Thermodynamic properties of a rotating Bose-Einstein condensation in a deep optical lattice

In this paper, we suggest a conventional semiclassical approximation to calculate several thermodynamic quantities of a rotating Bose- Einstein condensation in a deep optical lattice. Expressions for the condensation fraction, critical temperature, and heat capacity are derived analytically. These expressions are obtained by considering the standard harmonic approximation of the deep optical lattice potential. The suggested approach is able to include the the finite size and the positive chemical potential effects simultaneously. The advantage of our suggested approach is in its simplicity, in comparison to the quantum-mechanical calculations (Bose-Hubbard model). Moreover, its generality allows the treatment of a finite temperature regime