Some current issues concerning statics and dynamics of inhomogeneous superfluid gases
Faculty of Sciences. Physics
Physics and chemistry of liquids. - London
, p. 433-445
After a brief introduction to the static Gross-Pitaevskii (GP) differential equation for the ground state of a Bose-Einstein condensed gas and an example of its use in describing a vortex array in a trapped condensate, a recent generalization is reviewed. By starting from the Bogoliubov-de Gennes equations for superfluid fermions, an integral equation results. This is shown to contain the static GP equation as a limiting case, by means of a low-order gradient expansion of the order parameter. The time-dependent GP approximation is then presented and illustrated by a numerical example concerning drop emission under gravity from a gaseous condensate in an optical lattice. Further selected topics of present interest relating more generally to the dynamics of trapped superfluid gases concern the effects of temperature on collective excitations in a Bose gas and the fingerprints that these excitations in a gas of paired fermions contain of the crossover from a Bardeen-Cooper-Schrieffer correlated assembly to a Bose-Einstein condensate of composite bosons. Finally, some directions are pointed in which interaction of first-principles theory with experiment should prove fruitful.