Oscillatory behavior of large eigenvalues in quantum Rabi models

TL;DR

This paper analyzes the asymptotic behavior of large eigenvalues in quantum Rabi models, providing detailed formulas that help determine model parameters and advancing understanding of their spectral properties.

Contribution

It offers the first three terms of eigenvalue asymptotics for quantum Rabi models, improving previous results and aiding parameter identification.

Findings

Derived the first three asymptotic terms for eigenvalues

Connected asymptotics to model parameters

Enhanced previous spectral analysis of quantum Rabi models

Abstract

We investigate the large $n$ asymptotics of the $n$-th eigenvalue for a class of unbounded self-adjoint operators defined by infinite Jacobi matrices with discrete spectrum. In the case of the quantum Rabi model we obtain the first three terms of the asymptotics which determine the parameters of the model. This paper is based on our previous paper [5] that it completes and improves.