Momentum distribution and correlation function of quasicondensates in elongated traps

We calculate the spatial correlation function and momentum distribution of a phase-fluctuating, elongated three-dimensional condensate in a trap and in free expansion. We take the inhomogeneous density profile into account via a local-density approximation. We find an almost Lorentzian momentum distribution, in stark contrast with a Heisenberg-limited Thomas-Fermi condensate.