Scattering matrices and Weyl functions
Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt
Abstract
For a scattering system \AΘ,A0\ consisting of selfadjoint extensions AΘ and A0 of a symmetric operator A with finite deficiency indices, the scattering matrix \S()\ and a spectral shift function ξΘ 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 potentials, to Dirac operators and to Schrödinger operators with point interactions.
Create a lesson
Related papers
On the Geometric Structure of Hyperbolic Clifford Bundles and Associated Spin Groups
Eduardo Notte-Cuello
Koopman-von Neumann formalism meets contact Hamiltonian systems
Federico Zadra
Lossless propagation bounds for long-range fermionic interactions
Stefan Teufel
Supersymmetric Neuromorphic FitzHugh--Nagumo model
D. Maroulakos, A. Wal, S. K. Mishra et al.
Separatrix splitting in a multiferroic neuromorphic oscillator: toward Arnold diffusion
D. Maroulakos, Z. Toklikishvili, A. Wal et al.
Anderson localisation in infinite and finite resonator crystals with long-range interactions
Habib Ammari, Xin Fu, Wenjia Jing et al.