Hamiltonian formulation of the effective kinetic theory for superfluid Fermi liquids

TL;DR

This paper develops a Hamiltonian-based local kinetic theory for superfluid Fermi liquids at finite temperature, incorporating Landau damping through a quasiparticle distribution function and coupled equations.

Contribution

It introduces a novel Hamiltonian formulation of the effective kinetic theory for superfluid Fermi liquids, including damping effects and a new variable for quasiparticle distributions.

Findings

Hamiltonian structure established for the kinetic theory.

Constructed Hamiltonian to quadratic order.

Inclusion of Landau damping effects at finite temperature.

Abstract

We present in a local form the time dependent effective description of a superfluid Fermi liquid which includes Landau damping effects at $T\neq 0$. This is achieved by the introduction of an additional variable, the quasiparticle distribution function, which obeys a simple kinetic equation. The transport equation is coupled with first order equations for the Goldstone mode and the particle density. We prove that a main feature of this formulation is its Hamiltonian structure relative to a certain Poisson bracket. We construct the Hamiltonian to quadratic order.