Abstract
Describing partially-condensed Bose gases poses a long-standing theoretical challenge. We present exact stochastic Ehrenfest relations for the stochastic projected Gross-Pitaevskii equation, including both number and energy damping mechanisms, and all projector terms that arise from the energy cutoff separating system from reservoir. We test the theory by applying it to the center of mass fluctuations of a harmonically trapped prolate system, finding close agreement between c-field simulations and analytical results. The formalism lays the foundation to analytically explore experimentally accessible hot Bose-Einstein condensates.
Highlights
2.1 Gross-Pitaevskii equationH = d3r ψ∗(r, t) − 2∇2 + V (r, t) + g |ψ(r, t)|2 ψ(r, t), (1)where V (r, t) is an external potential and the interaction strength g = 4π 2as/m is the twobody interaction strength in the cold-collision regime [22] via the s-wave scattering length as and atomic mass m
We find that the analtyic solution of the stochastic Ehrenfest relations (SERs) for the center of mass is in close agreement with stochastic projected Gross-Pitaevskii equation (SPGPE) simulations
We have developed a set of exact stochastic Ehrenfest relations (SERs) for the complete stochastic projected Gross-Pitaevskii equation [10], an equation of motion which has significant application in the study of finite-temperature Bose-Einstein condensates [3, 9, 11]
Summary
Where V (r, t) is an external potential and the interaction strength g = 4π 2as/m is the twobody interaction strength in the cold-collision regime [22] via the s-wave scattering length as and atomic mass m. The Gross-Pitaevskii equation may be generated by taking the functional derivative of the Gross-Pitaevskii Hamiltonian i ∂ ψ(r, t) = δH = Lψ(r, t), (2). ∂t δψ∗(r, t) where the Gross-Pitaevskii operator is.
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