# Asymptotic completeness in dissipative scattering theory

## TL;DR

This paper investigates the conditions for asymptotic completeness of wave operators in a dissipative quantum scattering framework, linking spectral singularities to the absence of real resonances in Schrödinger operators.

## Contribution

It establishes a precise criterion connecting spectral singularities with asymptotic completeness in dissipative scattering theory.

## Key findings

- Wave operators are asymptotically complete iff no spectral singularities on the real axis.
- Spectral singularities correspond to real resonances in Schrödinger operators.
- Provides a characterization of spectral singularities in the context of dissipative operators.

## Abstract

We consider an abstract pseudo-Hamiltonian for the nuclear optical model, given by a dissipative operator of the form $H = H_V - i C^* C$, where $H_V = H_0 + V$ is self-adjoint and $C$ is a bounded operator. We study the wave operators associated to $H$ and $H_0$. We prove that they are asymptotically complete if and only if $H$ does not have spectral singularities on the real axis. For Schr\"odinger operators, the spectral singularities correspond to real resonances.