Three-Term Asymptotic Formula for Large Eigenvalues of the Quantum Rabi Model with a Resonant Bias

We investigate the asymptotic distribution of large eigenvalues of the asymmetric quantum Rabi model with an integer static bias. For this model, we consider a variant of the generalized rotating-wave approximation, corresponding to perturbations of double eigenvalues. Using this idea, we obtain a three-term asymptotic formula for the m-th eigenvalue with the remainder estimate \(O(m^{-1/2}\ln m)\) $O(m^{-1/2}lnm)$ when m tends to infinity.