Energy relaxation in the Gross-Pitaevskii equation

TL;DR

This paper introduces a dissipation term in the Gross-Pitaevskii equation to model energy relaxation in condensed bosons, applicable to solid-state Bose-Einstein condensates like magnons and excitons, aligning with superfluid phenomenology.

Contribution

A novel dissipation term in the Gross-Pitaevskii equation that captures stimulated relaxation in solid-state Bose-Einstein condensates.

Findings

Supercurrents remain stable below a critical speed.

Supercurrents decay when exceeding the critical speed.

Model aligns with superfluid behavior.

Abstract

We introduce a dissipation term in the Gross-Pitaevskii equation that describes the stimulated relaxation of condensed bosons due to scattering with a different type of particles. This situation applies to Bose-Einstein condensates of quasi-particles in the solid state, such as magnons and excitons. Our model is compatible with the phenomenology of superfluidity: supercurrents are stable up to a critical speed and decay when they are faster.