BEC From a Time-Dependent Variational Point of View

TL;DR

This paper develops a generalized dynamical framework for trapped Bose gases at finite temperature using a time-dependent variational approach, extending the Gross-Pitaevskii equations to include thermal and anomalous densities.

Contribution

It introduces a new set of coupled equations derived from a variational principle that unify condensate, thermal cloud, and anomalous density dynamics.

Findings

Generalizes Gross-Pitaevskii equations for finite temperature.

Provides a consistent coupling between condensate and thermal components.

Derives equations applicable to trapped Bose gases at finite temperature.

Abstract

We use the time-dependent variational of Balian and Veneroni to derive a set of equations governing the dynamics of a trapped Bose gas at finite temperature. We show that this dynamics generalizes the Gross-Pitaevskii equations in that it introduces a consistent coupling between the evolution of the condensate density, the thermal cloud and the anomalous density.