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search.filters.applied.f.access: openAccess × Author: Kaiser, Hans-Christoph × Author: Rehberg, Joachim × End date: 2009 × Start date: 2000 × DDC: 510 × Type: Text × Version: publishedVersion ×

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Now showing 1 - 4 of 4
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    Direct computation of elliptic singularities across anisotropic, multi-material edges
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Haller-Dintelmann, Robert; Kaiser, Hans-Christoph; Rehberg, Joachim
    We characterise the singularities of elliptic div-grad operators at points or edges where several materials meet on a Dirichlet or Neumann part of the boundary of a two- or three-dimensional domain. Special emphasis is put on anisotropic coefficient matrices. The singularities can be computed as roots of a characteristic transcendental equation. We establish uniform bounds for the singular values for several classes of three- and fourmaterial edges. These bounds can be used to prove optimal regularity results for elliptic div-grad operators on three-dimensional, heterogeneous, polyhedral domains with mixed boundary conditions. We demonstrate this for the benchmark Lshape problem.
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    Analyticity for some operator functions from statistical quantum mechanics : dedicated to Günter Albinus
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Hoke, Kurt; Kaiser, Hans-Christoph; Rehberg, Joachim; Albinus, Günter
    For rather general thermodynamic equilibrium distribution functions the density of a statistical ensemble of quantum mechanical particles depends analytically on the potential in the Schrödinger operator describing the quantum system. A key to the proof is that the resolvent to a power less than one of an elliptic operator with non-smooth coefficients, and mixed Dirichlet/Neumann boundary conditions on a bounded up to three-dimensional Lipschitz domain factorizes over the space of essentially bounded functions.
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    Modeling and simulation of strained quantum wells in semiconductorlasers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2000) Bandelow, Uwe; Kaiser, Hans-Christoph; Koprucki, Thomas; Rehberg, Joachim
    A model allowing for efficiently obtaining band structure information on semiconductor Quantum Well structures will be demonstrated which is based on matrix-valued kp-Schrödinger operators. Effects such as confinement, band mixing, spin-orbit interaction and strain can be treated consistently. The impact of prominent Coulomb effects can be calculated by including the Hartree interaction via the Poisson equation and the bandgap renormalization via exchange-correlation potentials, resulting in generalized (matrix-valued) Schrödinger-Poisson systems. Band structure information enters via densities and the optical response function into comprehensive simulations of Multi Quantum Well lasers. These device simulations yield valuable information on device characteristics, including effects of carrier transport, waveguiding and heating and can be used for optimization.
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    Monotonicity properties of the quantum mechanical particle density
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Kaiser, Hans-Christoph; Neidhardt, Hagen; Rehberg, Joachim
    An elementary proof of the anti-monotonicity of the quantum mechanical particle density with respect to the potential in the Hamiltonian is given for a large class of admissible thermodynamic equilibrium distribution functions. In particular the zero temperature case is included.