Transverse zero-sound waves in two-component Fermi liquid

The spectra of transverse zero-sound waves in a two-component degenerate Fermi liquid were studied. The ranges of the existence of two and one waves were determined depending on the liquid interaction parameters.     

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)     

Renormalization group and Fermi liquid theory

We give a Hamiltonian-based interpretation of microscopic Fermi liquid theory within a renormalization group framework. The Fermi liquid fixed-point Hamiltonian with its leading-order corrections is identified and we show that the mean field calculations for this model correspond to the Landau phenomenological approach. This is illustrated first of all for the Kondo and Anderson models of magnetic impurities which display Fermi liquid behaviour at low temperatures. We then show how these results can be deduced by a reorganization of perturbation theory, in close parallel to that for the renormalized φ⁴ field theory. The Fermi liquid results follow from the two lowest order diagrams of the renormalized perturbation expansion. The calculations for the impurity models are simpler than for the general case because the self-energy depends on frequency only. We show, however, that a similar renormalized expansion can be derived also for the case of a translationally invariant system. The parameters specifying the Fermi liquid fixed-point Hamiltonian are related to the renormalized vertices appearing in the perturbation theory. The collective zero sound modes appear in the quasiparticle-quasihole ladder sum of the renormalized perturbation expansion. The renormalized perturbation expansion can in principle be used beyond the Fermi liquid regime to higher temperatures. This approach should be particularly useful for heavy fermions and other strongly correlated electron systems, where the renormalization of the single-particle excitations are particularly large.

We briefly look at the breakdown of Fermi liquid theory from a renormalized perturbation theory point of view. We show how a modified version of the approach can be used in some situations, such as the spinless Luttinger model, where Fermi liquid theory is not applicable. Other examples of systems where the Fermi liquid theory breaks down are also briefly discussed.     

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.     

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.     

Induced gravity and gauge interactions revisited

It has been shown that the primary, old-fashioned idea of Sakharov's induced gravity and gauge interactions, in the “one-loop dominance” version, works astonishingly well yielding phenomenologically reasonable results. As a byproduct, the issue of the role of the UV cutoff in the context of the induced gravity has been reexamined (an idea of self-cutoff induced gravity). As an additional check, the black hole entropy has been used in the place of the action. Finally, it has been explicitly shown that the induced coupling constants of gauge interactions of the standard model assume qualitatively realistic values.     

Transverse waves and the liquid and gaseous states

The distinction between liquid and gas, in a computer simulated Lennard-Jones fluid, persists above the critical temperature, the liquid supporting both transverse and longitudinal waves while the gas displays only longitudinal waves.     

Conductivity rules in the Fermi and charge-spin separated liquid

Ioffe–Larkin rule applies for the pure charge-spin separation regardless of its dimensionality. Here, an extension to this rule as a result of the coexistence of spinon, holon and electron as a single entity in the 2-dimensional (2D) system is derived, which is also in accordance with the original rule.     

Composite elementary particles and self-damping of Fermi interactions

It is shown that the bootstrap and Z=0 mechanisms of composite elementary particle theories emerge from a Fermi theory. The self-damping of Fermi interactions is demonstrated: Such theories are finite at the outset and need no indefinite metric for their definition. A mathematically rigorous peratization scheme is set up rendering unrenormalizable theories finite in terms of perturbation theory.     

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.