Number of vortices generated in a rotating Bose-Einstein condensates in two-dimensional optical lattice

In the present paper we calculate the number of vortices generated in a rotating Bose-Einstein condensate in two-dimensional optical lattice. Our approach enabled us to parametrize the vortices number in terms of the thermodynamic potential $q(T)$ for the system under consideration. The thermodynamic potential is calculated using the semiclassical approximation approach. The finite size and the interatomic interaction effects are investigated. The calculated results show that the vortices number as a function of the angular velocity of rotation rate depends on the normalized temperature, number of particles, interatomic interaction, and optical potential