2 00 1 Local invariants in effective hydrodynamics of trapped dilute - gas Bose – Einstein condensates

In the framework of mean-field approximation the dynamics of BoseEinstein condensates can be described by the hydrodynamic-like equations. These equations are analyzed here with account of mutual interaction between condensate and non-condensate atoms. The Lagrange invariants and freezing-in invariants of such a system have been found. This allows to get some necessary conditions for creation of an atom laser with controlled parameters of the beam. Particularly, the atom laser beam can carry quite well defined angular momentum. This can be practically realized in the most simple case, when the vorticity of condensate appears to be a freezingin field. The optimal conditions for a source mode regime are found out in the paper.