Generalized spin-boson models with non-normalizable form factors

TL;DR

This paper extends generalized spin-boson models to include non-normalizable form factors, providing a rigorous framework for more physical scenarios and analyzing the RWA case with advanced mathematical techniques.

Contribution

It introduces a broader class of GSB models with weaker growth constraints on form factors and offers a nonperturbative analysis of the RWA spin-boson model.

Findings

Non-normalizable form factors can be rigorously incorporated into GSB models.

GSB models with singular form factors can be approximated by regular models.

Enhanced analysis of the RWA spin-boson model with explicit resolvent and self-adjointness characterization.

Abstract

Generalized spin-boson (GSB) models describe the interaction between a quantum mechanical system and a structured boson environment, mediated by a family of coupling functions known as form factors. We propose an extension of the class of GSB models which can accommodate non-normalizable form factors, provided that they satisfy a weaker growth constraint, thus accounting for a rigorous description of a wider range of physical scenarios; we also show that such "singular" GSB models can be rigorously approximated by GSB models with normalizable form factors. Furthermore, we discuss in greater detail the structure of the spin-boson model with a rotating wave approximation (RWA): for this model, the result is improved via a nonperturbative approach which enables us to further extend the class of admissible form factors, as well as to compute its resolvent and characterize its self-adjointness domain.