# Dynamics of Hot Bose-Einstein Condensates: stochastic Ehrenfest relations for number and energy damping

## TL;DR

This paper develops exact stochastic Ehrenfest relations for hot Bose-Einstein condensates, accounting for damping mechanisms, and validates the theory through simulations of center of mass fluctuations in a trapped system.

## Contribution

It introduces a novel analytical framework for describing number and energy damping in hot Bose-Einstein condensates using stochastic Ehrenfest relations.

## Key findings

- Close agreement between simulations and analytical results
- Foundation for exploring hot Bose-Einstein condensates analytically
- Enhanced understanding of damping mechanisms in BECs

## Abstract

Describing partially-condensed Bose gases poses a long-standing theoretical challenge. We present exact stochastic Ehrenfest relations for the stochastic projected Gross-Pitaevskii equation, including both number and energy damping mechanisms, and all projector terms that arise from the energy cutoff separating system from reservoir. We test the theory by applying it to the centre of mass fluctuations of a harmonically trapped prolate system, finding close agreement between c-field simulations and analytical results. The formalism lays the foundation to analytically explore experimentally accessible hot Bose-Einstein condensates.