Time dependent quantum scattering theory on complete manifolds with a corner of codimension 2

TL;DR

This paper establishes the existence, orthogonality, and asymptotic completeness of wave operators for a compatible Laplacian on complete manifolds with a codimension 2 corner, using time-dependent methods from many-body quantum theory.

Contribution

It introduces a novel analysis of wave operators and asymptotic completeness for Laplacians on manifolds with corners of codimension 2, extending quantum scattering theory to complex geometric settings.

Findings

Proves existence and orthogonality of wave operators.

Demonstrates asymptotic completeness for the Laplacian.

Employs time-dependent methods from many-body Schrödinger equations.

Abstract

We show the existence and orthogonality of wave operators naturally associated to a compatible Laplacian on a complete manifold with a corner of codimension 2. In fact, we prove asymptotic completeness i.e. that the image of these wave operators is equal to the space of absolutely continuous states of the compatible Laplacian. We achieve this last result using time dependent methods coming from many-body Schr\"odinger equations.