Relaxation of particle-hole type excitation in a Fermi system within the diffusion approximation of kinetic theory for the case of constant diffusion and drift coefficients

TL;DR

This paper investigates the relaxation dynamics of particle-hole excitations in a Fermi system using a nonlinear diffusion model, proposing a phenomenological relaxation time formula dependent on excitation energy and mass number.

Contribution

It introduces a numerical approach to solve the diffusion equation for particle-hole excitations and proposes a new phenomenological expression for relaxation time.

Findings

Relaxation time depends on excitation energy.

Relaxation time depends on the mass number.

Numerical solutions illustrate the relaxation process.

Abstract

The time evolution of the distribution function for a particle-hole excitation in a Fermi system was calculated using the direct numerical solution of a nonlinear diffusion equation in momentum space. A phenomenological expression for calculating the relaxation time of such an excitation to its equilibrium value has been proposed. It is shown that the relaxation time is dependent on both the excitation energy and the mass number.