768:—usually described as pairs of electrons—that move through the crystal lattice without resistance. A broken Cooper pair is called a Bogoliubov quasiparticle. It differs from the conventional quasiparticle in metal because it combines the properties of a negatively charged electron and a positively charged hole (an electron void). Physical objects like impurity atoms, from which quasiparticles scatter in an ordinary metal, only weakly affect the energy of a Cooper pair in a conventional superconductor. In conventional superconductors, interference between Bogoliubov quasiparticles is difficult for an STM to detect. Because of their complex global electronic structures, however, high-Tc cuprate superconductors are another matter. Thus Davis and his colleagues were able to resolve distinctive patterns of quasiparticle interference in Bi-2212.
256:(PDE) on a 3×10-dimensional vector space—one dimension for each coordinate (x, y, z) of each particle. Directly and straightforwardly trying to solve such a PDE is impossible in practice. Solving a PDE on a 2-dimensional space is typically much harder than solving a PDE on a 1-dimensional space (whether analytically or numerically); solving a PDE on a 3-dimensional space is significantly harder still; and thus solving a PDE on a 3×10-dimensional space is quite impossible by straightforward methods.
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1022:. "As we have seen, the quasiparticle consists of the original real, individual particle, plus a cloud of disturbed neighbors. It behaves very much like an individual particle, except that it has an effective mass and a lifetime. But there also exist other kinds of fictitious particles in many-body systems, i.e. 'collective excitations'. These do not center around individual particles, but instead involve collective, wavelike motion of
225:
3537:
3513:
882:) is a quasiparticle made of two particles coupled by hydrodynamic forces. These classical quasiparticles were observed as the elementary excitations in a 2D colloidal crystal driven by viscous flow. The pairs are stabilized because the forces the particles exert on each other are of the same magnitude and
381:
that involves the precession of many spins. In the first case, the magnon is envisioned as a quasiparticle, in the second case, as a collective excitation. However, both (a) and (b) are equivalent and correct descriptions. As this example shows, the intuitive distinction between a quasiparticle and a
837:
can be used to describe the rotation of molecules in solvents. First postulated theoretically in 2015, the existence of the angulon was confirmed in
February 2017, after a series of experiments spanning 20 years. Heavy and light species of molecules were found to rotate inside
497:
This section contains examples of quasiparticles and collective excitations. The first subsection below contains common ones that occur in a wide variety of materials under ordinary conditions; the second subsection contains examples that arise only in special contexts.
385:
The problems arising from the collective nature of quasiparticles have also been discussed within the philosophy of science, notably in relation to the identity conditions of quasiparticles and whether they should be considered "real" by the standards of, for example,
297:
When the material is characterized as having "several elementary excitations", this statement presupposes that the different excitations can be combined. In other words, it presupposes that the excitations can coexist simultaneously and independently. This is never
789:
and carry an effective magnetic charge as well as being endowed with other typical quasiparticle properties such as an effective mass. They may be formed through spin flips in frustrated pyrochlore ferromagnets and interact through a
Coulomb
321:
Therefore, using quasiparticles / collective excitations, instead of analyzing 10 particles, one needs to deal with only a handful of somewhat-independent elementary excitations. It is, therefore, an effective approach to simplify the
193:
that occurs inside the solid. Therefore, while it is quite possible to have a single particle (electron, proton, or neutron) floating in space, a quasiparticle can only exist inside interacting many-particle systems such as solids.
361:
which differs from its real mass. On the other hand, a collective excitation is usually imagined to be a reflection of the aggregate behavior of the system, with no single real particle at its "core". A standard example is the
357:: it is built around a real particle at its "core", but the behavior of the particle is affected by the environment. A standard example is the "electron quasiparticle": an electron in a crystal behaves as if it had an
1696:
Li, Mingda; Tsurimaki, Yoichiro; Meng, Qingping; Andrejevic, Nina; Zhu, Yimei; Mahan, Gerald D.; Chen, Gang (2018). "Theory of electron–phonon–dislon interacting system—toward a quantized theory of dislocations".
201:) by all the other electrons and protons in the solid (which may themselves be in motion). It is these strong interactions that make it very difficult to predict and understand the behavior of solids (see
886:(in contrast to momentum-conserving forces which are opposite by Newton's 3rd law). The resulting pairs ("duons") are zero-frequency excitations that emerge at the Dirac cones of the crystal's spectrum.
