Genuine phase diffusion of a Bose-Einstein condensate in the microcanonical ensemble: A classical field study

TL;DR

This study demonstrates that in a classical field model, a Bose-Einstein condensate's phase exhibits genuine diffusion in the microcanonical ensemble, with a diffusion coefficient following a simple scaling law and extending insights to quantum fields.

Contribution

It provides the first detailed analysis of phase diffusion in a Bose-Einstein condensate within the microcanonical ensemble using classical and quantum field models.

Findings

Phase variance grows linearly with time.

Diffusion coefficient follows a simple scaling law.

Approximate calculations agree with numerical results.

Abstract

Within the classical field model, we find that the phase of a Bose-Einstein condensate undergoes a true diffusive motion in the microcanonical ensemble, the variance of the condensate phase change between time zero and time $t$ growing linearly in $t$. The phase diffusion coefficient obeys a simple scaling law in the double thermodynamic and Bogoliubov limit. We construct an approximate calculation of the diffusion coefficient, in fair agreement with the numerical results over the considered temperature range, and we extend this approximate calculation to the quantum field.