3 Citations
Spectral decomposition of some non-self-adjoint operators
- Mathematics
- 2022
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
- MathematicsJournal de Mathématiques Pures et Appliquées
- 2021
Generic nature of asymptotic completeness in dissipative scattering theory
- Mathematics, Physics
- 2020
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
- Mathematics
- 2003
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
- Mathematics, Physics
- 2016
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
- Mathematics
- 1984
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
- Mathematics
- 1968
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
- Physics, Mathematics
- 2019
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
- MathematicsAsymptot. Anal.
- 2014
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
- Mathematics
- 1984
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
- MathematicsOxford Scholarship Online
- 2018
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…