Oscillatory Behavior of Large Eigenvalues in Quantum Rabi Models

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 1st three terms of the asymptotics that determine the parameters of the model. This paper is based on our previous paper [5] that it completes and improves.

Automated summary

This paper investigates 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. It obtains the first three terms of the asymptotics for the quantum Rabi model to determine the parameters of the model. This work is based on a previous paper and completes and improves upon its findings.