Spectral transitions in some Rabi models

TL;DR

This paper investigates spectral transitions in various quantum Rabi models, using subordinacy theory to analyze the spectrum and establish the absence of eigenvalues and singular spectrum across parameter ranges.

Contribution

It applies subordinacy theory to identify and analyze the essential spectrum in multiple Rabi models, providing new insights into their spectral properties.

Findings

Identified the essential spectrum in the models

Proved absence of eigenvalues within the essential spectrum

Confirmed no singular spectrum in the models

Abstract

We consider the transition from discrete to continuous spectrum which occurs in some quantum Rabi models. The subordinacy theory is used to detect and locate the essential spectrum of the intensity-dependent Rabi model, the anisotropic two-photon Rabi model, and the two-photon Rabi-Stark model for the whole range of parameters. The absence of a singular spectrum and the absence of eigenvalues in the interior of the essential spectrum are proved for all models considered.