We calculate the shift in the critical temperature of Bose-Einstein condensation for a dilute Bose-Fermi mixture confined by a harmonic potential to lowest order in both the Bose-Bose and Bose-Fermi coupling constants. The relative importance of the effect on the critical temperature of the boson-boson and boson-fermion interactions is investigated as a function of the parameters of the mixture...

‎Using the explicit forms of eigenstates for linearized operator related to a matrix version of Nonlinear Schrödinger equation‎, ‎soliton perturbation theory is developed for the $F=1$ bright spinor Bose-Einstein condensates‎. ‎A small disturbance of the integrability condition can be considered as a small correction to the integrable equation‎. ‎By choosing appropriate perturbation‎, ‎the soli...

A long standing problem in the theory of superfluidity concerns the question of how close is the connection between Bose condensation and superfluidity[1]. For the case of superfluid He, the Bose condensate fraction is quite small (if not virtually zero), yet the superfluid fraction goes to unity in the limit of low temperatures T → 0. For the superfluid He case, the observation of superfluidit...

The theory of resonant generation of nonground-state Bose-Einstein condensates is extended to Bose-condensed systems at finite temperature. The generalization is based on the notion of representative statistical ensembles for Bose systems with broken global gauge symmetry. Self-consistent equations are derived describing an arbitrary nonequilibrium nonuniform Bose system. The notion of finite-t...

Starting from a Lagrangian density of a superfluid Bose-Fermi mixture we derive a coupled set of nonlinear Schrödinger equations for the system. In the absense of interspecies Bose-Fermi interaction the Bose component satisfies a standard Gross-Pitaevskii equation, whereas the Fermi component satisfies a Ginzburg-Landau-type equation suitable for the Fermi superfluid. To study dynamics we use t...

We study an ideal Bose gas of N atoms contained in a box formed by two identical planar and parallel surfaces S , enclosed by a mantle of height a perpendicular to them. Calling r0 the mean atomic distance, we assume S ≫ r 0 , while a may be comparable to r0. In the bidimensional limit (a/r0 ≡ γ << 1) we find a macroscopic number of atoms in the condensate at temperatures T ∼ O(1/ log(N)); ther...

The ground state properties of interacting Bose gases in external potentials, as considered in recent experiments, are usually described by means of the Gross-Pitaevskii energy functional. We present here the first proof of the asymptotic exactness of this approximation for the ground state energy and particle density of a dilute Bose gas with a positive interaction.

Starting from an effective action for the order parameter field, we derive a coupled set of generalized hydrodynamic equations for a Bose condensate in an optical lattice at finite temperatures. Using the linearized hydrodynamic equations, we study the microscopic mechanism of the Landau instability due to the collisional damping process between condensate and noncondensate atoms. It is shown t...

We report on the study of the momentum distribution of a one-dimensional Bose gas in an optical lattice. From the momentum distribution we extract the condensed fraction of the gas and thereby measure the depletion of the condensate and compare it with a theorical estimate. We have measured the coherence length of the gas for systems with average occupation n̄ > 1 and n̄ < 1 per lattice site. 1 T...

Some recent progress in the mathematical physics of rapidly rotating, dilute Bose gases in anharmonic traps is reviewed.