310:
297:
296:
280:
234:
232:
231:
226:
221:
216:
208:
206:
205:
204:
102:Arthur Eddington
98:degenerate stars
87:rest mass energy
33:occurs when the
2236:
2235:
2231:
2230:
2229:
2227:
2226:
2225:
2196:
2195:
2194:
2182:
2172:
2170:
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2158:
2148:
2146:
2134:
2124:
2122:
2112:
2110:
2098:
2090:
2088:
2083:
2014:Baryonic matter
2002:
1956:
1927:Saturated fluid
1867:Crystallization
1828:
1802:Antiferromagnet
1742:
1716:
1660:
1651:
1611:
1601:
1564:
1552:
1550:
1543:
1535:. p. 791.
1521:
1516:
1515:
1472:
1468:
1425:
1421:
1401:
1397:
1389:
1342:
1333:
1329:
1320:
1316:
1307:
1305:
1295:
1291:
1236:
1232:
1187:Physics-Uspekhi
1183:
1179:
1130:
1126:
1113:
1112:
1108:
1093:
1089:
1074:
1060:
1053:
1038:
1009:
1002:
987:
973:
969:
924:
920:
915:
911:
903:
899:
894:
869:
853:Ralph H. Fowler
832:and separately
811:Albert Einstein
780:
756:superconductors
724:
716:Main articles:
714:
697:
655:
636:
624:
618:
581:, beyond which
550:
542:Main articles:
540:
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96:The concept of
61:approximation.
39:state of matter
28:
17:
12:
11:
5:
2234:
2224:
2223:
2218:
2213:
2208:
2193:
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2016:
2010:
2008:
2004:
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2001:
2000:
1995:
1993:Trouton's rule
1990:
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1862:Critical point
1859:
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1844:
1838:
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1764:Liquid crystal
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1697:Strange matter
1694:
1692:Rydberg matter
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1679:
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1563:
1562:External links
1560:
1559:
1558:
1541:
1520:
1517:
1514:
1513:
1486:(7): 837â915.
1466:
1439:(2): 191â233.
1419:
1395:
1392:on 2019-04-06.
1338:(1926-11-01).
1327:
1314:
1303:Universe Today
1289:
1250:(9): 907â910.
1244:Nature Physics
1230:
1177:
1124:
1106:
1087:
1072:
1051:
1036:
1000:
985:
967:
938:(2): 114â122.
918:
909:
896:
895:
893:
890:
889:
888:
882:
876:
868:
865:
828:Early in 1927
795:Walther Nernst
779:
776:
762:interactions.
754:in electrical
752:Cooper pairing
736:strange quarks
732:Strange matter
713:
710:
696:
693:
660:, also termed
653:
634:
620:Main article:
617:
614:
558:nuclear fusion
539:
536:
522:
519:
511:strange matter
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129:Main article:
126:
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70:quantum states
15:
9:
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2216:Exotic matter
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2049:Mpemba effect
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2029:Cooling curve
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2015:
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1952:Vitrification
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1918:
1917:Recombination
1915:
1913:
1912:Melting point
1910:
1908:
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1857:Critical line
1855:
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1847:Boiling point
1845:
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1779:Exotic matter
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1549:on 2012-05-11
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1349:(in German).
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1148:
1143:
1140:(8): 084007.
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1120:
1116:
1110:
1104:
1103:0-387-58013-1
1100:
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864:
862:
858:
854:
851:Also in 1927
849:
847:
843:
839:
835:
831:
826:
824:
823:absolute zero
820:
816:
812:
808:
804:
800:
799:specific heat
796:
791:
788:
784:
775:
772:
768:
763:
761:
757:
753:
749:
745:
741:
737:
733:
729:
723:
719:
709:
707:
703:
692:
690:
686:
685:Chandrasekhar
682:
678:
673:
670:
665:
663:
659:
652:
649:of 1.44
648:
644:
640:
633:
629:
628:neutron stars
623:
613:
611:
607:
602:
598:
593:
588:
584:
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563:
559:
554:
549:
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531:
528:
518:
516:
512:
507:
504:
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495:atomic nuclei
490:
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458:
456:
440:
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431:
427:
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417:
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344:
339:
331:
328:
321:
317:
311:
307:
303:
293:
289:
285:
276:
273:
265:
264:absolute zero
261:
257:
253:
249:
242:
239:is pressure,
238:
222:
217:
213:
210:
196:
192:
189:
182:
178:
168:
166:
161:
158:
152:
150:
146:
142:
141:absolute zero
138:
132:
122:
120:
119:compact stars
115:
111:
107:
103:
99:
94:
92:
88:
83:
80:
75:
71:
67:
62:
60:
56:
52:
51:neutron stars
48:
44:
40:
36:
32:
26:
22:
2178:Solar System
2074:Superheating
1947:Vaporization
1942:Triple point
1937:Supercooling
1902:Lambda point
1852:Condensation
1769:Time crystal
1747:Other states
1687:Quantum Hall
1681:
1551:. Retrieved
1547:the original
1527:
1483:
1479:
1469:
1436:
1432:
1422:
1414:
1398:
1387:the original
1350:
1346:
1330:
1317:
1306:. Retrieved
1302:
1292:
1247:
1243:
1233:
1190:
1186:
1180:
1137:
1133:
1127:
1118:
1109:
1094:
1090:
1063:
1021:
976:
970:
935:
931:
921:
912:
900:
850:
830:Enrico Fermi
827:
792:
781:
764:
760:strong force
728:quark matter
725:
722:Strange star
698:
677:neutron star
674:
666:
650:
643:white dwarfs
639:solar masses
631:
625:
622:Neutron star
606:neutron star
587:solar masses
576:
566:White dwarfs
555:
551:
532:
524:
508:
491:
487:helium flash
483:
479:
454:
384:
259:
255:
251:
240:
236:
174:
162:
153:
134:
110:Arthur Milne
106:Ralph Fowler
97:
95:
90:
89:) is called
84:
78:
63:
47:white dwarfs
43:astrophysics
30:
29:
2166:Outer space
2154:Spaceflight
1983:Latent heat
1932:Sublimation
1877:Evaporation
1812:Ferromagnet
1807:Ferrimagnet
1789:Dark matter
1721:High energy
790:mechanics.
