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. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Liquid is one of the principal States of matter. A liquid is a Fluid that has the particles loose and can freely form a distinct surface at the boundaries of In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature 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. Lev Davidovich Landau ( Russian language: Ле́в Дави́дович Ланда́у ( January 22, 1908 &ndash April 1, 1968 Year 1956 ( MCMLVI) was a Leap year starting on Sunday (link will display full calendar of the Gregorian calendar. A Fermi gas, or Free electron gas, is a collection of non-interacting Fermions. 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. This article is about the elemental isotope For the record label Helium 3 see Muse or A&E Records. Superfluidity is a phase of matter or description of Heat capacity in which unusual effects are observed when Liquids, typically of Helium-4 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 ) 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. Isotopes (Greek isos = "equal" tópos = "site place" are any of the different types of atoms ( Nuclides Helium ( He) is a colorless odorless tasteless non-toxic Inert Monatomic Chemical The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. The electrons in a normal (non-superconducting) metal also form a Fermi liquid. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J Superconductivity is a phenomenon occurring in certain Materials generally at very low Temperatures characterized by exactly zero electrical resistance The M acro E xpansion T emplate A ttribute L anguage complements TAL, providing macros which allow the reuse of code across
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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 non-interacting fermions with so-called quasiparticles, each of which carries the same spin, charge and momentum as the original particles. A Fermi gas, or Free electron gas, is a collection of non-interacting Fermions. In Physics, a quasiparticle refers to a particle -like entity arising in certain systems of interacting particles In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product 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
The following differences to the non-interacting Fermi gas arise:
Energy
The energy of a many-particle state is not simply a sum of the single-particle energies of all occupied states. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός Instead, the change in energy for a given change δnk in occupation of states k contains terms both linear and quadratic in δnk (for the Fermi gas, it would only be linear, δnkεk, where εk 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 and compressibility
Specific heat, compressibility, spin-susceptibility and other quantities show the same qualitative behaviour (e. Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity In Thermodynamics and Fluid mechanics, compressibility is a measure of the relative volume change of a Fluid or Solid as a response g. dependence on temperature) as in the Fermi gas, but the magnitude is (sometimes strongly) changed.
Interactions
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). Werner Heisenberg (5 December 1901 in Würzburg &ndash1 February 1976 in Munich) was a German theoretical physicist best known for enunciating the In Quantum physics, the Heisenberg uncertainty principle states that locating a particle in a small region of space makes the Momentum of the particle uncertain
Structure
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). In Mathematics, Green's function is a type of function used to solve inhomogeneous Differential equations subject to boundary conditions 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.
Distribution
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.
Resistance
In a metal the resistance at low temperatures is dominated by electron-electron scattering in combination with Umklapp scattering. Umklapp scattering (also U-process or Umklapp process) is an anharmonic Phonon -phonon (or Electron -phonon Scattering process 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.
Instabilities of the Fermi Liquid
The experimental observation of exotic phases in strongly correlated systems has triggered an enormous effort from the theoretical community to try to understand their microscopical origin. One possible route to detect instabilities of a FL is precisely the analysis done by Pomeranchuk[1]. . Due to that, the Pomeranchuk instability has been studied by several authors [2] with different techniques in the last few years and in particular, the instability of the FL towards the nematic phase was investigated for several models
References
- ^ I. J. Pomeranchuk, Sov. Phys. JETP 8, 361 (1958)
- ^ Actually, this is a subject of investigation, see for example: [1] .
See also
Classical fluids are systems of particles which retain a definite volume and are at sufficiently high temperatures (compared to their Fermi Energy) that Quantum effects A Tomonaga-Luttinger liquid, more often referred to as simply a Luttinger liquid, is a theoretical model describing interacting Electrons (or other FermionsDapyx Software network: MP3 Explorer | Ebook Manager | Zenithic