267:
with higher and higher energy above the ground state. In many contexts, only the "low-lying" excited states, with energy reasonably close to the ground state, are relevant. This occurs because of the
290:
is added to the crystal (in other words, if the crystal is made to vibrate slightly at a particular frequency) then the crystal is now in a low-lying excited state. The single phonon is called an
244:
describe every particle in a macroscopic system. For example, a barely-visible (0.1mm) grain of sand contains around 10 nuclei and 10 electrons. Each of these attracts or repels every other by
209:
classical particle is relatively simple; it would move in a straight line at constant velocity. This is the motivation for the concept of quasiparticles: The complicated motion of the
377:
can be considered in one of two perfectly equivalent ways: (a) as a mobile defect (a misdirected spin) in a perfect alignment of magnetic moments or (b) as a quantum of a collective
294:. More generally, low-lying excited states may contain any number of elementary excitations (for example, many phonons, along with other quasiparticles and collective excitations).
473:
between the charged particles are neglected. When a kinetic equation of the mean-field type is a valid first-order description of a system, second-order corrections determine the
302:
true. For example, a solid with two identical phonons does not have exactly twice the excitation energy of a solid with just one phonon, because the crystal vibration is slightly
1876:
1229:
1215:
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469:. In the plasma approximation, charged particles are considered to be moving in the electromagnetic field collectively generated by all other particles, and hard
353:
There is a difference in the way that quasiparticles and collective excitations are intuitively envisioned. A quasiparticle is usually thought of as being like a
213:
particles in a solid can be mathematically transformed into the much simpler motion of imagined quasiparticles, which behave more like non-interacting particles.
40:
is a concept used to describe a collective behavior of a group of particles that can be treated as if they were a single particle. Formally, quasiparticles and
466:
398:
By investigating the properties of individual quasiparticles, it is possible to obtain a great deal of information about low-energy systems, including the
1298:
Hoffman, J. E.; McElroy, K.; Lee, D. H.; Lang, K. M.; Eisaki, H.; Uchida, S.; Davis, J. C.; et al. (2002). "Imaging
Quasiparticle Interference in Bi
748:
314:, they are treated as free, independent entities, and then corrections are included via interactions between the elementary excitations, such as "phonon-
545:. In many other respects, especially in metals under ordinary conditions, these so-called Landau quasiparticles closely resemble familiar electrons; as
623:
as affected by its interactions with the material. In particular, the photon quasiparticle has a modified relation between wavelength and energy (
2874:
1375:
Banerjee, A.; Bridges, C. A.; Yan, J.-Q.; et al. (4 April 2016). "Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet".
2980:
334:, the elementary excitations are so far from being independent that it is not even useful as a starting point to treat them as independent.
777:
is a particle which equals its own antiparticle, and can emerge as a quasiparticle in certain superconductors, or in a quantum spin liquid.
128:, although the precise distinction is not universally agreed upon. Thus, electrons and electron holes (fermions) are typically called
3517:
2624:
570:
is a quasiparticle consisting of the lack of an electron in a state; it is most commonly used in the context of empty states in the
2973:
2862:
820:
1493:
Schmidt, Richard; Lemeshko, Mikhail (18 May 2015). "Rotation of
Quantum Impurities in the Presence of a Many-Body Environment".
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17:
538:
358:
72:
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is a collective excitation associated with the electrons' spin structure in a crystal lattice. It is a quantum of a
2841:
87:
or a hole band in a metal behave as though the material instead contained positively charged quasiparticles called
719:
arise in a two-dimensional system subject to a large magnetic field, most famously those systems that exhibit the
558:
1554:
Lemeshko, Mikhail (27 February 2017). "Quasiparticle
Approach to Molecules Interacting with Quantum Solvents".
723:. These quasiparticles are quite unlike normal particles in two ways. First, their charge can be less than the
720:
1438:
Shaginyan, V. R.; et al. (2012). "Identification of
Strongly Correlated Spin Liquid in Herbertsmithite".
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253:
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331:
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Quasiparticles and collective excitations are a type of low-lying excited state. For example, a crystal at
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3186:
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as affected by the other forces and interactions in the solid. The electron quasiparticle has the same
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3150:
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2345:
756:
542:
140:
33:
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2901:
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1897:
450:
744:. An anyon has a simple kind of memory which is being investigated for use in quantum computing.
249:
2836:
2173:
1133:
1097:
Ohtsu, Motoichi; Kobayashi, Kiyoshi; Kawazoe, Tadashi; Yatsui, Takashi; Naruse, Makoto (2008).
901:
812:
730:. In fact, they have been observed with charges of e/3, e/4, e/5, and e/7. Second, they can be
507:
268:
1098:
987:
980:
216:
In summary, quasiparticles are a mathematical tool for simplifying the description of solids.
