Uniqueness for Dissipative Schrödinger-Poisson Systems

Abstract

The paper is devoted to the dissipative Schrödinger-Poisson system. We indicate conditions in terms of the Schrödinger-Poisson data which guarantee the uniqueness of the solution. Moreover, it is shown that if the system is sufficiently small shrunken, then it always admits a unique solution. K

Scattering Matrix, Phase Shift, Spectral Shift and Trace Formula for One-dimensional Dissipative Schrödinger-type Operators

“…Such dissipative Schrödinger-type operators naturally appear in the theory of dissipative Schrödinger-Poisson system which is used to describe quantum transport in semi-conductors, see [9,17,23]. From [14] it s known that purely dissipative operators are completely described by the characteristic function which is an analytic contraction-valued operator function defined in the lower half-plane.…”

“…[11], for the the Lax-Phillips scattering theory under consideration. The results are interesting from a pure operator theoretic view point but, additionally, provide optimal estimates for the carrier density operator of a dissipative Schrödinger-Poisson system in [23]. In…”