Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas

We present Quantum Monte Carlo calculations with up to N=576000 interacting bosons in a quasi two-dimensional trap geometry closely related to recent experiments with atomic gases. The density profile of the gas and the non-classical moment of inertia yield intrinsic signatures for the Kosterlitz--Thouless transition temperature T_KT. From the reduced one-body density matrix, we compute the condensate fraction, which is quite large for small systems. It decreases slowly with increasing system sizes, vanishing in the thermodynamic limit. We interpret our data in the framework of the local-density approximation, and point out the relevance of our results for the analysis of experiments.