General collisionless kinetic approach to studying excitations in arbitrary-spin quantum atomic gases

TL;DR

This paper introduces a comprehensive kinetic framework for analyzing high-frequency collective excitations in quantum gases of arbitrary spin, accounting for multipolar interactions and external fields, applicable to both Bose and Fermi systems.

Contribution

It presents a novel, general kinetic approach with a dispersion equation for studying high-frequency modes in arbitrary-spin quantum gases, including multipolar interactions.

Findings

Derived a general dispersion relation for collective modes.

Analyzed spin waves and zero sound in Bose and Fermi gases.

Provided a unified framework for high-frequency excitations in quantum gases.

Abstract

We develop a general kinetic approach to studying high-frequency collective excitations in arbitrary-spin quantum gases. To this end, we formulate a many-body Hamiltonian that includes the multipolar exchange interaction as well as the coupling of a multipolar moment with an external field. By linearizing the respective collisionless kinetic equation, we find a general dispersion equation that allows us to examine the high-frequency collective modes for arbitrary-spin atoms obeying one or another quantum statistics. We analyze some of its particular solutions describing spin waves and zero sound for Bose and Fermi gases.