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We consider a stationary Schrödinger-Poisson system on a bounded interval of the real axis. The Schrödinger operator is defined on the bounded domain with transparent boundary conditions. This allows to model a non-zero current flow trough the boundary of the interval. We prove that the system always admits a solution and give explicit a priori estimates… (More)

We describe an embedding of a quantum mechanically described structure into a macroscopic flow. The open quantum system is partly driven by an adjacent macroscopic flow acting on the boundary of the bounded spatial domain designated to quantum mechanics. This leads to an essentially non– selfadjoint Schrödinger–type operator, the spectral properties of… (More)

- Karoline Disser, Hans-Christoph Kaiser, Joachim Rehberg
- SIAM J. Math. Analysis
- 2015

- Robert Haller-Dintelmann, Wolfgang Höppner, Hans-Christoph Kaiser, Joachim Rehberg, Günter M. Ziegler
- 2010

We investigate optimal elliptic regularity (within the scale of Sobolev spaces) of anisotropic div-grad operators in three dimensions at a multi-material vertex on the Neumann boundary part of the polyhedral spatial domain. The gradient of a solution to the corresponding elliptic PDE (in a neighbourhood of the vertex) is integrable to an index greater than… (More)

Using a classical theorem of Sobolevskii on equations of parabolic type in a Banach space and recently obtained results on elliptic operators with discontinuous coefficients including mixed boundary conditions we prove that quasilinear parabolic systems in diagonal form admit a local, classical solution in the space of p–integrable functions, for some p >… (More)

We regard drift–diffusion equations for semiconductor devices in Lebesgue spaces. To that end we reformulate the (generalized) van Roosbroeck system as an evolution equation for the potentials to the driving forces of the currents of electrons and holes. This evolution equation falls into a class of quasi-linear parabolic systems which allow unique, local… (More)

- Paul N. Racec, Stanley Schade, Hans-Christoph Kaiser
- J. Comput. Physics
- 2013

We present a node-centered finite volume method for computing a representative range of eigenvalues and eigenvectors of the Schrödinger operator on a three-dimensional cylindrically symmetric bounded domain with mixed boundary conditions. More specifically, we deal with a semiconductor nanowire which consists of a dominant host material and contains… (More)

We investigate optimal elliptic regularity of anisotropic div–grad operators in three dimensions at the crossing of a material interface and an edge of the spatial domain on the Neumann boundary part within the scale of Sobolev spaces.

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