Scattering theory for Lindblad master equations

TL;DR

This paper develops a scattering theory framework for quantum systems described by Lindblad master equations, analyzing particle-target interactions including re-emission and capture scenarios.

Contribution

It introduces a general scattering theory for Lindbladians with bounded interactions, extending dissipative operator analysis to quantum scattering processes.

Findings

Established scattering theory for Lindblad dynamics

Analyzed models with re-emission and capture of particles

Provided mathematical tools for dissipative quantum scattering

Abstract

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.