  Temporal correlations in the harmonically trapped finite temperature Bose gas
are studied through the calculation of appropriate phase correlation functions.
A wide parameter regime is covered to ascertain the role that temperature
fluctuations and trap geometry play in the temporal coherence of the 1D to 3D
crossover region. Bogoliubov analysis is used to establish results in the 1D
and spherical limits. Formalism is then developed using the projected
Gross-Pitaevskii equation to calculate correlation functions in 3D simulations
of varying trap elongation and temperature.
