Theory Of Normal Fermi Liquids Research Articles

Theory of disordered superconductors with applications to nonlinear current response

Abstract I present a review of the theory and basic equations for charge transport in superconducting alloys starting from the Keldysh formulation of the quasiclassical transport equations developed by Eilenberger, Larkin and Ovchinnikov, and Eliashberg. This formulation is the natural extension of Landau’s theory of normal Fermi liquids to the superconducting state of strongly correlated metals. For dirty metals the transport equations reduce to equations for charge diffusion, with the current response given by the Drude conductivity at low temperatures. The extension of the diffusion equation for the charge and current response of a strongly disordered normal metal to the superconducting state yields Usadel’s equations for the nonequilibrium quasiclassical Keldysh propagator. The conditions for the applicability of the Usadel equations are discussed, the pair-breaking effect of disorder on the current response, including the nonlinear current response to an electromagnetic field in the dirty limit, τ ≪ ℏ/Δ, are reported. The same nonlinearity is shown to lead to source currents for photon generation and nonlinear Kerr rotation driven by the nonlinear response to excitation of the superconductor by a multi-mode electromagnetic field. The potential relevance of the nonlinear source currents to superconducting radio-frequency cavities as detectors of axion-like dark matter candidates is briefly discussed.

Neutral-current interactions of low-energy neutrinos in dense neutron matter

We report the results of a calculation of the response of cold neutron matter to neutral-current interactions with low energy neutrinos, carried out using an effective interaction and effective operators consistently derived within the formalism of Correlated Basis Functions. The neutrino mean free path obtained from the calculated responses turns out to be strongly affected by both short and long range correlations, leading to a sizable increase with respect to the prediction of the Fermi gas model. The consistency between the proposed approach and Landau theory of normal Fermi liquids also has been investigated, using a set of Landau parameters obtained from the matrix elements of the effective interaction.

Landau-Silin kinetic equation in the theory of normal Fermi liquid

In the frame of the Kadanoff-Baym version of the Green’s function method in quantum statistical mechanics it is proved that the Landau-Silin kinetic equation for a normal quantum Fermi liquid is valid in the case when the widths of oneparticle energy levels are taken into account exactly.

Chiral nuclear dynamics with three-body forces

We review recent progress in implementing high-precision chiral two- and three-body forces in nuclear many-body systems beyond light nuclei. We begin with applications to finite nuclei, which we study through the nuclear shell model and self-consistent mean field theory. We then turn our attention to infinite nuclear matter treated within the framework of Landau’s theory of normal Fermi liquids.

Second-order quasiparticle interaction in nuclear matter with chiral two-nucleon interactions

We employ Landau's theory of normal Fermi liquids to study the quasiparticle interaction in nuclear matter in the vicinity of saturation density. Realistic low-momentum nucleon-nucleon interactions evolved from the Idaho N3LO chiral two-body potential are used as input potentials. We derive for the first time exact results for the central part of the quasiparticle interaction computed to second order in perturbation theory, from which we extract the L=0 and L=1 Landau parameters as well as some relevant bulk equilibrium properties of nuclear matter. The accuracy of the intricate numerical calculations is tested with analytical results derived for scalar-isoscalar boson exchange and (modified) pion exchange at second order. The explicit dependence of the Fermi liquid parameters on the low-momentum cutoff scale is studied, which provides important insight into the scale variation of phase-shift equivalent two-body potentials. This leads naturally to explore the role that three-nucleon forces must play in the effective interaction between two quasiparticles.

Kinetic equations in the theory of normal Fermi liquid

On the basis of an improved approximation for the spectral function of one-particle states, it is shown that the Landau-Silin kinetic equations for normal Fermi liquids of neutral and electrically charged particles are valid in a finite temperature region above the temperature of the superfluid transition.

Structure of the collision integral in the theory of normal fermi liquids

A dynamical derivation of the evolution equations for the density matrices under influence of impurity scattering in the theory of normal Fermi liquids is given. In the kinetic region of the evolution the collision integral is derived, taking into account the interaction of the quasiparticles. In the special case, if the energy functional depends only on the density of the quasiparticles, an explicit expression for the collision integral is given. Furthermore, the response of the system to an external perturbation is determined by the interaction of the quasiparticles. The collision integral is used to solve the kinetic equation and to determine the electrical impurity conductivity of the normal Fermi liquid.

