Scattering matrices for dissipative quantum systems

@article{Faupin2019ScatteringMF,
  title={Scattering matrices for dissipative quantum systems},
  author={J'er'emy Faupin and François Nicoleau},
  journal={Journal of Functional Analysis},
  year={2019}
}
Spectral decomposition of some non-self-adjoint operators
Abstract. We consider non-self-adjoint operators in Hilbert spaces of the form H = H0 +CWC, where H0 is self-adjoint, W is bounded and C is a metric operator, C bounded and relatively compact with
Large time behavior of solutions to Schrödinger equation with complex-valued potential
  • Maha Aafarani
  • Mathematics
    Journal de Mathématiques Pures et Appliquées
  • 2021
Generic nature of asymptotic completeness in dissipative scattering theory
We review recent results obtained in the scattering theory of dissipative quantum systems representing the long-time evolution of a system $S$ interacting with another system $S'$ and susceptible of

References

SHOWING 1-10 OF 63 REFERENCES
On a framework of scattering for dissipative systems
In this paper we study the existence of scattering solutions for some dissipative systems which contain elastic wave with dissipative boundary conditions in a half space of R3 (cf. Dermenjian-Guillot
Scattering Theory for Lindblad Master Equations
We study scattering theory for a quantum-mechanical system consisting of a particle scattered off a dynamical target that occupies a compact region in position space. After taking a trace over the
Open Quantum Systems And Feynman Integrals
Every part of physics offers examples of non-stability phenomena, but probably nowhere are they so plentiful and worthy of study as in the realm of quantum theory. The present volume is devoted to
Eigenfunction Expansions Associated with the Schrödinger Operator with a Complex Potential and the Scattering Theory
The present paper is devoted to a detailed description of the results summarized in the author's preceding note [1]. The purpose °f [1] was a generalization to the non-selfadjoint case of the
Two-channel hamiltonians and the optical model of nuclear scattering
We study some qualitative properties of the scattering operator for a two-channel Hamiltonian which describes elastic neutron scattering from a heavy nucleus. Conditions are given under which the
On the wave operator for dissipative potentials with small imaginary part
We determine the range of the incoming wave operator for the pair of operators $(-\Delta, -\Delta + V_1(x) - i\epsilon V_2(x))$ on $L^2(\bR^n)$ under the conditions $n\ge 3$ and $0$ is a regular
Multiple commutator estimates and resolvent smoothness in quantum scattering theory
We develop an abstract theory of multiple commutator estimates for a self-adjoint operator H and a suitable conjugate operator A which gives C k smoothness of the resolvent as a function of the
Spectral Theory and Differential Operators
This book gives an account of those parts of the analysis of closed linear operators acting in Banach or Hilbert spaces that are relevant to spectral problems involving differential operators, and
...
1
2
3
4
5
...