Norm preserving stochastic field equation for an ideal Bose gas in a trap: numerical implementation and applications

Stochastic field equations represent a powerful tool to describe the thermal state of a trapped Bose gas. Often, such approaches are confronted with the old problem of an ultraviolet catastrophe, which demands a cutoff at high energies. In [arXiv:0809.1002, Phys. B 42, 081001 (2009)] we introduce a quantum stochastic field equation, avoiding the cutoff problem through a fully quantum approach based on the Glauber-Sudarshan P-function. For a close link to actual experimental setups the theory is formulated for a fixed particle number and thus based on the canonical ensemble. In this work the derivation and the non-trivial numerical implementation of the equation is explained in detail. We present applications for finite Bose gases trapped in a variety of potentials and show results for ground state occupation numbers and their equilibrium fluctuations. Moreover, we investigate spatial coherence properties by studying correlation functions of various orders.