Elementary Excitations in Quantum Fermi Liquid

TL;DR

This paper extends Landau's Fermi liquid theory by including quantum diffraction effects, deriving a new kinetic equation, and revealing novel excitation modes such as a quantum correction-induced mode and a new frequency spectrum branch.

Contribution

It introduces a generalized kinetic equation incorporating de Broglie wave diffraction, leading to new insights into zero sound and quantum excitations in Fermi liquids.

Findings

Zero sound can exist in an ideal Fermi gas.

A new quantum correction mode is identified.

A new frequency spectrum branch due to weak interaction is disclosed.

Abstract

Landau's theory of Fermi liquids is generalized by incorporating the de Broglie waves diffraction. A newly derived kinetic equation of the Fermi particles is used to derive a general dispersion relation and the excitation of zero sound is studied. A new mode is found due to the quantum correction. It is shown that the zero sound can exist even in an ideal Fermi gas. We also disclose a new branch of frequency spectrum due to the weak interaction.