Superfluid to Mott insulator quantum phase transition in permanent magnetic lattices

In this thesis we study quantum degenerate Bose gases at finite temperatures in optical and magnetic lattices and in particular the superfluid to Mott insulator quantum phase transition. We investigate ultracold atoms with the gauge P representation and a truncated number-state basis. In studying the many-body physics problems which involve nonlinear terms in the Hamiltonian of the system, the gauge P representation gives more stable results and also the sampling error is reduced, compared with the positive P representation. We consider a grand canonical ensemble of Bose gases and use the Bose-Hubbard model which can describe the dynamics of ultracold atoms in periodic potentials such as optical and magnetic lattices. In our calculations, we consider open boundary conditions.