Rieffel's pseudodifferential calculus and spectral analysis of quantum Hamiltonians

TL;DR

This paper applies Rieffel's pseudodifferential calculus to analyze spectral properties of quantum Hamiltonians linked to topological dynamical systems, revealing how their spectra relate to the underlying dynamical structure.

Contribution

It introduces a novel approach using Rieffel's calculus to connect spectral analysis of quantum operators with the topology of dynamical systems.

Findings

Spectral and essential spectra are characterized by the quasi-orbit structure.

Semi-classical spectral behavior is analyzed.

Functorial properties facilitate the spectral study of operator families.

Abstract

We use the functorial properties of Rieffel's pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are extracted from the quasi-orbit structure of the dynamical system. The semi-classical behavior of the families of spectra is also studied.