Limits of validity for a semiclassical mean-field two-fluid model for Bose-Einstein condensation thermodynamics

We reinvestigate the Bose-Einstein condensation (BEC) thermodynamics of a weakly interacting dilute Bose gas under the action of a trap using a semiclassical two-fluid mean-field model in order to find the domain of applicability of the model. Such a model is expected to break down once the condition of diluteness and weak interaction is violated. We find that this breakdown happens for values of coupling and density near the present experimental scenario of BEC. With the increase of the interaction coupling and density the model may lead to unphysical results for thermodynamic observables.Comment: Five latex pages, four postscript figures, Accepted in Physica

Generation of oblique dark solitons in supersonic flow of Bose-Einstein condensate past an obstacle

Nonlinear and dispersive properties of Bose-Einstein condensate (BEC) provide a possibility of formation of various nonlinear structures such as vortices and bright and dark solitons (see, e.g., [1]). Yet another type of nonlinear wave patterns has been observed in a series of experiments on the BEC flow past macroscopic obstacles [2]. In [3] these structures have been associated with spatial dispersive shock waves. Spatial dispersive shock waves represent dispersive analogs of the the well-known viscous spatial shocks (oblique jumps of compression) occurring in supersonic flows of compressible fluids past obstacles. In a viscous fluid, the shock can be represented as a narrow region within which strong dissipation processes take place and the thermodynamic parameters of the flow undergo sharp change. On the contrary, if viscosity is negligibly small compared with dispersion effects, the shock discontinuity resolves into an expanding in space oscillatory structure which transforms gradually, as the distance from the obstacle increases, into a \fan" of stationary solitons. If the obstacle is small enough, then such a \fan" reduces to a single spatial dark soliton [4]. Here we shall present the theory of these new structures in BEC

Dissipationless shock waves in repulsive Bose-Einstein condensates

We consider formation of dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms. It is shown that big enough initial inhomogeneity of density leads to wave breaking phenomenon followed by generation of a train of dark solitons. Analytical theory is confirmed by numerical simulations.Comment: 7 pages, 5 figures in JPG forma

Critical numbers of attractive Bose-condensed atoms in asymmetric traps

The recent Bose-Einstein condensation of ultracold atoms with attractive interactions led us to consider the novel possibility to probe the stability of its ground state in arbitrary three-dimensional harmonic traps. We performed a quantitative analysis of the critical number of atoms through a full numerical solution of the mean field Gross-Pitaevskii equation. Characteristic limits are obtained for reductions from three to two and one dimensions, in perfect cylindrical symmetries as well as in deformed ones.Comment: 5 pages, 3 figures. To appear in Phys. Rev.