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A more accurate semiclassical theory for ultracold gases is derived, in whichthe occupation of high energy modes is dynamically constrained to theBose-Einstein distribution. This regularized version of the SGPE modelpreserves the proper nonlinear energy dependence of coupling to the thermalreservoir. As a result, inclusion of high energy modes above $k_BT$ does notcause a UV divergence. Instead, the reservoir becomes a constraint on the highenergy tails which are included explicitly in the system. Millions of modes canbe treated because computational cost scales slowly, like in othersemiclassical methods. Implementations in 1d and 3d are presented, among theman accurate treatment of the famous case of the quadrupole mode (Jin et al,1997), which had so far eluded satisfactory simulations with any field theory.Our study reveals that observed frequencies and damping of the thermal clouddepended on the experimental signal to noise ratio.

A semiclassical field theory that is freed of the ultraviolet catastrophe