Thermodynamic parameters of a rotating bose einstein condensation in 2D optical lattice / Hend Ahmed Sayed Abdelghany ; Supervised Abdelhamid A. Galal , Ali Y. Ellithi , Ahmed S. Hassan

Thesis (M.Sc.) - Cairo University - Faculty of Science - Department of Physics

In this thesis, we provide a consistent thermodynamic picture of rotating Bose Einstein condensation in a combined harmonic-optical potential. An expression for condensation fraction, critical temperature and heat capacity are derived analytically using a modi{uFB01}ed semiclassical approximation. In this approximation the sum over the energy levels for the thermodynamical quantities is replaced directly by an ordinary integral weighed with appropriate density of states. The suggested approach is able to include the {uFB01}nite size and positive chemical potential effect simultaneously. The above mentioned thermodynamical parameters are calculated for two di{uFB00}erent physical regimes of the combined harmonic - optical potential. The {uFB01}rst one, which is characterized by a shallow optical lattice and low energy states, the eigenstates of the combined potential are approximated by localized states in a pseudo-band structure. While the second regime, which is characterized by a very deep optical lattice and high energy, the eigenvalue states of the combined potential are approximated by eigenvalue states of a highly anisotropic 3D harmonic oscillator

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