A semiclassical field theory that is freed of the ultraviolet catastrophe

A more accurate semiclassical theory for ultracold gases is derived, in which the occupation of high energy modes is dynamically constrained to the Bose-Einstein distribution. This regularized version of the SGPE model preserves the proper nonlinear energy dependence of coupling to the thermal reservoir. As a result, inclusion of high energy modes above $k_BT$ does not cause a UV divergence. Instead, the reservoir becomes a constraint on the high energy tails which are included explicitly in the system. Millions of modes can be treated because computational cost scales slowly, like in other semiclassical methods. Implementations in 1d and 3d are presented, among them an 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 cloud depended on the experimental signal to noise ratio.