197:
Motion in a solid is extremely complicated: Each electron and proton is pushed and pulled (by
3293:
3272:
3206:
2923:
1015:
952:
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is a quantized field associated with the quantization of the lattice displacement field of a
537:. However, its mass can differ substantially from that of a normal electron; see the article
430:
252:
predicts exactly how this system will behave. But the Schrödinger equation in this case is a
67:, its motion is disturbed in a complex way by its interactions with other electrons and with
44:
are closely related phenomena that arise when a microscopically complicated system such as a
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1716:
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272:
8:
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3181:
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1921:
869:
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189:
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1400:
1337:
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1151:
856:
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478:
474:
441:. For these systems a strong similarity exists between the notion of quasiparticle and
106:
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1982:
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One simplifying factor is that the system as a whole, like any quantum system, has a
202:
148:
144:
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1155:
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3333:
3313:
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3303:
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3155:
3135:
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2335:
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2002:
1913:
1781:
1724:
1668:
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1643:
1615:
1601:
1585:
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1524:
1520:
1471:
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1404:
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1341:
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482:
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245:
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is a coupled optical phonon and dressed photon consisting of a plasmon and photon.
658:(wherein all the electrons simultaneously oscillate with respect to all the ions).
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3004:
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2821:
2805:
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2155:
2080:
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1972:
921:
828:
522:
458:
1842:(1963, 1975). Prentice-Hall, New Jersey; Dover Publications, New York, New York.
1147:
337:
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2826:
2562:
2350:
2123:
2045:
2040:
1962:
1835:
1785:
1728:
911:
847:
550:
526:
485:. In other words, every type of mean-field kinetic equation, and in fact every
387:
240:
The principal motivation for quasiparticles is that it is almost impossible to
68:
421:, etc. Each of these is a separate contribution to the overall heat capacity.
3557:
3401:
3368:
3348:
3252:
3221:
3052:
2913:
2765:
2524:
2494:
2426:
2285:
2065:
1992:
1977:
1793:
1440:
1172:(The Frontiers Collection), Berlin, Germany: Springer 2007, esp. pp. 243–246.
872:. It is a quantum of vibration and static strain field of a dislocation line.
587:
is a collective excitation associated with the vibration of atoms in a rigid
575:
566:
403:
399:
279:
264:
233:
89:
84:
64:
1345:
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is a collective excitation associated with the rotation of a fluid (often a
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2441:
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2133:
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1997:
1952:
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1532:
1416:
1353:
1065:
Stalin's great science : the times and adventures of Soviet physicists
765:
571:
434:
366:, which characterizes the vibrational motion of every atom in the crystal.
283:
260:
229:
99:, a quasiparticle derived from the vibrations of atoms in a solid, and the
80:
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2414:
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2105:
1967:
1328:
1063:
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is a quasiparticle which comes about when an electron interacts with the
374:
342:
Usually, an elementary excitation is called a "quasiparticle" if it is a
492:
3373:
3211:
3047:
2648:
2542:
2532:
2514:
2404:
2305:
2240:
1957:
1882:
1817:
704:
596:
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However, these two visualizations leave some ambiguity. For example, a
303:
152:
1280:
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3257:
3042:
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2643:
2609:
2602:
2479:
2469:
2464:
2436:
2204:
1987:
1408:
1037:"Ultracold atoms permit direct observation of quasiparticle dynamics"
633:
609:
470:
378:
481:-type collision term, in which figure only "far collisions" between
409:
In the heat capacity example, a crystal can store energy by forming
382:
collective excitation is not particularly important or fundamental.
2886:
2714:
2669:
2653:
2614:
2587:
2300:
2295:
2275:
2245:
2235:
2230:
2050:
2025:
2020:
1947:
1768:
1752:"Quasiparticles, flat bands and the melting of hydrodynamic matter"
1711:
1568:
1507:
1391:
824:
794:
786:
518:
438:
350:. However, the precise distinction is not universally agreed upon.
176:
151:. The theory of quasiparticles was started by the Soviet physicist
60:
49:
1454:
1266:
1201:
306:. However, in many materials, the elementary excitations are very
187:. None of these are quasiparticles; instead a quasiparticle is an
3481:
3448:
3426:
3406:
2795:
2785:
2755:
2709:
2704:
2679:
2597:
2582:
2509:
2504:
2409:
2394:
2340:
2315:
2280:
2209:
2191:
1930:
811:
is represented by quasiparticle produced as a result of electron
800:
737:
676:
663:
650:
592:
534:
418:
414:
343:
184:
117:
101:
1639:"Discovery of Lorentz-violating type II Weyl fermions in LaAlGe"
224:
75:
travelling unperturbed in vacuum. Such an electron is called an
3416:
3411:
3017:
2775:
2770:
2399:
2386:
2377:
2199:
2113:
2012:
1637:
Xu, S. Y.; Alidoust, N.; Chang, G.; et al. (2 June 2017).
