Editing Quasiparticle

{{Short description|Concept in condensed matter physics}}
{{Use dmy dates|date=October 2020}}

In [[condensed matter physics]], a '''quasiparticle''' 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 '''collective excitations''' are closely related phenomena that arise when a microscopically complicated system such as a [[solid]] behaves as if it contained different weakly interacting [[particle]]s in [[vacuum]].

For example, as an [[electron]] travels through a [[semiconductor]], its motion is disturbed in a complex way by its interactions with other electrons and with [[atomic nucleus|atomic nuclei]]. The electron behaves as though it has a different [[effective mass (solid-state physics)|effective mass]] travelling unperturbed in vacuum. Such an electron is called an ''electron quasiparticle''.<ref name=Kaxiras/> In another example, the aggregate motion of electrons in the [[valence band]] of a [[semiconductor]] or a hole band in a metal<ref name="ashcroftandmermin">{{cite book |last1=Ashcroft |url=https://archive.org/details/solidstatephysic00ashc/page/299 |title=Solid State Physics |last2=Mermin |date=1976 |publisher=Holt, Rinehart, and Winston |isbn=978-0030839931 |edition=1st |pages=[https://archive.org/details/solidstatephysic00ashc/page/299 299–302] |language=en |url-access=registration}}</ref> behave as though the material instead contained positively charged quasiparticles called ''[[electron hole]]s''. Other quasiparticles or collective excitations include the ''[[phonon]]'', a quasiparticle derived from the vibrations of atoms in a solid, and the ''[[plasmon]]'', a particle derived from [[plasma oscillation]].

These phenomena are typically called ''quasiparticles'' if they are related to [[fermion]]s, and called ''collective excitations'' if they are related to [[boson]]s,<ref name=Kaxiras/> although the precise distinction is not universally agreed upon.<ref name="Mattuck">{{Cite book |last=Mattuck |first=Richard D. |url={{google books|plainurl=y|id=pe-v8zfxE68C|page=10}}|page=10|title=A Guide to Feynman Diagrams in the Many-body Problem |date=1992-01-01 |publisher=Courier Corporation |isbn=978-0-486-67047-8 |language=en|quote=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 ''all'' the particles in the system simultaneously.}}</ref> Thus, electrons and electron holes (fermions) are typically called ''quasiparticles'', while phonons and plasmons (bosons) are typically called ''collective excitations''.

The quasiparticle concept is important in [[condensed matter physics]] because it can simplify the [[many-body problem]] in [[quantum mechanics]]. The theory of quasiparticles was started by the Soviet physicist [[Lev Landau]] in the 1930s.<ref>{{Cite web|date=2021-03-18|title=Ultracold atoms permit direct observation of quasiparticle dynamics|url=https://physicsworld.com/ultracold-atoms-permit-direct-observation-of-quasiparticle-dynamics/|access-date=2021-03-26|website=Physics World|language=en-GB}}</ref><ref>{{Cite book |last=Kozhevnikov |first=A. B. |url=https://www.worldcat.org/oclc/62416599 |title=Stalin's great science : the times and adventures of Soviet physicists |date=2004 |publisher=Imperial College Press |isbn=1-86094-601-1 |location=London, England |language=en-uk |oclc=62416599}}</ref>

==Overview==

===General introduction===
[[Solid]]s are made of only three kinds of [[particle physics|particles]]: [[electron]]s, [[proton]]s, and [[neutron]]s. None of these are quasiparticles; instead a quasiparticle is an ''[[emergent phenomenon]]'' 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.

Motion in a solid is extremely complicated: Each electron and proton is pushed and pulled (by [[Coulomb's law]]) 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 [[many-body problem]]). On the other hand, the motion of a ''non-interacting'' 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 ''real'' particles in a solid can be mathematically transformed into the much simpler motion of imagined quasiparticles, which behave more like non-interacting particles.

In summary, quasiparticles are a mathematical tool for simplifying the description of solids.

===Relation to many-body quantum mechanics===
[[Image:Energy levels.svg|thumb|right|Any system, no matter how complicated, has a [[ground state]] along with an infinite series of higher-energy [[excited state]]s.]]
The principal motivation for quasiparticles is that it is almost impossible to ''directly'' describe every particle in a macroscopic system. For example, a barely-visible (0.1mm) grain of sand contains around 10<sup>17</sup> nuclei and 10<sup>18</sup> electrons. Each of these attracts or repels every other by [[Coulomb's law]]. In principle, the [[Schrödinger equation]] predicts exactly how this system will behave. But the Schrödinger equation in this case is a [[partial differential equation]] (PDE) on a 3×10<sup>18</sup>-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<sup>18</sup>-dimensional space is quite impossible by straightforward methods.

