Heat capacity of trapped bosons in a combined harmonic-lattice potential

In this paper, the heat capacity per particle C(T)/NkB of the trapped bosons in a combined harmonic-lattice potential is calculated within the semicalssical approximation. The main effects which can alter the ideal gas are included simultaneously in the present approach. The calculated results show that the heat capacity has a significant dependence on the lattice depth and temperature. Classical results are recovered at sufficiently high temperature, and that it reproduces the Dulong-Petit law type. Moreover, the behavior of the heat capacity in a deep lattice can be used as an indicator for the quantum phase transition superfluid-Mott insulator. It decreases as the system gets closer to the Mott transition. The calculated results provide a solid theoretical foundation of the current experiments