864:
807:
708:
637:, especially near a resonance of the material. For example, an
620:
604:
583:
410:
370:
363:
287:
180:
95:
79:. In another example, the aggregate motion of electrons in the
53:
3391:
3012:
2800:
2740:
2592:
2451:
2330:
2270:
2225:
2118:
2096:
1939:
1750:
Saeed, Imran; Pak, Hyuk Kyu; Tlusty, Tsvi (26 January 2023).
1124:
Gelfert, Axel (2003). "Manipulative success and the unreal".
741:
731:
699:
347:
338:
Distinction between quasiparticles and collective excitations
168:
125:
93:. Other quasiparticles or collective excitations include the
45:
2567:
2499:
2459:
2035:
2030:
1096:
132:, while phonons and plasmons (bosons) are typically called
219:
3022:
1695:
48:
behaves as if it contained different weakly interacting
1879:
by Jacqui Hayes, Cosmos 6 June 2008. Accessed June 2008
1840:
Methods of
Quantum Field Theory in Statistical Physics
986:(1st ed.). Holt, Rinehart, and Winston. pp.
541:. Its electric field is also modified, as a result of
326:
in quantum mechanics. This approach is not useful for
1297:
1251:. New York, New York: Penguin Press. pp. 89–90.
493:
Examples of quasiparticles and collective excitations
1018:
A guide to
Feynman diagrams in the many-body problem
842:
droplets, in good agreement with the angulon theory.
654:
is a collective excitation, which is the quantum of
437:, which was originally invented for studying liquid
71:. The electron behaves as though it has a different
1374:
1126:International Studies in the Philosophy of Science
979:
449:. The dynamics of Landau's theory is defined by a
1186:. New York, New York: Penguin Press. p. 88.
641:is a superposition of an exciton and a photon; a
3555:
971:
578:. A hole has the opposite charge of an electron.
533:) electron, and like a normal electron, it is a
275:are unlikely to occur at any given temperature.
1636:
1616:"Existence of a new quasiparticle demonstrated"
1492:
736:, an exotic type of particle that is neither a
232:along with an infinite series of higher-energy
1749:
977:
957:. Cambridge University Press. pp. 65–69.
2981:
1898:
228:Any system, no matter how complicated, has a
2995:
1026:the particles in the system simultaneously."
691:
645:is a superposition of a phonon and a photon.
393:
1068:. London, England: Imperial College Press.
1061:
859:, which cannot be broken by real particles.
3071:
2988:
2974:
1905:
1891:
1877:Curious 'quasiparticles' baffle physicists
1860:(1998). Westview Press, Boulder, Colorado.
1853:(1999). Westview Press, Boulder, Colorado.
785:arise in condensed matter systems such as
139:The quasiparticle concept is important in
1767:
1710:
1672:
1567:
1506:
1453:
1437:
1390:
1327:
1287:. Lawrence Livermore National Laboratory.
1137:
1011:
1009:
1007:
954:Atomic and Electronic Structure of Solids
946:
944:
942:
940:
938:
936:
429:The idea of quasiparticles originated in
346:and a "collective excitation" if it is a
1912:
1553:
1184:Fundalmentals : Ten Keys to Reality
223:
1249:Fundamentals : Ten Keys to Reality
1181:
1123:
950:
821:strongly correlated quantum spin liquid
680:is an electron and hole bound together.
501:
220:Relation to many-body quantum mechanics
163:
14:
3556:
2376:
1873:– Scientists find new 'quasiparticles'
1246:
1004:
933:
310:to being independent. Therefore, as a
271:, which implies that very-high-energy
205:). On the other hand, the motion of a
2969:
1886:
951:Kaxiras, Efthimios (9 January 2003).
112:These phenomena are typically called
3512:
489:, involves a quasiparticle concept.
3536:
477:, and generally take the form of a
27:Concept in condensed matter physics
24:
1811:
627:), as described by the material's
330:systems, however. For example, in
25:
3595:
1864:
1849:(1966). W.A. Benjamin, New York.
3535:
3523:
3511:
3500:
3499:
2949:
2842:Timeline of particle discoveries
171:are made of only three kinds of
1743:
1689:
1630:
1608:
1547:
1486:
1431:
1368:
1291:
1273:
1240:
1222:
1208:
1851:Volume I: Normal Fermi Liquids
1586:10.1103/PhysRevLett.118.095301
1525:10.1103/PhysRevLett.114.203001
1175:
1162:
1117:
1090:
1055:
1029:
721:fractional quantum Hall effect
13:
1:
3098:Spontaneous symmetry breaking
1858:Quantum Many-Particle Systems
1856:J. W. Negele, and H. Orland,
1847:The Theory of Quantum Liquids
1285:Science and Technology Review
927:
332:strongly correlated materials
254:partial differential equation
2858:History of subatomic physics
857:special theory of relativity
143:because it can simplify the
7:
1845:D. Pines, and P. Nozières,
1838:, and I. E. Dzyaloshinski,
1232:. June 2008. Archived from
1148:10.1080/0269859032000169451
1100:Principles of Nanophotonics
1062:Kozhevnikov, A. B. (2004).
