A 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, and when the system is translationally invariant. 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 Russian 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. Fig. ... A liquid will assume the shape of its container. ... Fermions, named after Enrico Fermi, are particles which form totally-antisymmetric composite quantum states. ... Temperature is the physical property of a system which underlies the common notions of hot and cold; the material with the higher temperature is said to be hotter. ... Look up Phenomenology in Wiktionary, the free dictionary Phenomenology is a current in philosophy that takes the intuitive experience of phenomena (what presents itself to us in conscious experience) as its starting point and tries to extract the essential features of experiences and the essence of what we experience. ... Lev Davidovich Landau (Ле́в Дави́дович Ланда́у) (January 22, 1908 – April 1, 1968) was a prominent Soviet physicist and winner of the Nobel Prize for Physics whose broad field of work included the theory of superconductivity and superfluidity, quantum electrodynamics, nuclear physics and particle physics. ... 1956 (MCMLVI) was a leap year starting on Sunday of the Gregorian calendar. ... A Fermi gas is a collection of non-interacting fermions. ...

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 (non-superconducting) metal also form a Fermi liquid. Superfluidity is a phase of matter characterised by the complete absence of viscosity. ... In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i. ... Isotopes are forms of an element whose nuclei have the same atomic number–-the number of protons in the nucleus--but different atomic masses because they contain different numbers of neutrons. ... General Name, Symbol, Number helium, He, 2 Chemical series noble gases Group, Period, Block 18, 1, s Appearance colorless Atomic mass 4. ... Properties In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... Properties In physics, the neutron is a subatomic particle with no net electric charge and a mass of 939. ... Properties The electron is a fundamental subatomic particle which carries a negative electric charge. ... A magnet levitating above a high-temperature superconductor (with boiling liquid nitrogen underneath) demonstrates the Meissner effect. ... Hot metal work from a blacksmith In chemistry, a metal (Greek: Metallon) is an element that readily forms ions (cations) and has metallic bonds, and metals are sometimes described as a lattice of positive ions (cations) in a cloud of electrons. ...

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 for the non-interacting fermions 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). In physics, a quasiparticle refers to a particle-like entity arising in certain systems of interacting particles. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is generated by the motion of its center of mass about an external point. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... In physics, momentum is the product of the mass and velocity of an object. ... In physics, a particle is an object, or body, with only a few degrees-of-freedom, including position, and perhaps orientation in space. ...

However, the following differences to the non-interacting Fermi gas arise:

• The energy of a many-particle state is not simply a sum of the single-particle energies of all occupied states. Instead, the change in energy for a given change δn_k in occupation of states k contains terms both linear and quadratic in δn_k (for the Fermi gas, it would only be linear, δn_kε_k, where ε_k denotes the single-particle energies). The linear contribution corresponds to renormalized single-particle energies, which involve, e.g., a change in the effective mass of particles. The quadratic terms correspond to a sort of "mean-field" interaction between quasiparticles, which is parameterized by so-called Landau Fermi liquid parameters and determines the behaviour of density oscillations (and spin-density oscillations) in the Fermi liquid. Still, these mean-field interactions do not lead to a scattering of quasi-particles with a transfer of particles between different momentum states.

• Specific heat, compressibility, spin-susceptibility and other quantities show the same qualitative behaviour (e.g. dependence on temperature) as in the Fermi gas, but the magnitude is (sometimes strongly) changed.

• In addition to the mean-field interactions, some weak interactions between quasiparticles remain, which lead to scattering of quasiparticles off each other. Therefore, quasiparticles acquire a finite lifetime. However, at low enough energies above the Fermi surface, this lifetime becomes very long, such that the product of excitation energy (expressed in frequency) and lifetime is much larger than one. In this sense, the quasiparticle energy is still well-defined (in the opposite limit, Heisenberg's uncertainty relation would prevent an accurate definition of the energy).

• Green's function and momentum distribution of quasiparticles behave as for the fermions in the Fermi gas (apart from the broadening of the delta peak in the Green's function by the finite lifetime).

• The structure of the "bare" particle's (as opposed to quasiparticle) Green's function is similar to that in the Fermi gas (where, for a given momentum, the Green's function in frequency space is a delta peak at the respective single-particle energy). The delta peak in the density-of-states is broadened (with a width given by the quasiparticle lifetime). In addition (and in contrast to the quasiparticle Green's function), its weight (integral over frequency) is suppressed by a quasiparticle weight factor 0 < Z < 1. The remainder of the total weight is in a broad "incoherent background", corresponding to the strong effects of interactions on the fermions at short time-scales.

• The distribution of particles (as opposed to quasiparticles) over momentum states at zero temperature still shows a discontinuous jump at the Fermi surface (as in the Fermi gas), but it does not drop from 1 to 0: the step is only of size Z.

• In a metal the resistance at low temperatures is dominated by electron-electron scattering in combination with Umklapp scattering. For a Fermi liquid, the resistance from this mechanism varies as T², which is often taken as an experimental check for Fermi liquid behaviour (in addition to the linear temperature-dependence of the specific heat), although it only arises in combination with the lattice.