Theory of Bose-Einstein condensation in trapped gases

The phenomenon of Bose-Einstein condensation of dilute gases in traps is re viewed from a theoretical perspective. Mean-field theory provides a framewo rk to understand the main features of the condensation and the role of inte ractions between particles. Various properties of these systems are discuss ed, including the density profiles and the energy of the ground-state confi gurations, the collective oscillations and the dynamics of the expansion, t he condensate fraction and the thermodynamic functions. The thermodynamic l imit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental re sults. Effects of superfluidity including the existence of quantized vortic es and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference ph enomena. The review also assesses the accuracy and limitations of the mean- field approach. [S0034-6861(99)00103-8].