Michael Baro, Hagen Neidhardt
Dissipative Schroedinger-type operator as a model for
generation and recombination
(454K, postscript)
ABSTRACT. 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.