Scattering theory for Lindblad master equations

Marco Falconi (1, 2) , Jérémy Faupin (3) , Jürg Fröhlich (4) , Baptiste Schubnel (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IADM - Institut für Analysis, Dynamik und Modellierung
3 IECL - Institut Élie Cartan de Lorraine
4 ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]

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 degrees of freedom of the target, the dynamics of the particle is generated by a Lindbladian acting on the space of trace-class operators. We study scattering theory for a general class of Lindbladians with bounded interaction terms. First, we consider models where a particle approaching the target is always re-emitted by the target. Then we study models where the particle may be captured by the target. An important ingredient of our analysis is a scattering theory for dissipative operators on Hilbert space.

Domaines: Physique mathématique [math-ph]

Marco Falconi, Jérémy Faupin, Jürg Fröhlich, Baptiste Schubnel. Scattering theory for Lindblad master equations. Communications in Mathematical Physics, 2017, 350 (3), pp.1185-1218. ⟨10.1007/s00220-016-2737-1⟩. ⟨hal-01279979⟩