Compression modulus of asymmetric nuclear matter

The formula for the compression modulus of asymmetric nuclear matter is derived within the framework of the Landau theory of normal Fermi liquids. The net effect of neutron excess is to make nuclear matter at a fixed density ϱ = ϱ n + ϱ p more incompressible. The increase in the compression modulus is well described by the formula K eα 2, with α = (ϱ n − ϱ p ) ϱ and K e ≈ 270 MeV. When the compression modulus is calculated at the equilibrium density of asymmetric nuclear matter, the net increase reads K e eqα 2, with K e eq ≈ 150 MeV. In the case of strongly asymmetric nuclear matter ( ϱ p ⪡ ϱ) corresponding to the liquid interior of neutron stars, the effect of admixture of protons is to make the matter more compressible, as compared to the pure neutron matter case, the decrease of the compression modulus being proportional to the proton fraction.

T-approximation in the theory of normal fermi liquid

The coefficient of viscosity of3He is used as an example for considering the problem of calculating the macrocharacteristics of Fermi systems within the framework of the statistical eikonal T-approximation. It is shown that within the framework of the microscopic theory, it is possible to obtain an expression, without phenomenological parameters, which describes the viscosity not only in the temperature range in which the Landau theory is applicable but also in the range of little degeneracy.

Isospin and density waves in asymmetric nuclear matter

The excitation of small density oscillations (zero sound) and isospin oscillations (isospin sound) in cold asymmetric nuclear matter (in the ground state ϱ 0 n > ϱ 0 p , ϱ 0 = ϱ 0 n + ϱ 0 p = 0.17 nucleons/fm 3) is investigated within the framework of the Landau theory of normal Fermi liquids. There is only one undamped mode of excitation, which consists predominantly of isospin oscillations, with some admixture of density oscillations. The phase velocity of this undamped wave depends very weakly on the neutron excess and is close to that of a pure isospin wave (isospin sound) in symmetric nuclear matter of the same density. At the neutron excess corresponding to that existing in heavy nuclei the amplitude of the density oscillations constitutes about 30 % of the amplitude of the neutron excess density oscillations. Calculation with a suitably parametrized charge dependent quasiparticle interaction in asymmetric nuclear matter shows that for ( ϱ 0 n − ϱ 0 p)/ ϱ 0 > 0.63 both zero sound and isospin sound are strongly damped.

Zero sound in dense neutron matter

Propagation of zero sound in dense neutron matter is investigated within the framework of the Landau theory of normal Fermi liquids. The effect of the spin polarization of the medium is studied. A calculation performed using the quasi-particle interaction derived from the Reid soft-core nucleon-nucleon potential shows that zero sound can propagate in neutron matter for densities greater than ϱ ∗ ≈ 0.4–0.5 neutrons/fm 3 , and is strongly damped at densities below ϱ ∗.

Collective excitations of nuclear matter

Collective excitations of infinite nuclear matter are investigated within the framework of the Landau theory of normal Fermi liquids. Numerical results are obtained using the existing sets of the Landau parameters of the quasi-particle interaction in nuclear matter. In the hydrodynamic regime all possible modes of the collective vibrations of the breathing, isospin, spin and spin-isospin type can be excited. In the collisionless regime the breathing mode is strongly damped, and only the longitudinal isospin, spin, and spin-isospin modes may propagate, the velocity of propagation being slightly greater than the quasi-particle velocity at the Fermi surface.

Polarization effects in the equation of state for neutron star matter

A new method is given for calculating the equation of state for dense neutron matter taking into consideration the polarization of the medium around a quasiparticle within Landau's theory of normal Fermi liquids. We find that polarization effects make the matter more incompressible.

A note on the sum rule for the parameters in Migdal's theory of nuclei

The Pauli principle sum rule is violated if the interaction of quasiparticles in Landau's theory of normal Fermi liquids is calculated by functional differentiation of the binding energy obtained by Brueckner's method. The reason is the unsymmetrical treatment of particles and holes in Brueckner's theory. The fact that the phenomenologically determined values of Migdal's parameters also violate the sum rule is discussed.