Symmetry breaking induced by random fluctuations for Bose-Einstein condensates in a double-well trap

TL;DR

This study investigates how random external forces induce symmetry-breaking in coupled Bose-Einstein condensates within a double-well trap, revealing energy diffusion leads to a stationary distribution independent of initial conditions.

Contribution

It introduces a model describing how random fluctuations cause symmetry-breaking and energy diffusion in Bose-Einstein condensates, providing a complete description of their stationary dynamics.

Findings

Energy diffusion enables the system to visit symmetry-breaking states.

The stationary energy distribution depends only on the total number of atoms.

Initial conditions are lost over time, simplifying the system's long-term behavior.

Abstract

This paper is devoted to the study of the dynamics of two weakly-coupled Bose-Einstein condensates confined in a double-well trap and perturbed by random external forces. Energy diffusion due to random forcing allows the system to visit symmetry-breaking states when the number of atoms exceeds a threshold value. The energy distribution evolves to a stationary distribution which depends on the initial state of the condensate only through the total number of atoms. This loss of memory of the initial conditions allows a simple and complete description of the stationary dynamics of the condensate which randomly visits symmetric and symmetry-breaking states.