Multi-mode description of an interacting Bose-Einstein condensate

We study the equilibrium dynamics of a weakly interacting Bose-Einstein con densate tapped in a box. In our approach we use a semiclassical approximati on similar to the description of a multi-mode laser. In dynamical equations derived from a full N-body quantum Hamiltonian we substitute all creation (and annihilation) operators (of a particle in a given box state) by approp riate c-number amplitudes. The set of nonlinear equations obtained in this way is solved numerically. We show that on the time scale of a few miliseco nds the system exhibits relaxation - reaches an equilibrium with population s of different eigenstates fluctuating around their mean values. (C) 2001 O ptical Society of America.