Dissipative Schrödinger-type operator as a model for generation and recombination

Non-selfadjoint operators play an important role in the modeling of open quantum systems. We consider a one-dimensional Schroedinger-type operator with dissipative boundary conditions and dissipative delta potentials. An explicit description of the characteristic function, the minimal dilation and the generalized eigenfunctions of the dilation is given. The quantities of carrier and current densities are rigorously defined. Furthermore we will show that the current is not constant and that the variation of the current depend essentially on the chosen density matrix and imaginary parts of the delta potentials. This correspondence can be used to model a recombination-generation rate in the open quantum system.