890:
158:
10:
3600:
3278:Spin gapless semiconductor
3187:Nearly free electron model
1786:10.1038/s41567-022-01893-5
1472:10.1209/0295-5075/97/56001
1103:. CRC Press. p. 205.
631:. It may also be termed a
505:
457:. A similar equation, the
424:
105:, a particle derived from
3495:
3457:
3382:
3326:
3286:
3235:
3227:Density functional theory
3202:electronic band structure
3169:
3118:
3111:
3080:
3069:
3003:
2947:
2850:
2814:
2731:
2692:
2662:
2636:
2632:
2623:
2555:
2523:
2450:
2385:
2367:
2263:
2218:
2190:
2181:
2172:
2154:
2132:
2104:
2095:
2011:
1938:
1929:
1920:
978:Ashcroft; Mermin (1976).
757:Bogoliubov quasiparticles
692:More specialized examples
394:Effect on bulk properties
3569:Condensed matter physics
3397:Bogoliubov quasiparticle
3141:Quantum spin Hall effect
3033:Bose–Einstein condensate
2997:Condensed matter physics
2875:mathematical formulation
2470:Eta and eta prime mesons
1729:10.1088/1367-2630/aaa383
855:, the foundation of the
707:). It is a quantum of a
671:of its surrounding ions.
543:electric field screening
141:condensed matter physics
34:condensed matter physics
2537:Double-charm tetraquark
1556:Physical Review Letters
1495:Physical Review Letters
1346:10.1126/science.1072640
1216:"Physics Today Article"
1182:Wilczek, Frank (2021).
752:in ferromagnetic metals
124:if they are related to
116:if they are related to
1699:New Journal of Physics
1665:10.1126/sciadv.1603266
1247:Wilcek, Frank (2021).
902:List of quasiparticles
813:spin-charge separation
515:electron quasiparticle
508:List of quasiparticles
269:Boltzmann distribution
237:
134:collective excitations
122:collective excitations
77:electron quasiparticle
42:collective excitations
3273:Topological insulator
3207:Anderson localization
2934:Wave–particle duality
2924:Relativistic particle
2061:Electron antineutrino
1281:"Josephson Junctions"
292:elementary excitation
227:
18:Collective excitation
3151:Aharonov–Bohm effect
3038:Fermionic condensate
2164:Faddeev–Popov ghosts
1914:Particles in physics
1170:Particle Metaphysics
1016:Richard D. Mattuck,
815:, and can form both
760:in superconductors.
502:More common examples
467:plasma approximation
447:quantum field theory
273:thermal fluctuations
250:Schrödinger equation
248:. In principle, the
164:General introduction
3542:Physics WikiProject
3217:tight binding model
3197:Fermi liquid theory
3182:Free electron model
3131:Quantum Hall effect
3112:Electrons in solids
2939:Particle chauvinism
2882:Subatomic particles
1778:2023NatPh..19..536S
1721:2018NJPh...20b3010L
1657:2017SciA....3E3266X
1578:2017PhRvL.118i5301L
1517:2015PhRvL.114t3001S
1464:2012EL.....9756001S
1401:2016NatMa..15..733B
1338:2002Sci...297.1148H
1322:(5584): 1148–1151.
982:Solid State Physics
870:crystal dislocation
817:quantum spin liquid
656:plasma oscillations
629:index of refraction
625:dispersion relation
619:quasiparticle is a
531:elementary particle
190:emergent phenomenon
59:For example, as an
3584:Mesoscopic physics
3564:Physical phenomena
3103:Critical phenomena
1829:Soviet Phys. JETP.
1822:Soviet Phys. JETP.
