  We present a novel quantum stochastic evolution equation for a matter field
describing the canonical state of a weakly interacting ultracold Bose gas. In
the ideal gas limit our approach is exact. This numerically very stable
equation suppresses high-energy fluctuations exponentially, which enables us to
describe condensed and thermal atoms within the same formalism. We present
applications to ground state occupation and fluctuations, density profile of
ground state and thermal cloud, and ground state number statistics. Our main
aim are spatial coherence properties which we investigate through the
determination of interference contrast and spatial density correlations.
Parameters are taken from actual experiments [1].
  [1] S. Hofferberth et al., Nature Physics 4, 489 (2008).
