凝聚态物理导论-中科院课件-苏刚Chapter4

Chapter 4 Elementary Excitations §4.1 Prolog
The ground-state wavefunction of the many-body interacting electrons in condensed matter is unimaginably complicated and rather interesting. It is also impossible to get an exact solution in absolutely most cases. Then, how to describe the responses of the solids (condensed matter) to experimental probes such as photons, beams of atoms or ions, the electrons emerging from an STM tip, or changes in temperature? What determines the electrical or thermal transport properties of solids (condensed matter) ? All these questions are beyond the scope of a ground-state theory.
Note that the use of term quasiparticle seems to be ambiguous. Some authors use the term in order to distinguish them from real particles, others (including author of the above passage) to describe an excitation similar to a single particle excitation as opposed to a collective excitation. Both definitions mutually exclude each other as with the former definition collective excitations which are no "real" particles are considered to be quasiparticles. 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 or not they should be considered "real" by the standards of, for example, entity realism.
Joaquin Luttinger
Lev Davidovich Landau
Similarities to Fermi gas: The Fermi liquid is qualitatively analogous to the non-interacting Fermi gas, in the following sense: The system's dynamics and thermodynamics at low excitation energies and temperatures may be described by substituting the noninteracting fermions with so-called quasiparticles, each of which carries the same spin, charge and momentum as the original particles. Physically these may be thought of as being particles whose motion is disturbed by the surrounding particles and which themselves perturb the particles in their vicinity. Each many-particle excited state of the interacting system may be described by listing all occupied momentum states, just as in the non-interacting system. As a consequence, quantities such as the heat capacity of the Fermi liquid behave qualitatively in the same way as in the Fermi gas (e.g. the heat capacity rises linearly with temperature). Differences from Fermi gas: Energy, specific heat, compressibility, interactions, dressed particlesnger liquid
Fermi liquid is a generic term for a quantum mechanical liquid of fermions that arises under certain physical conditions when the temperature is sufficiently low. The interaction between the particles of the many-body system does not need to be small (see e.g. electrons in a metal). The phenomenological theory of Fermi liquids, which was introduced by the Soviet physicist Lev Davidovich Landau in 1956, explains why some of the properties of an interacting fermion system are very similar to those of the Fermi gas (i.e. non-interacting fermions), and why other properties differ. Liquid He-3 is a Fermi liquid at low temperatures (but not low enough to be in its superfluid phase.) He-3 is an isotope of Helium, with 2 protons, 1 neutron and 2 electrons per atom; because there is an odd number of fermions inside the atom, the atom itself is also a fermion. The electrons in a normal (nonsuperconducting) metal also form a Fermi liquid.
Electron-hole excitation
Quasiparticle
From Wikipedia, the free encyclopedia
/wiki/Quasiparticle
In the language of many-body quantum mechanics, a quasiparticle is a type of lowlying excited state of the system (a state possessing energy very close to the ground state energy) that is known as an elementary excitation. As a result of this closeness, most of the other low-lying excited states can be viewed as states in which multiple quasiparticles are present, because interactions between quasiparticles become negligible at sufficiently low temperatures. 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. Most many-body systems possess two types of elementary excitations. The first type, the quasiparticles, correspond to single particles whose motions are modified by interactions with the other particles in the system. The second type of excitation corresponds to a collective motion of the system as a whole. These excitations are called , and they include phenomena such as zero sound, plasmons, and spin waves. 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 quasi-particle 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.