782:Magnetic monopoles
749:Stoner excitations
716:Composite fermions
475:entropy production
238:
107:plasma oscillation
63:travels through a
3551:
3550:
3437:Exciton-polariton
3322:
3321:
3294:Thermoelectricity
2963:
2962:
2919:Massless particle
2727:
2726:
2723:
2722:
2688:
2687:
2551:
2550:
2363:
2362:
2359:
2358:
2311:Magnetic monopole
2259:
2258:
2150:
2149:
2091:
2090:
2071:Muon antineutrino
2056:Electron neutrino
1834:A. A. Abrikosov,
1230:"Cosmos magazine"
964:978-0-521-52339-4
917:Composite fermion
907:Mean-field theory
897:Fractionalization
876:Hydrodynamic pair
840:superfluid helium
762:Superconductivity
639:exciton-polariton
589:crystal structure
487:mean-field theory
483:virtual particles
465:in the so-called
461:, is valid for a
443:dressed particles
417:, and/or forming
413:, and/or forming
324:many-body problem
316:phonon scattering
203:many-body problem
149:quantum mechanics
145:many-body problem
16:(Redirected from
3591:
3539:
3538:
3527:
3515:
3514:
3503:
3502:
3442:Phonon polariton
3334:Amorphous magnet
3314:Electrostriction
3309:Flexoelectricity
3304:Ferroelectricity
3299:Piezoelectricity
3156:Josephson effect
3136:Spin Hall effect
3116:
3115:
3093:Phase transition
3075:
3058:Luttinger liquid
3005:States of matter
2990:
2983:
2976:
2967:
2966:
2953:
2929:Virtual particle
2700:Mesonic molecule
2634:
2633:
2630:
2629:
2475:Bottom eta meson
2383:
2382:
2374:
2373:
2346:W′ and Z′ bosons
2336:Sterile neutrino
2321:Majorana fermion
2188:
2187:
2179:
2178:
2102:
2101:
2081:Tau antineutrino
1936:
1935:
1927:
1926:
1907:
1900:
1893:
1884:
1883:
1806:
1805:
1771:
1747:
1741:
1740:
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1693:
1687:
1686:
1676:
1644:Science Advances
1634:
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1606:
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1571:
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1544:
1510:
1490:
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1435:
1429:
1428:
1409:10.1038/nmat4604
1394:
1378:Nature Materials
1372:
1366:
1365:
1331:
1329:cond-mat/0209276
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1002:
1001:
985:
975:
969:
968:
948:
853:Lorentz symmetry
774:Majorana fermion
643:phonon-polariton
615:In materials, a
561:upon scattering.
557:can image their
451:kinetic equation
355:dressed particle
21:
3599:
3598:
3594:
3593:
3592:
3590:
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3588:
3554:
3553:
3552:
3547:
3491:
3472:Granular matter
3467:Amorphous solid
3453:
3378:
3364:Antiferromagnet
3354:Superparamagnet
3327:Magnetic phases
3318:
3282:
3231:
3192:Bloch's theorem
3165:
3107:
3088:Order parameter
3081:Phase phenomena
3076:
3067:
2999:
2994:
2964:
2959:
2943:
2897:Nuclear physics
2846:
2810:
2746:Davydov soliton
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2255:
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2168:
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2128:
2087:
2007:
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1911:
1867:
1814:
1812:Further reading
1809:
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1651:(6): e1603266.
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1301:
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1279:
1278:
1274:
1259:
1245:
1241:
1236:on 9 June 2008.
1228:
1227:
1223:
1214:
1213:
1209:
1194:
1180:
1176:
1168:B. Falkenburg,
1167:
1163:
1139:10.1.1.405.2111
1122:
1118:
1111:
1095:
1091:
1076:
1060:
1056:
1046:
1044:
1043:. 18 March 2021
1035:
1034:
1030:
1014:
1005:
998:
976:
972:
965:
949:
934:
930:
922:Composite boson
893:
829:Herbertsmithite
725:electron charge
694:
529:as a "normal" (
510:
504:
495:
459:Vlasov equation
455:mean-field type
427:
400:flow properties
396:
340:
222:
207:non-interacting
166:
161:
28:
23:
22:
15:
12:
11:
5:
3597:
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3579:Quasiparticles
3576:
3574:Quantum phases
3571:
3566:
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3545:
3533:
3530:Physics Portal
3521:
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3477:Liquid crystal
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3404:
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3380:
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3366:
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3346:
3344:Superdiamagnet
3341:
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3306:
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3268:Superconductor
3265:
3260:
3255:
3250:
3248:Mott insulator
3245:
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2956:Physics portal
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2899:
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2884:
2879:
2878:
2877:
2870:Standard Model
2867:
2866:
2865:
2854:
2852:
2848:
2847:
2845:
2844:
2839:
2837:Quasiparticles
2834:
2829:
2824:
2818:
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2812:
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2809:
2808:
2803:
2798:
2793:
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2778:
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2737:
2735:
2733:Quasiparticles
2729:
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2725:
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2720:
2718:
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2696:
2694:
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2559:
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2548:
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2540:
2529:
2527:
2525:Exotic hadrons
2521:
2520:
2518:
2517:
2512:
2507:
2502:
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2492:
2487:
2482:
2477:
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2389:
2380:
2371:
2365:
2364:
2361:
2360:
2357:
2356:
2354:
2353:
2351:X and Y bosons
2348:
2343:
2338:
2333:
2328:
2323:
2318:
2313:
2308:
2303:
2298:
2293:
2288:
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2196:
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2185:
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2169:
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2151:
2148:
2147:
2145:
2144:
2138:
2136:
2130:
2129:
2127:
2126:
2124:W and Z bosons
2121:
2116:
2110:
2108:
2099:
2093:
2092:
2089:
2088:
2086:
2085:
2084:
2083:
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2073:
2068:
2063:
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2033:
2028:
2023:
2017:
2015:
2009:
2008:
2006:
2005:
2000:
1995:
1990:
1985:
1980:
1978:Strange (quark
1975:
1970:
1965:
1960:
1955:
1950:
1944:
1942:
1933:
1924:
1918:
1917:
1910:
1909:
1902:
1895:
1887:
1881:
1880:
1874:
1866:
1865:External links
1863:
1862:
1861:
1854:
1843:
1832:
1827:L. D. Landau,
1825:
1813:
1810:
1808:
1807:
1762:(4): 536–544.
