Editing Quasiparticle (section)

==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.