The Schrödinger-Poisson system on open domains

We investigate here the derivation of uniform bounds with respect to the scaled Planck constant $ \varepsilon $ for solutions to the open transient Schrödinger-Poisson system introduced in [9]. The uniform estimates stem from a careful analysis of the non-local in time transparent boundary conditions which allow to restrict the original problem posed on an unbounded domain to a bounded domain of interest. The obtained bounds can be used to perform the semi-classical limit of the system. We also give an existence and uniqueness result of weak solutions while they were previously defined in a strong sense. See [11] for more details.

Olivier Pinaud 2010-07-30