Filters

2006 - 20094

More filters

20194
Reset filters

Settings

Author: Behrndt, Jussi × Author: Neidhardt, Hagen × End date: 2009 × Start date: 2000 × Has files: Yes × Type: Text × WGL Institute: WIAS ×

Search Results

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Scattering theory for open quantum systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Behrndt, Jussi; Malamud, Mark M.; Neidhardt, Hagen; Exner, Pavel
    Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator $A_D$ in a Hilbert space $sH$ is used to describe an open quantum system. In this case the minimal self-adjoint dilation $widetilde K$ of $A_D$ can be regarded as the Hamiltonian of a closed system which contains the open system $[A_D,sH]$, but since $widetilde K$ is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family $[A(mu)]$ of maximal dissipative operators depending on energy $mu$, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schrödinger-Poisson systems.
  • Thumbnail Image
    Item
    Scattering matrices and Weyl functions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Behrndt, Jussi; Malamud, Mark M.; Neidhardt, Hagen
    For a scattering system consisting of two selfadjoint extensions of a symmetric operator A with finite deficiency indices, the scattering matrix and the spectral shift function are calculated in terms of the Weyl function associated with the boundary triplet for A* and a simple proof of the Krein-Birman formula is given. The results are applied to singular Sturm-Liouville operators with scalar- and matrix-valued potentials, to Dirac operators and to Schroedinger operators with point interactions.
  • Thumbnail Image
    Item
    Finite rank perturbations, scattering matrices and inverse problems : dedicated to the memory of our friend Peter Jonas (18.7.1941 - 18.7.2007)
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Behrndt, Jussi; Malamud, Mark M.; Neidhardt, Hagen; Jonas, Peter
    In this paper the scattering matrix of a scattering system consisting of two selfadjoint operators with finite dimensional resolvent difference is expressed in terms of a matrix Nevanlinna function. The problem is embedded into an extension theoretic framework and the theory of boundary triplets and associated Weyl functions for (in general nondensely defined) symmetric operators is applied. The representation results are extended to dissipative scattering systems and an explicit solution of an inverse scattering problem for the Lax-Phillips scattering matrix is presented.
  • Thumbnail Image
    Item
    Trace formulae for dissipative and coupled scattering systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Behrndt, Jussi; Malamud, Mark; Neidhardt, Hagen
    For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract Titchmarsh-Weyl function and a variant of the Birman-Krein formula is proved.