Asymptotic behavior of large eigenvalues of Jaynes-Cummings type models

TL;DR

This paper analyzes the asymptotic behavior of large eigenvalues in a class of unbounded operators related to the Jaynes-Cummings model, providing insights into their spectral properties without the RWA.

Contribution

It establishes the asymptotic behavior of large eigenvalues for a broad class of operators including the Jaynes-Cummings Hamiltonian without RWA.

Findings

Derived asymptotic formulas for large eigenvalues

Extended spectral analysis to non-RWA Jaynes-Cummings models

Provided mathematical framework for spectral properties of unbounded operators

Abstract

We consider a class of unbounded self-adjoint operators including the Hamiltonian of the Jaynes-Cummings model without the rotating-wave approximation (RWA). The corresponding operators are defined by infinite Jacobi matrices with discrete spectrum. Our purpose is to give the asymptotic behavior of large eigenvalues.