767:quark stars
689:white dwarf
597:white dwarf
548:White dwarf
181:temperature
2200:Categories
1998:Volatility
1961:Quantities
1922:Regelation
1897:Ionization
1872:Deposition
1824:Superglass
1794:Antimatter
1728:QCD matter
1707:Supersolid
1702:Superfluid
1665:Low energy
1553:2012-01-31
1519:References
1308:2021-01-15
1257:1903.09121
1082:1319408575
1037:0030839939
986:1447121244
815:Max Planck
718:Quark star
687:limit for
669:wavelength
658:beta decay
610:black hole
503:conduction
25:Degeneracy
2130:Astronomy
2118:Chemistry
1508:250915046
1500:0034-4885
1453:0890-9997
1383:123334672
1375:0044-3328
1336:Fermi, E.
1284:1745-2481
1225:119231427
1200:1102.5735
1172:119120610
1147:1012.0154
995:840277483
962:0035-8711
892:Citations
846:Fermi gas
817:, and by
641:), or by
470:Fermi gas
318:ℏ
290:π
177:ideal gas
157:Fermi gas
66:Fermi gas
59:Fermi gas
2059:Spinodal
2007:Concepts
1887:Freezing
1461:27757582
1018:(1976).
867:See also
793:In 1914
746:quarks.
527:fermions
474:Bose gas
114:Sirius B
2190:Science
2106:Physics
2092:Portals
2019:Binodal
1907:Melting
1842:Boiling
1759:Crystal
1754:Colloid
1355:Bibcode
1262:Bibcode
1205:Bibcode
1152:Bibcode
940:Bibcode
778:History
691:stars.
246:is the
137:fermion
125:Concept
1647:Plasma
1628:Liquid
1539:
1506:
1498:
1459:
1451:
1381:
1373:
1282:
1223:
1170:
1101:
1080:
1070:
1046:934604
1044:
1034:
993:
983:
960:
679:, the
453:where
383:where
235:where
72:. The
2142:Stars
1637:Vapor
1623:Solid
1616:State
1504:S2CID
1457:JSTOR
1405:arXiv
1390:(PDF)
1379:S2CID
1343:(PDF)
1252:arXiv
1221:S2CID
1195:arXiv
1168:S2CID
1142:arXiv
813:, by
803:gases
601:stars
1608:list
1537:ISBN
1496:ISSN
1449:ISSN
1371:ISSN
1280:ISSN
1099:ISBN
1078:OCLC
1068:ISBN
1042:OCLC
1032:ISBN
991:OCLC
981:ISBN
958:ISSN
904:see
744:down
742:and
720:and
562:ions
546:and
147:and
108:and
49:and
1633:Gas
1488:doi
1441:doi
1363:doi
1270:doi
1213:doi
1160:doi
948:doi
809:by
801:of
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1494:.
1484:53
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1478:.
1455:.
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1431:.
1413:.
1377:.
1369:.
1361:.
1351:36
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1301:.
1278:.
1268:.
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1248:16
1246:.
1242:.
1219:.
1211:.
1203:.
1191:53
1189:.
1166:.
1158:.
1150:.
1138:84
1136:.
1117:.
1076:.
1054:^
1040:.
1030:.
1028:39
1014:;
1003:^
989:.
956:.
946:.
936:87
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930:.
863:.
825:.
740:up
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1227:.
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1144::
1121:.
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654:â
651:M
637:(
635:â
632:M
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399:P
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358:5
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252:N
244:B
241:k
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218:V
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190:P
27:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.