Time-dependent dissipation in nonlinear Schrödinger systems

Abstract

A coupled nonlinear Schrödinger–Poisson equation is considered which contains a time-dependent dissipation function as a specific model of dissipation effects in nonlinear quantum transport theory and other areas. The Wigner–Poisson equation associated with this system is derived. Using conservation and quasiconservation laws and certain growth assumptions for the nonlinearities and the dissipation function, global existence of solutions to the Cauchy problem of the time-dependent Schrödinger–Poisson system is shown both for small (attractive case) or arbitrary data (repulsive case).