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Trotter-Kato product formula for unitary groups
Pavel Exner, Hagen Neidhardt
Let and be non-negative self-adjoint operators in a separable Hilbert space such that its form sum is densely defined. It is shown that the Trotter product formula hold…
On the unitary equivalence of absolutely continuous parts of self-adjoint extensions
Mark M. Malamud, Hagen Neidhardt
The classical Weyl-von Neumann theorem states that for any self-adjoint operator in a separable Hilbert space there exists a (non-unique) Hilbert-Schmidt operator…
Finite Rank Perturbations, Scattering Matrices and Inverse Problems
Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt
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 Ne…
Trace formulae for dissipative and coupled scattering systems
Jussi Behrndt, Mark M. Malamud, Hagen Neidhardt
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…
The effect of time-dependent coupling on non-equilibrium steady states
Horia D. Cornean, Hagen Neidhardt, Valentin A. Zagrebnov
Consider (for simplicity) two one-dimensional semi-infinite leads coupled to a quantum well via time dependent point interactions. In the remote past the system is decoupled, and e…
On Eisenbud's and Wigner's R-matrix: A general approach
J. Behrndt, H. Neidhardt, E. R. Racec +2
The main objective of this paper is to give a rigorous treatment of Wigner's and Eisenbud's -matrix method for scattering matrices of scattering systems consisting of two selfad…