Decay of the Kohn mode in hydrodynamic regime

TL;DR

This paper develops a hydrodynamic model to analyze the decay of Kohn modes in interacting liquids confined in quasi-one-dimensional traps, revealing how anharmonicity and interactions influence mode lifetimes.

Contribution

It provides an analytical solution for the excitation spectrum of sloshing modes, including effects of anharmonicity and interactions, extending the understanding of Kohn mode decay.

Findings

Kohn mode remains protected in harmonic traps due to the Kohn theorem.

Anharmonicity and interactions cause the Kohn mode to acquire a finite lifetime.

Other sloshing modes thermalize faster than the Kohn mode.

Abstract

We develop a hydrodynamic description of the collective modes of interacting liquids in a quasi-one-dimensional confining potential. By solving Navier-Stokes equations we determine analytically excitation spectrum of sloshing oscillations. For parabolic confinement, the lowest frequency eigenmode is not renormalized by interactions and is protected from decay by the Kohn theorem, which states that center of mass motion decouples from internal dynamics. We find that the combined effect of potential anharmonicity and interactions results in the depolarization shift and final lifetime of the Kohn mode. All other excited modes of sloshing oscillations thermalize with the parametrically faster rates. Our results are significant for the interpretation of recent experiments with trapped Fermi gases that observed weak violation of the Kohn theorem.