Stability of Bose-Einstein condensates confined in traps

Bose-Einstein condensation has been realized as dilute atomic vapors. This achievement has generated immense interest in this field. This article revi ew of recent theoretical research into the properties of trapped dilute-gas Bose-Einstein condensates. Among these propel ties, stability of Bose-Eins tein condensates confined in traps is mainly discussed. Static properties o f the ground state ale investigated by using the variational method. The an alysis is extended to the stability of two-component condensates. Time-deve lopment of the condensate is well-described by the Gross-Pitaevskii equatio n which is known in nonlinear physics as the no nlinear Schrodinger equatio n. For the case that the inter-atomic potential is effectively attractive, a singularity of the solution emerges in a finite time. This phenomenon whi ch we call collapse explains the upper bound for the number of atoms in suc h condensates under traps.