Invariance of the Kohn (sloshing) mode in a conserving theory

TL;DR

This paper proves that the center of mass oscillation in a many-body system within a harmonic trap remains unaffected by interactions when using conserving approximations, applicable across various conditions.

Contribution

It demonstrates that conserving approximations preserve the Kohn mode in many-body systems, extending the understanding of collective oscillations under broad conditions.

Findings

Kohn mode invariance is maintained under conserving approximations.

The proof applies to zero and finite temperatures, as well as nonequilibrium states.

The result holds in both linear and nonlinear response regimes.

Abstract

It is proven that the center of mass (COM or Kohn) oscillation of a many-body system in a harmonic trap coincides with the motion of a single particle as long as conserving approximations are applied to treat the interactions. The two conditions formulated by Kadanoff and Baym \cite{kb-book} are shown to be sufficient to preserve the COM mode. The result equally applies to zero and finite temperature, as well as to nonequilibrium situations, and to the linear and nonlinear response regimes.