 02139 Kaiser H.Ch., Neidhardt H., Rehberg J
 Density and current of a dissipative
Schr\"odinger operator
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Mar 20, 02

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Abstract. A net current flow through an open 1dimensional Schr\"odingerPoisson
system is modeled by replacing selfadjoint boundary conditions
by dissipative ones. To give a rigorous
definition of carrier and current densities the wellknown dilation
theory of dissipative operators is used where the selfadjoint
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\"odingerPoisson
system is outlined
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