Iwo Bialynicki-Birula, Zofia Bialynicka-Birula
Abstract
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. García-Ripoll, V. M. Pérez-García, and V. Vekslerchik, Phys. Rev. E 64, 056602 (2001)] is extended to 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.