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The Theory of a Fermi Liquid

L.D. LANDAU

Published Jan 1, 1957• 756 citations
OpenAlex

Abstract

A theory of the Fermi liquid is constructed, based on the representation of the perturbation theory as a functional of the distribution function. The effective mass of the excitation is found, along with the compressibility and the magnetic susceptibility of the Fermi liquid. Expressions are obtained for the momentum and energy flow.

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Journal of Mathematical Physics•Sep 1, 1969•3 citations

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On the theory of superfluid Fermi liquid with spin-triplet pairing in a magnetic field

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The Fermi-liquid approach generalized to superfluid systems is used to derive general formulas for the normal and abnormal distribution functions (DF) for quasiparticles of a superfluid Fermi liquid (SFL) consisting of electrically neutral fermions with spin-triplet pairing (the spin of a pair s=1, the orbital angular momentum l of the pair being an arbitrary odd number) in a static uniform magnetic field, taking into account the Landau spin-exchange Fermi-liquid interaction at temperatures 0<T<Tc (Tc is the temperature of phase transition from the normal to the superfluid state). In deriving the DF, the explicit form of the energy functional (EF) for SFL is not used. A system of coupled equations is obtained for the order parameter, energy of quasiparticles, and effective magnetic field for the SFL under investigation in the case of an EF quadratic in DF. The obtained DF and the system of equations are applicable for describing both unitary and nonunitary phases of superfluid He3 in a magnetic field, e.g., for determining the magnetization and magnetic susceptibility of these phases.

Low Temperature Physics•May 1, 1998•10 citations

The Fermi Liquid

Hui Zhai

1. Introduce density distribution and momentum distribution of non-interacting Fermi gas. 2. Discuss the transport property of a Fermi gas through a quantum point contact. 3. Discuss Fermi surface as a key of a non-interacting Fermi gas and its generalization to a Fermi liquid. 4. Introduce the effective mass and the quasi-particle residue as two key parameters of the Fermi liquid. 5. Introduce the self-energy and the universal relations between the effective mass, the quasi-particle residue and the self-energy. 6. Discuss Fermi polaron as an example of the Fermi liquid, and show these universal relations with this example. 7. Discuss the divergence of the effective mass and vanishing of quasi-particle residue when Fermi liquid description fails. 8. Introduce the radio-frequency spectroscopy and how it measures the polaron energy and the quasi-particle residue. 9. Summarize different spectroscopy measurements in ultracold atomic systems.

Cambridge University Press eBooks•Jan 30, 2021•0 citations

Theory of a superfluid Fermi liquid

Alexander I. Akhiezer, Красильников Владимир Владимирович, S. V. Peletminskiǐ +1 more

A Fermi-liquid approach to the theory of superfluidity is developed, based on a generalization of the combinatoric expression for the entropy to the case in which the state of the Fermi liquid is described not only by a normal but also by an anomalous distribution function. The energy of the superfluid Fermi liquid is given in the form of a functional of these distribution functions. In the weak-coupling approximation the Fermi-liquid approach is equivalent to the BCS theory. The interaction between the Fermi liquid and an electromagnetic field is gauge invariant. In addition to the singlet-pairing theory the triplet-pairing theory is also developed. A unified variational principle that gives rise to the theory of superfluidity (superconductivity) is used to obtain the London equations and the Ginzburg–Landau equation. Applications of this theory are made to the derivation of an equation for ideal two-component hydrodynamics.

Physics-Uspekhi•Feb 28, 1993•13 citations

Some questions in the theory of a superfluid Fermi liquid with triplet pairing in a magnetic field

A. N. Tarasov

General expressions are obtained in explicit form for the anomalous and normal distribution functions of quasiparticles in nonunitary phases of a superfluid paramagnetic Fermi liquid consisting of electrically neutral fermions with triplet pairing (the pairs have spin s=1 and an arbitrary odd value of the orbital angular momentum l) in a uniform static magnetic field. A generalized Fermi-liquid approach is used which takes into account the exchange Fermi-liquid interaction but does not specify the form of the energy functional of the superfluid Fermi liquid. The results are valid at any temperature in the interval 0⩽T⩽Tc, where Tc is the temperature of the phase transition from the normal to the superfluid state. When an explicit form of the energy functional is specified, the general formulas for the distribution function can be used to describe the various nonunitary phases of a superfluid Fermi liquid of the He3 type in a high magnetic field. In particular, for He3-A1, He3-A2, and the nonunitary two-dimensional phase of He3 in a high magnetic field at 0⩽T⩽Tc, an energy functional quadratic in the distribution function is used to find a system of coupled equations for the order parameter and the effective magnetic field and to obtain an expression is obtained for the nonlinear magnetic susceptibility.

