  We present a stochastic matter field equation for an interacting many-body
Bose system in equilibrium at ultracold finite temperature. Moreover, the
proposed equation can be used for non-equilibrium dynamics on phenomenological
grounds. This stochastic differential equation is based on a field phase space
representation reflecting the underlying canonical density operator (fixed
particle number N). Remarkably, it allows for an efficient numerical
implementation. We apply our canonical c-field method to interference
experiments with quasi-one dimensional Bose gases. Crucial features of these
interference patterns are reproduced very well and also statistical properties
in terms of distributions, e.g. for the contrasts, agree well with experimental
results.
