Dynamic Structure Factor of Normal Fermi Gas from Collisionless to Hydrodynamic Regime

TL;DR

This paper investigates the dynamic structure factor of a normal Fermi gas across different regimes using the moment method, revealing a smooth transition from zero to first sound and characteristic hydrodynamic features.

Contribution

It introduces a comprehensive analysis of the Fermi gas's dynamic structure factor across regimes using the moment method, bridging collisionless and hydrodynamic behaviors.

Findings

Smooth crossover from zero to first sound with temperature and interaction.

Presence of Rayleigh peak characteristic of hydrodynamic regime.

Comparison confirms the moment method's effectiveness.

Abstract

The dynamic structure factor of a normal Fermi gas is investigated by using the moment method for the Boltzmann equation. We determine the spectral function at finite temperatures over the full range of crossover from the collisionless regime to the hydrodynamic regime. We find that the Brillouin peak in the dynamic structure factor exhibits a smooth crossover from zero to first sound as functions of temperature and interaction strength. The dynamic structure factor obtained using the moment method also exhibits a definite Rayleigh peak ($/omega /sim 0$), which is a characteristic of the hydrodynamic regime. We compare the dynamic structure factor obtained by the moment method with that obtained from the hydrodynamic equations.