General introduction Solids are made of only three kinds of
particles:
electrons,
protons, and
neutrons. 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 along with an infinite series of higher-energy
excited states. 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 1017 nuclei and 1018 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 3×1018-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 3×1018-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 states 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). 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 1018 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 materials, 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.
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
flow properties and
heat capacity. In the heat capacity example, a crystal can store energy by forming
phonons, and/or forming
excitons, and/or forming
plasmons, etc. Each of these is a separate contribution to the overall heat capacity.
History The idea of quasiparticles originated in
Lev Landau's theory of
Fermi liquids, which was originally invented for studying liquid
helium-3. For these systems a strong similarity exists between the notion of quasiparticle and
dressed particles in
quantum field theory. The dynamics of Landau's theory is defined by a
kinetic equation of the
mean-field type. A similar equation, the
Vlasov equation, is valid for a
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
collisions 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-type collision term, in which figure only "far collisions" between
virtual particles. In other words, every type of mean-field kinetic equation, and in fact every
mean-field theory, involves a quasiparticle concept. ==Common examples ==