Temporal correlations of elongated Bose gases at finite temperature

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.