One simplifying factor is that the system as a whole, like any quantum system, has a [[ground state]] and various [[excited state]]s 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 [[Boltzmann distribution]], which implies that very-high-energy [[thermal fluctuations]] are unlikely to occur at any given temperature.

Quasiparticles and collective excitations are a type of low-lying excited state. For example, a crystal at [[absolute zero]] is in the [[ground state]], but if one [[phonon]] 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 ''elementary excitation''. More generally, low-lying excited states may contain any number of elementary excitations (for example, many phonons, along with other quasiparticles and collective excitations).<ref>{{cite book |last1=Ohtsu |first1=Motoichi |last2=Kobayashi |first2=Kiyoshi |last3=Kawazoe |first3=Tadashi |last4=Yatsui |first4=Takashi |last5=Naruse |first5=Makoto |title=Principles of Nanophotonics |date=2008 |publisher=CRC Press |isbn=9781584889731 |page=205 |url=https://books.google.com/books?id=3za2u8FnCgUC&pg=PA205 |language=en}}</ref>

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 ''exactly'' 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 [[anharmonic]]. However, in many materials, the elementary excitations are very ''close'' to being independent. Therefore, as a ''starting point'', they are treated as free, independent entities, and then corrections are included via interactions between the elementary excitations, such as "phonon-[[phonon scattering]]".

Therefore, using quasiparticles / collective excitations, instead of analyzing 10<sup>18</sup> particles, one needs to deal with only a handful of somewhat-independent elementary excitations. It is, therefore, an effective approach to simplify the [[many-body problem]] in quantum mechanics. This approach is not useful for ''all'' systems, however. For example, in [[strongly correlated material]]s, the elementary excitations are so far from being independent that it is not even useful as a starting point to treat them as independent.

===Distinction between quasiparticles and collective excitations===
Usually, an elementary excitation is called a "quasiparticle" if it is a [[fermion]] and a "collective excitation" if it is a [[boson]].<ref name="Kaxiras" /> However, the precise distinction is not universally agreed upon.<ref name="Mattuck" />

There is a difference in the way that quasiparticles and collective excitations are intuitively envisioned.<ref name=Mattuck/> A quasiparticle is usually thought of as being like a [[dressed particle]]: 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 [[Effective mass (solid-state physics)|effective mass]] 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 [[phonon]], which characterizes the vibrational motion of every atom in the crystal.

However, these two visualizations leave some ambiguity. For example, a [[magnon]] in a [[ferromagnet]] 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 [[spin wave]] 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 collective excitation is not particularly important or fundamental.

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, [[entity realism]].<ref>{{Cite journal |doi = 10.1080/0269859032000169451|title = Manipulative success and the unreal|journal = International Studies in the Philosophy of Science|volume = 17|issue = 3|pages = 245–263|year = 2003|last1 = Gelfert|first1 = Axel|citeseerx = 10.1.1.405.2111|s2cid = 18345614}}</ref><ref>B. Falkenburg, ''Particle Metaphysics'' (The Frontiers Collection), Berlin, Germany: Springer 2007, esp. pp. 243–246.</ref>

===Effect on bulk properties===
By investigating the properties of individual quasiparticles, it is possible to obtain a great deal of information about low-energy systems, including the [[quantum fluid|flow properties]] and [[heat capacity]].

In the heat capacity example, a crystal can store energy by forming [[phonon]]s, and/or forming [[exciton]]s, and/or forming [[plasmon]]s, etc. Each of these is a separate contribution to the overall heat capacity.

===History===
The idea of quasiparticles originated in [[Lev Davidovich Landau|Lev Landau's]] theory of [[Fermi liquid]]s, which was originally invented for studying liquid [[helium-3]]. For these systems a strong similarity exists between the notion of quasiparticle and [[dressed particle]]s in [[quantum field theory]]. The dynamics of Landau's theory is defined by a [[kinetic theory of gases|kinetic equation]] of the [[mean-field theory|mean-field type]]. A similar equation, the [[Vlasov equation]], is valid for a [[Plasma (physics)|plasma]] in the so-called [[plasma approximation]]. In the plasma approximation, charged particles are considered to be moving in the electromagnetic field collectively generated by all other particles, and hard [[collision]]s 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 [[entropy production]], and generally take the form of a [[Boltzmann equation|Boltzmann]]-type collision term, in which figure only "far collisions" between [[virtual particle]]s. In other words, every type of mean-field kinetic equation, and in fact every [[mean-field theory]], involves a quasiparticle concept.

