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Abstract: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.

In this article a system containing two species of identical bosons interacting via a harmonic oscillator potential is considered. It is assumed that the number of bosons of each species is the same and that bosons belonging to the same species repel each other while those belonging to different species attract. The Hamiltonian is diagonalized and the energy spectrum of the system is written down. The behaviour of the system in the thermodynamic limit is studied within the framework of the grand canonical ensemble, and thermodynamic parameters, such as the internal energy, entropy and specific heat capacity are calculated. It is shown that the system exhibits a single species Bose–Einstein condensation when the coupling strengths are equal and a dual species condensation when they are different.