Non-diffusive phase spreading of a Bose-Einstein condensate at finite temperature

TL;DR

This paper demonstrates that the phase of a finite temperature Bose-Einstein condensate spreads linearly over time, indicating super-diffusive behavior, supported by simulations and analytical calculations.

Contribution

It introduces the concept of non-diffusive, linear phase spreading in Bose-Einstein condensates at finite temperature, extending classical results to the quantum regime.

Findings

Phase spreads linearly in time at long durations.

Super-diffusive behavior is linked to energy conservation.

Analytical and simulation results agree on phase dynamics.

Abstract

We show that the phase of a condensate in a finite temperature gas spreads linearly in time at long times rather than in a diffusive way. This result is supported by classical field simulations, and analytical calculations which are generalized to the quantum case under the assumption of quantum ergodicity in the system. This super-diffusive behavior is intimately related to conservation of energy during the free evolution of the system and to fluctuations of energy in the prepared initial state.