1756:Nature Physics
1742:
1688:
1629:
1607:
1546:
1501:(20): 203001.
1485:
1430:
1385:(7): 733–740.
1367:
1311:
1307:
1303:
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1290:
1272:
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1239:
1221:
1207:
1192:
1174:
1161:
1132:(3): 245–263.
1116:
1109:
1089:
1074:
1054:
1028:
1003:
997:978-0030839931
996:
970:
963:
931:
929:
926:
925:
924:
919:
914:
912:Pseudoparticle
909:
904:
899:
892:
889:
888:
887:
873:
860:
843:
832:
804:
791:
778:
769:
764:is carried by
753:
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690:
689:
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681:
672:
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579:
562:
551:quantum corral
539:effective mass
513:In solids, an
503:
500:
494:
491:
426:
423:
395:
392:
388:entity realism
359:effective mass
339:
336:
312:starting point
265:excited states
234:excited states
221:
218:
165:
162:
160:
157:
155:in the 1930s.
130:quasiparticles
114:quasiparticles
90:electron holes
73:effective mass
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6:
4:
3:
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3253:Semiconductor
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3222:Hubbard model
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2914:Exotic matter
2912:
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2902:Eightfold way
2900:
2898:
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2892:Antiparticles
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2563:Atomic nuclei
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2541:
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2531:
2530:
2528:
2526:
2522:
2516:
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2511:
2508:
2506:
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2501:
2498:
2496:
2495:Upsilon meson
2493:
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2481:
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2427:Lambda baryon
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2208:
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2183:Superpartners
2180:
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2100:
2098:
2094:
2082:
2079:
2077:
2074:
2072:
2069:
2067:
2066:Muon neutrino
2064:
2062:
2059:
2057:
2054:
2053:
2052:
2049:
2047:
2044:
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2039:
2037:
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2032:
2029:
2027:
2024:
2022:
2019:
2018:
2016:
2014:
2010:
2004:
2001:
1999:
1998:Bottom (quark
1996:
1994:
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69:atomic nuclei
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38:quasiparticle
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3504:
3422:Pines' demon
3383:
3161:Kondo effect
3063:Time crystal
2954:
2732:
2625:Hypothetical
2573:Exotic atoms
2442:Omega baryon
2432:Sigma baryon
2422:Delta baryon
2174:Hypothetical
2156:Ghost fields
2142:Higgs boson
2076:Tau neutrino
1968:Charm (quark
1857:
1850:
1846:
1839:
1828:
1821:
1818:L. D. Landau
1759:
1755:
1745:
1702:
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1632:
1620:. Retrieved
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1234:the original
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669:polarization
662:
649:
642:
638:
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616:
603:
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572:valence band
565:
559:interference
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431:Lev Landau's
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384:
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352:
341:
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263:and various
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121:
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29:
3459:Soft matter
3359:Ferromagnet
3177:Drude model
3146:Berry phase
3126:Hall effect
2907:Quark model
2675:Theta meson
2578:Positronium
2490:Omega meson
2485:J/psi meson
2415:Antineutron
2326:Dark photon
2291:Graviphoton
2250:Stop squark
1958:Down (quark
1871:PhysOrg.com
685:plasmariton
375:ferromagnet
3558:Categories
3374:Spin glass
3369:Metamagnet
3349:Paramagnet
3236:Conduction
3212:BCS theory
3053:Superfluid
3048:Supersolid
2649:Heptaquark
2610:Superatoms
2543:Pentaquark
2533:Tetraquark
2515:Quarkonium
2405:Antiproton
2306:Leptoquark
2241:Neutralino
2003:antiquark)
1993:antiquark)
1988:Top (quark
1983:antiquark)
1973:antiquark)
1963:antiquark)
1953:antiquark)
1922:Elementary
1769:2203.13615
1712:1708.07143
1618:. Phys.org
1569:1610.01604
1508:1502.03447
1392:1504.08037
1267:2020020086
1202:2020020086
928:References
790:potential.