==Common examples ==
{{See also|List of quasiparticles}}
This section contains most common examples of quasiparticles and collective excitations. 

*In solids, an electron quasiparticle is an [[electron]] as affected by the other forces and interactions in the solid. The electron quasiparticle has the same [[electric charge|charge]] and [[Spin (physics)|spin]] as a "normal" ([[elementary particle]]) electron, and like a normal electron, it is a [[fermion]]. However, its mass can differ substantially from that of a normal electron; see the article [[effective mass (solid-state physics)|effective mass]].<ref name="Kaxiras">{{cite book |author=Kaxiras |first=Efthimios |url=https://books.google.com/books?id=WTL_vgbWpHEC&pg=PA65 |title=Atomic and Electronic Structure of Solids |date=9 January 2003 |publisher=Cambridge University Press |isbn=978-0-521-52339-4 |pages=65–69 |language=en}}</ref> Its electric field is also modified, as a result of [[electric field screening]]. In many other respects, especially in metals under ordinary conditions, these so-called Landau quasiparticles{{Citation needed|date=August 2008}} closely resemble familiar electrons; as [[Michael F. Crommie|Crommie's]] "[[quantum corral]]" showed, an [[Scanning tunneling microscope|STM]] can image their [[interference (wave propagation)|interference]] upon scattering.
*A [[electron hole|hole]] 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 [[valence band]] of a [[semiconductor]].<ref name="Kaxiras"/> A hole has the opposite charge of an electron.
*A [[phonon]] is a collective excitation associated with the vibration of atoms in a rigid [[crystal structure]]. It is a [[quantum]] of a [[sound wave]].<ref>{{Cite book |last=Wilczek |first=Frank |title=Fundalmentals : Ten Keys to Reality |date=2021 |publisher=Penguin Press |isbn=9780735223790 |location=New York, New York |page=88 |language=en-us |lccn=2020020086}}</ref>
*A [[magnon]] is a collective excitation<ref name=Kaxiras/> associated with the electrons' spin structure in a crystal lattice. It is a quantum of a [[spin wave]].
*In materials, a photon quasiparticle is a [[photon]] as affected by its interactions with the material. In particular, the photon quasiparticle has a modified relation between wavelength and energy ([[dispersion relation]]), as described by the material's [[index of refraction]]. It may also be termed a [[polariton]], especially near a resonance of the material. For example, an [[exciton-polariton]] is a superposition of an exciton and a photon; a [[Phonon polariton|phonon-polariton]] is a superposition of a phonon and a photon.
*A [[plasmon]] is a collective excitation, which is the quantum of [[plasma oscillation]]s (wherein all the electrons simultaneously oscillate with respect to all the ions).
*A [[polaron]] is a quasiparticle which comes about when an electron interacts with the [[polarization density|polarization]] of its surrounding ions.
*An [[exciton]] is an electron and hole bound together.

==See also==
*[[Fractionalization]]
*[[List of quasiparticles]]
*[[Mean-field theory]]
*[[Pseudoparticle]]
*[[Composite fermion]]
*[[Composite boson]]

==References==
{{Reflist|30em}}

==Further reading==
*[[Lev Landau|L. D. Landau]], ''Soviet Phys. JETP.'' 3: 920 (1957)
*L. D. Landau, ''Soviet Phys. JETP.'' 5: 101 (1957)
*A. A. Abrikosov, [[Lev Gor'kov|L. P. Gor'kov]], and I. E. Dzyaloshinski, ''Methods of Quantum Field Theory in Statistical Physics'' (1963, 1975). Prentice-Hall, New Jersey; Dover Publications, New York, New York.
*D. Pines, and P. Nozières, ''The Theory of Quantum Liquids'' (1966). W.A. Benjamin, New York. ''Volume I: Normal Fermi Liquids'' (1999). Westview Press, Boulder, Colorado.
*J. W. Negele, and H. Orland, ''Quantum Many-Particle Systems'' (1998). Westview Press, Boulder, Colorado.

==External links==
*[https://web.archive.org/web/20081012203117/http://www.physorg.com/news131631206.html PhysOrg.com] – Scientists find new 'quasiparticles'
*[https://web.archive.org/web/20080609005023/http://www.cosmosmagazine.com/news/2038/curious-quasiparticles-have-a-quarter-charge-electron Curious 'quasiparticles' baffle physicists] by Jacqui Hayes, Cosmos 6 June 2008. Accessed June 2008

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