Low Temperature Physics•Nov 1, 2000•9 citations
We generalize the Fermi-liquid theory to NNN component systems with SU(N)\mathrm{SU}(N)SU(N) symmetry. We evaluate the Fermi-liquid parameters, effective mass, compressibility, and spin susceptibilities for a repulsive gas. We emphasize the important role of induced density fluctuations when NNN is large. These fluctuations dramatically modify the properties of the gas, in particular the spin susceptibilities, from mean-field predictions.
The Fermi-liquid approach generalized to superfluid systems is used to derive general formulas for the normal and abnormal distribution functions (DF) for quasiparticles of a superfluid Fermi liquid (SFL) consisting of electrically neutral fermions with spin-triplet pairing (the spin of a pair s=1, the orbital angular momentum l of the pair being an arbitrary odd number) in a static uniform magnetic field, taking into account the Landau spin-exchange Fermi-liquid interaction at temperatures 0<T<Tc (Tc is the temperature of phase transition from the normal to the superfluid state). In deriving the DF, the explicit form of the energy functional (EF) for SFL is not used. A system of coupled equations is obtained for the order parameter, energy of quasiparticles, and effective magnetic field for the SFL under investigation in the case of an EF quadratic in DF. The obtained DF and the system of equations are applicable for describing both unitary and nonunitary phases of superfluid He3 in a magnetic field, e.g., for determining the magnetization and magnetic susceptibility of these phases.
1. Introduce density distribution and momentum distribution of non-interacting Fermi gas. 2. Discuss the transport property of a Fermi gas through a quantum point contact. 3. Discuss Fermi surface as a key of a non-interacting Fermi gas and its generalization to a Fermi liquid. 4. Introduce the effective mass and the quasi-particle residue as two key parameters of the Fermi liquid. 5. Introduce the self-energy and the universal relations between the effective mass, the quasi-particle residue and the self-energy. 6. Discuss Fermi polaron as an example of the Fermi liquid, and show these universal relations with this example. 7. Discuss the divergence of the effective mass and vanishing of quasi-particle residue when Fermi liquid description fails. 8. Introduce the radio-frequency spectroscopy and how it measures the polaron energy and the quasi-particle residue. 9. Summarize different spectroscopy measurements in ultracold atomic systems.
A Fermi-liquid approach to the theory of superfluidity is developed, based on a generalization of the combinatoric expression for the entropy to the case in which the state of the Fermi liquid is described not only by a normal but also by an anomalous distribution function. The energy of the superfluid Fermi liquid is given in the form of a functional of these distribution functions. In the weak-coupling approximation the Fermi-liquid approach is equivalent to the BCS theory. The interaction between the Fermi liquid and an electromagnetic field is gauge invariant. In addition to the singlet-pairing theory the triplet-pairing theory is also developed. A unified variational principle that gives rise to the theory of superfluidity (superconductivity) is used to obtain the London equations and the Ginzburg–Landau equation. Applications of this theory are made to the derivation of an equation for ideal two-component hydrodynamics.
General expressions are obtained in explicit form for the anomalous and normal distribution functions of quasiparticles in nonunitary phases of a superfluid paramagnetic Fermi liquid consisting of electrically neutral fermions with triplet pairing (the pairs have spin s=1 and an arbitrary odd value of the orbital angular momentum l) in a uniform static magnetic field. A generalized Fermi-liquid approach is used which takes into account the exchange Fermi-liquid interaction but does not specify the form of the energy functional of the superfluid Fermi liquid. The results are valid at any temperature in the interval 0⩽T⩽Tc, where Tc is the temperature of the phase transition from the normal to the superfluid state. When an explicit form of the energy functional is specified, the general formulas for the distribution function can be used to describe the various nonunitary phases of a superfluid Fermi liquid of the He3 type in a high magnetic field. In particular, for He3-A1, He3-A2, and the nonunitary two-dimensional phase of He3 in a high magnetic field at 0⩽T⩽Tc, an energy functional quadratic in the distribution function is used to find a system of coupled equations for the order parameter and the effective magnetic field and to obtain an expression is obtained for the nonlinear magnetic susceptibility.