Quasicondensation and coherence in the quasi-two-dimensional trapped   Bose gas
  We simulate a trapped quasi-two-dimensional Bose gas using a classical field method. To interpret our results we identify the uniform Berezinskii-Kosterlitz-Thouless (BKT) temperature $T_{BKT}$ as where the system phase space density satisfies a critical value. We observe that density fluctuations are suppressed in the system well above $T_{BKT}$ when a quasi-condensate forms as the first occurrence of degeneracy. At lower temperatures, but still above $T_{BKT}$, we observe the development of appreciable coherence as a prominent finite-size effect, which manifests as bimodality in the momentum distribution of the system.   At $T_{BKT}$ algebraic decay of off-diagonal correlations occurs near the trap center with an exponent of 0.25, as expected for the uniform system.   Our results characterize the low temperature phase diagram for a trapped quasi-2D Bose gas and are consistent with observations made in recent experiments. 
R.N. Bisset, M.J. Davis, T.P. Simula, and P.B. Blakie