Fully Coupled Pauli-Fierz Systems at Zero and Positive Temperature

TL;DR

This paper provides a detailed operator-theoretic spectral analysis of finite-dimensional quantum systems coupled to a massless field, covering both zero and positive temperature regimes without relying on modular theory.

Contribution

It offers a purely operator-theoretic approach to spectral analysis of coupled quantum systems at arbitrary coupling strength, including results at positive temperature.

Findings

Spectral properties of Hamiltonians at zero temperature

Analysis of Liouvilleans at positive temperature

Operator-theoretic proofs valid at arbitrary coupling

Abstract

The purpose of these notes is to give a fairly narrow but thorough introduction to the spectral analysis of Hamiltonians and standard Liouvilleans describing finite dimensional small systems linearly coupled to a scalar massless field or reservoir. The Hamiltonians describe the system at zero temperature, and the standard Liouvillean implements unitarily the dynamics of the system at positive temperature. We focus our attention on results valid at arbitrary coupling strength and whose proofs are purely operator theoretic, i.e. for the standard Liouvillean does not make use of the underlying modular structure. This means that important structure results at positive temperature that does not seem to have a purely operator theoretic proof will only be reviewed.