Normal and anomalous densities in Bose–Einstein condensates with optical lattices
We study the quantum phase transition from the superfluid to the Mott insulator state in two- and three-dimensional Bose–Einstein condensate with optical lattices using Bose–Hubbard Hamiltonian within the generalized Hatree–Fock–Bogoliubov approximation. The behavior of the depletion and the anomalous fraction has been investigated in the Mott insulator phase. We found that at T = 0, these quantities become significant in two and three dimensions. It is shown also that the dimensionality of the lattice enhances the anomalous density.
Abstract A layer of random defects in the simple cubic Ising model with nearest neighbor ferromagnetic interactions of strength J is considered. Using the real space renormalization group method we calculate defect free energy in the whole temperature range. Specifically, we analyze: the layer of diluted defects, the layer of spin-glass type defects, and the layer of mixed defects. The free energy is strongly dependent on the value of couplings between the defect and the bulk.