Hilbert C*-modules and spectral analysis of many-body systems

TL;DR

This paper investigates the spectral properties of complex many-body Hamiltonians using advanced mathematical frameworks like graded C*-algebras and Hilbert C*-modules, focusing on essential spectrum and spectral types.

Contribution

It introduces a novel approach employing graded C*-algebras and Hilbert C*-modules to analyze spectral properties of non-particle-number-preserving many-body systems.

Findings

Characterization of the essential spectrum for the class of Hamiltonians

Establishment of Mourre estimates for these systems

Proof of absence of singular continuous spectrum in the studied models

Abstract

We study the spectral properties of a class of many channel Hamiltonians which contains those of systems of particles interacting through k-body and field type forces which do not preserve the number of particles. Our results concern the essential spectrum, the Mourre estimate, and the absence of singular continuous spectrum. The appropriate formalism involves graded C*-algebras and Hilbert C*-modules as basic tools.