Leggett-Rice Systems in Harmonic Traps

TL;DR

This paper investigates spin dynamics in trapped quantum gases using the Leggett equations, extending diffusion models and analyzing long-lived domain formation through perturbation theory, stability analysis, and simulations.

Contribution

It introduces an extension of the bounded diffusion model to trapped systems and analyzes the stability and formation of long-lived spin domains.

Findings

Extended diffusion description for trapped gases

Identified conditions for domain formation

Simulated experimental parameters for observing domains

Abstract

We present two results concerning the spin (or pseudo spin) dynamics of trapped quantum gases in the hydrodynamic regime described by the Leggett equations. First, we apply perturbation theory to extend the ``bounded diffusion'' description to trapped systems for small field inhomogeneities. Second, we study the formation of long-lived domains with a numerical stability analysis of the lowest-lying longitudinal diffusive modes. We also use computer simulations of pi-pulse experiments to determine the range of experimental parameters where the formation of domains can be observed.