We consider the ground state of a trapped Bose-Einstein condensate in two dimensions. In the mean-field approximation, the ground state density profile satisfies the Gross-Pitaevskii equation. We compute the leading quantum corrections to the density profile to second order in an expansion around the Thomas-Fermi limit. By summing the ladder diagrams,we are generalizing Schick’s result for the ...

We study the lengths of the cycles formed by trajectories in the Feynman-Kac representation of the Bose gas. We discuss the occurrence of infinite cycles and their relation to Bose-Einstein condensation.

This article reviews developments in the theory of rapidly rotating degenerate atomic gases. The main focus is on the equilibrium properties of a single component atomic Bose gas, which (at least at rest) forms a Bose-Einstein condensate. Rotation leads to the formation of quantized vortices which order into a vortex array, in close analogy with the behaviour of superfluid helium. Under conditi...

New, commutative probability tools for studying the problem of the Bose-Einstein condensate preservation under thermooeld and standard gauge-invariant perturbations are presented. In particular, a new result on the stability of a Bose-Einstein condensate under the thermooeld perturbations of a polynomial type is presented. The problem of the Bose-Einstein condensate preservation that do arises ...

We find that the key features of the evolution and collapse of a trapped Bose condensate with negative scattering length are predetermined by the particle flux from the non-equilibrium above-condensate cloud to the condensate and by 3-body recombination of Bose-condensed atoms. The collapse, starting once the number of Bose-condensed atoms N 0 reaches the critical value, ceases and turns to exp...

Repulsive Bose-Bose mixtures are known to either mix or phase-separate into pure components. Here we predict a mixed-bubble regime in which bubbles of the mixed phase coexist with one This is beyond-mean-field effect occurs for unequal masses intraspecies coupling constants and due competition between mean-field term, quadratic densities, nonquadratic correction. We find parameters all dimensio...

Bose-Einstein condensates of sodium atoms have been confined in an optical dipole trap using a single focused infrared laser beam. This eliminates the restrictions of magnetic traps for further studies of atom lasers and Bose-Einstein condensates. More than 5 3 106 condensed atoms were transferred into the optical trap. Densities of up to 3 3 1015 cm23 of Bose condensed atoms were obtained, all...

We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. LetM denote a Bose-Mesner algebra on a finite nonempty set X . Fix p ∈ X , and letM∗ and T denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra ofMwith respect to p. By a hyper-duality ofM, we mean an automorphism ψ of T such that ψ(M) =M∗, ψ(M∗) =M; ψ2(A) = ...

The study of low density, ultracold atomic Fermi gases is a promising avenue to understand fermion superfluidity from first principles. One technique currently used to bring Fermi gases in the degenerate regime is sympathetic cooling through a reservoir made of an ultracold Bose gas. We discuss a proposal for trapping and cooling of two-species Fermi-Bose mixtures into optical dipole traps made...