This paper deals with mathematical questions for Bose gases below the temperature TBEC where Bose-Einstein condensation sets in. The model considered is of two-component type, consisting of a kinetic equation for the distribution function of a gas of (quasi-)particles interacting with a Bose condensate, which is described by a Gross-Pitaevskii equation. Existence results and moment estimates ar...

In an earlier paper (J. Phys. A: Math. Gen. 26 (1993) 4689) we introduced the notion of cycle percolation in the Bose gas and conjectured that it occurs if and only if there is Bose-Einstein condensation. Here we give a complete proof of this statement for the perfect and the imperfect (mean-field) Bose gas and also show that in the condensate there is an infinite number of macroscopic cycles.

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 ...

Half-quantum vortices in strongly correlated Bose liquids. Abstract We discuss the structure of a vortex in a superfluid Bose liquid with a suppressed Bose-Einstein condensate and an intensive pair correlated condensate. The vortex represents the pair of half-quantum vortices topologically confined by the soliton. In strongly interacting and strongly correlated Bose liquid – su-perfluid 4 He – ...