Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder

We consider a time-dependent extension of a perturbative mean-field approach to the homogeneous dirty boson problem by considering how switching on and off a weak disorder potential affects the stationary state of an initially equilibrated Bose-Einstein condensate by the emergence of a disorder-induced condensate deformation. We find that in the switch on scenario the stationary condensate deformation turns out to be a sum of an equilibrium part, that actually corresponds to adiabatic switching on the disorder, and a dynamically-induced part, where the latter depends on the particular driving protocol. If the disorder is switched off afterwards, the resulting condensate deformation acquires an additional dynamically-induced part in the long-time limit, while the equilibrium part vanishes. We also present an appropriate generalization to inhomogeneous trapped condensates. Our results demonstrate that the condensate deformation represents an indicator of the generically non-equilibrium nature of steady states of a Bose gas in a temporally controlled weak disorder.

Automated summary

This study investigates a time-dependent extension to the perturbative mean-field approach for the homogeneous dirty boson problem, delving into the effects of switching on and off a weak disorder potential on the stationary state of a Bose-Einstein condensate. The results show that the condensate deformation serves as an indicator of the non-equilibrium nature of steady states in a temporally controlled weak disorder setting.