Center-of-mass motion in the many-body theory of Bose-Einstein condensates

The method of generating a family of new solutions starting from any wave function satisfying the nonlinear Schrödinger equation in a harmonic potential proposed recently @J. J. Garcı́a-Ripoll, V. M. Pérez-Garcı́a, and V. Vekslerchik, Phys. Rev. E 64, 056602 ~2001!# is extended to the many-body theory of mutually interacting particles. Our method is based on a generalization of the displacement operator known in quantum optics, and results in the separation of the center-of-mass motion from the internal dynamics of many-body systems. The center-of-mass motion is analyzed for an anisotropic rotating trap and a region of instability for intermediate rotational velocities is predicted.