Particle number fluctuations in a cloven trapped Bose gas at finite temperature

We study fluctuations in the atom number difference between two halves of a harmonically trapped Bose gas in three dimensions. We solve the problem analytically for noninteracting atoms. In the interacting case we find an analytical solution in the Thomas-Fermi and high temperature limit in good agreement with classical field simulations. In the large system size limit, fluctuations in the number difference are maximal for a temperature T similar or equal to 0.7T(c) where T-c is the critical temperature, independently of the trap anisotropy. The occurrence of this maximum is due to an interference effect between the condensate and the noncondensed fields.