Scattering theory for multistate Schr\"odinger operators

TL;DR

This paper develops scattering theory for multistate Schrödinger operators in molecular dynamics, establishing spectral properties and propagation estimates even with non-decaying potentials and many-body interactions.

Contribution

It introduces new spectral and propagation results for multistate Schrödinger operators, including non-decaying potentials and many-body structures, with Mourre and minimal velocity estimates.

Findings

Absence of singular continuous spectrum

Propagation estimates at speeds above a positive constant

Mourre and minimal velocity estimates for many-body operators

Abstract

We study multistate Schr\"odinger operators related to molecular dynamics. We consider potentials which do not necessarily decay and prove absence of the singular continuous spectrum and propagation estimates which mean the scattering at speed larger than a positive constant and decay of the state with potentials higher than considered energy at infinity. We also consider the multistate Schr\"odinger operators with many-body structures. We obtain the Mourre estimate and the minimal velocity estimate for the many-body operators. The lower bound of the velocity is determined by the distance between the energy and thresholds below the energy.