02-139 Kaiser H.-Ch., Neidhardt H., Rehberg J
Density and current of a dissipative Schr\"odinger operator (569K, Postscript) Mar 20, 02
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Abstract. A net current flow through an open 1-dimensional Schr\"odinger-Poisson system is modeled by replacing self-adjoint boundary conditions by dissipative ones. To give a rigorous definition of carrier and current densities the well-known dilation theory of dissipative operators is used where the self-adjoint dilation is regarded as the Hamiltonian of a larger closed system which contains the open one. The carrier density turns out to be performed by the generalized eigenstates of the dilation while the current density is related to the characteristic function of the dissipative operator. A rigorous setup of a dissipative Schr\"odinger-Poisson system is outlined

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