Stochastic Gross-Pitaievskii equation for BEC via coarse-grained effective action

ESTEBAN CALZETTA; BEI-LOK HU; ENRIC VERDAGUER

Hong-Kong

Congreso; International conference on the frontiers of nonlinear and complex systems; 2006

We sketch the major steps in a functional integral derivation of anew set of Stochastic Gross-Pitaevsky equations (GPE) for aBose-Einstein condensate (BEC) confined to a trap at zerotemperature with the averaged effects of non-condensate modesincorporated as stochastic sources. The closed-time-path (CTP)coarse-grained effective action (CGEA) or the equivalent influencefunctional method is particularly suitable because it can accountfor the full back-reaction of the noncondensate modes on thecondensate dynamics self-consistently. The Langevin equationsderived here containing nonlocal dissipation together with coloredand multiplicative noises are useful for a stochastic (asdistinguished from say, a kinetic) description of the nonequilibriumdynamics of a BEC.  This short paper contains original researchresults not yet published anywhere.