705:superfluid
597:sound wave
591:. It is a
506:See also:
471:collisions
433:theory of
304:anharmonic
282:is in the
153:Lev Landau
3432:Polariton
3339:Diamagnet
3287:Couplings
3263:Conductor
3258:Semimetal
3243:Insulator
3119:Phenomena
3043:Fermi gas
2887:Particles
2832:Particles
2791:Polariton
2781:Plasmaron
2751:Dropleton
2644:Hexaquark
2615:Molecules
2603:Protonium
2480:Phi meson
2465:Rho meson
2437:Xi baryon
2369:Composite
2205:Gravitino
1948:Up (quark
1802:247749037
1794:1745-2481
1737:119423231
1480:119288349
1455:1111.0179
1134:CiteSeerX
884:direction
795:Skyrmions
634:polariton
610:spin wave
547:Crommie's
479:Boltzmann
379:spin wave
177:electrons
173:particles
50:particles
3506:Category
3487:Colloids
2863:timeline
2715:R-hadron
2670:Glueball
2654:Skyrmion
2588:Tauonium
2301:Inflaton
2296:Graviton
2276:Curvaton
2246:Sfermion
2236:Higgsino
2231:Chargino
2192:Gauginos
2051:Neutrino
2036:Antimuon
2026:Positron
2021:Electron
1931:Fermions
1683:28630919
1594:28306270
1533:26047225
1417:27043779
1362:95868563
1354:12142440
1156:18345614
1084:62416599
1047:26 March
891:See also
846:Type-II
835:Angulons
825:minerals
823:in some
801:Hopfions
787:spin ice
519:electron
439:helium-3
419:plasmons
415:excitons
242:directly
185:neutrons
159:Overview
118:fermions
102:plasmons
61:electron
3518:Commons
3482:Polymer
3449:Polaron
3427:Plasmon
3407:Exciton
2851:Related
2822:Baryons
2796:Polaron
2786:Plasmon
2761:Fracton
2756:Exciton
2710:Diquark
2705:Pomeron
2680:T meson
2637:Baryons
2598:Pionium
2583:Muonium
2510:D meson
2505:B meson
2410:Neutron
2395:Nucleon
2387:Baryons
2378:Hadrons
2341:Tachyon
2316:Majoron
2281:Dilaton
2210:Photino
2046:Antitau
2013:Leptons
1774:Bibcode
1717:Bibcode
1674:5457030
1653:Bibcode
1622:1 March
1602:5190749
1574:Bibcode
1541:9111150
1513:Bibcode
1460:Bibcode
1425:3406627
1397:Bibcode
1334:Bibcode
1316:Science
1020:, p. 10
988:299–302
738:fermion
677:exciton
664:polaron
651:plasmon
593:quantum
535:fermion
453:of the
425:History
411:phonons
344:fermion
300:exactly
181:protons
3417:Phonon
3412:Magnon
3170:Theory
3028:Plasma
3018:Liquid
2827:Mesons
2776:Phonon
2771:Magnon
2693:Others
2663:Mesons
2556:Others
2452:Mesons
2400:Proton
2264:Others
2219:Others
2200:Gluino
2134:Scalar
2114:Photon
2097:Bosons
1940:Quarks
1800:
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851:break
808:Spinon
733:anyons
709:vortex
621:photon
617:photon
605:magnon
584:phonon
523:charge
517:is an
463:plasma
371:magnon
364:phonon
288:phonon
183:, and
169:Solids
126:bosons
96:phonon
54:vacuum
3392:Anyon
3013:Solid
2815:Lists
2806:Trion
2801:Roton
2741:Anyon
2568:Atoms
2331:Preon
2271:Axion
2226:Axino
2119:Gluon
2106:Gauge
1798:S2CID
1764:arXiv
1733:S2CID
1707:arXiv
1598:S2CID
1564:arXiv
1537:S2CID
1503:arXiv
1476:S2CID
1450:arXiv
1421:S2CID
1387:arXiv
1358:S2CID
1324:arXiv
1152:S2CID
827:like
742:boson
700:roton
595:of a
574:of a
373:in a
348:boson
308:close
83:of a
46:solid
3402:Hole
2766:Hole
2593:Onia
2500:Kaon
2460:Pion
2031:Muon
1790:ISSN
1679:PMID
1624:2017
1590:PMID
1529:PMID
1413:PMID
1350:PMID
1306:CaCu
1263:LCCN
1253:ISBN
1198:LCCN
1188:ISBN
1105:ISBN
1080:OCLC
1070:ISBN
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880:duon
878:(or
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798:and
740:nor
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