T approximation in the theory of a normal Fermi liquid

The characteristics determining the spectrum of Fermi systems are calculated in the framework of the statistical T approximation. It is shown that the effective mass can be estimated with greater accuracy than the energy gap. It is shown that it may be important to take into account corrections in the calculation of the microscopic characteristics at T=0 in the framework of the eikonal T approximation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 32–37, August, 1977.     

Spin vortices and stationary spin flows in a normal Fermi liquid

We solve the equations for the collisionless spin dynamics of a normal Fermi liquid, which describe structures resembling spin vortices coherently precessing in a uniform magnetic field. We examine their stability and relaxation, and consider various regimes of stationary magnetization transport along a channel. Zh. éksp. Teor. Fiz. 114, 1266–1283 (October 1998)     

Pendulum in a Fermi liquid

The Fermi-liquid theory formulated by Landau is a basic paradigm of the behavior of an interacting many-body system. We present a new application of this theory to calculate the "Landau force" on a macroscopic object. We show that immersing a pendulum in a Fermi liquid can increase its oscillation frequency, and evidence of this has been observed in mixtures of (3)He and (4)He.     

Zero-sound condensate in a Fermi liquid

We consider a normal Fermi liquid with a local scalar interaction given by the Landau parameter f₀. The system becomes unstable for f₀ < ?1 against a growth of scalar-mode excitations (Pomeranchuk instability). We show that the instability may be tamed by the formation of a static Bose condensate of the scalar modes. We study a possible reconstruction of the isospin-symmetric nuclear matter owing to the appearance of the condensate. Possibility of a novel metastable state at subnuclear densities is demonstrated.     

Viscoelasticity of a Fermi liquid

Infinite homogeneous Fermi systems in the degenerate regime are described by the Uehling-Uhlenbeck equation. The eigenvalue problem associated with the linearized collision operator is solved analytically. Initial value problems are studied with the help of the spectral representation of the time evolution operator. The dynamic transport coefficients of the system can then be calculated in the framework of linear response theory. As an example the viscoelastic behaviour of the Fermi liquid is related to the relaxation of a quadrupole deformation in momentum space. In this connection also the coupling of the driving field to 2p-2h excitations will be discussed. The theory is applied to normal liquid³He and to nuclear matter.     

Surface electromagnetic waves in a Fermi liquid

Surface electromagnetic waves propagating along a Fermi liquid-dielectric interface are investigated. A dispersion relation for the surface waves is obtained, and the frequency range of their existence is determined. The possibility of determining the contribution of a Fermi liquid to the dielectric permittivity of a metal from experiments on excitation of surface electromagnetic waves is shown.     

Coupling of the zero sound to transverse spin waves for neutral and normal Fermi liquids in dc magnetic field at precessing magnetization

Following the idea by Ketterson, this author showed that in neutral and normal Fermi liquids, the polarization effects lead to coupling of transverse spin waves to zero sound at precessing magnetization of the system. The observable effects, at the range of dc fields applied to³He, can appear only if the zero sound is degenerate with transverse spin waves excited in the reference frame rotating with the Larmor frequency about theH _dc-axis. This possibility is investigated at Landau parameters vanishing atl>1 and nonzero, though small, coupling of the density to the spin density and the particle current to the spin current, resulting from the polarization of the system byH _dc. The degeneration is, in general, possible but, at large values of the zero sound velocity with respect to the Fermi velocity, caused by large values of the Landau parameterF ₀ ^s and alsoF ₁ ^s for³He, atF ₀ ^a –0.7, it appears only at positiveF ₁ ^a . All experimental estimations of this parameter agree in its negativity excluding the degeneration of the zero sound and transverse spin waves for³He.     

Friedel oscillations in a two dimensional Fermi liquid

Within linear response the long range oscillations caused by short or long ranged impurities embedded in an otherwise homogeneous electron gas reflect the singularities of the static response function. By making use of the theory of the many-body local fields and the results of recent quantum Monte Carlo studies we have calculated the exact dependence of the amplitude of these oscillations on the density in a two dimensional electron Fermi liquid.     

Transverse spin dynamics of a spin-polarized Fermi liquid

A microscopic derivation of the equations of transverse spin dynamics of a spin-polarized Fermi liquid at zero temperature is given in the leading-order approximation in the frequencies and wave vectors characterizing the spin motion. The equations are applicable for arbitrary degree of polarization and arbitrary deviations of the spin direction from the equilibrium orientation. The solutions describing a coherently precessing two-domain structure and spin waves are examined. In contrast to the assertion discussed in the literature that spin waves are damped at zero temperature, spin waves are found to be undamped in the long-wavelength limit. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 9, 717–721 (10 May 1997)     

Fermi liquid theory: a renormalization group approach

We show how Fermi liquid theory results can be systematically recovered using a renormalization group (RG) approach. Considering a two-dimensional system with a circular Fermi surface, we derive RG equations at one-loop order for the two-particle vertex function in the limit of small momentum () and energy () transfer and obtain the equation which determines the collective modes of a Fermi liquid. The density-density response function is also calculated. The Landau function (or, equivalently, the Landau parameters F _l ^s and F _l ^a ) is determined by the fixed point value of the -limit of the two-particle vertex function (). We show how the results obtained at one-loop order can be extended to all orders in a loop expansion. Calculating the quasi-particle life-time and renormalization factor at two-loop order, we reproduce the results obtained from two-dimensional bosonization or Ward Identities. We discuss the zero-temperature limit of the RG equations and the difference between the Field Theory and the Kadanoff-Wilson formulations of the RG. We point out the importance of n-body () interactions in the latter. Received: 27 June 1997 / Received in final form: 17 December 1997 / Accepted: 26 January 1998     

Coherent spin precession in normal Fermi liquids

In the collisionless limit the Fermi liquid interaction gives rise to nondissipative spin currents. Due to these currents, a coherently precessing spin state may be formed in NMR-experiments with normal Fermi liquids. This state consists of two domains separated by a coherently precessing domain wall. In one of the domains the magnetization is oriented along, and in the other opposite, to the direction of the magnetic field. Such a state has been studied in NMR-experiments in liquid³He and³He-⁴He solutions. The conditions necessary for the formation of the state are considered. Possible other substances in which similar states may be observed are discussed.