Behaviour of large eigenvalues for the asymmetric quantum Rabi model

Article type: Research Article

Authors: Charif, Mirna^{a; b} | Fino, Ahmad^c | Zielinski, Lech^{a; *}

Affiliations: [a] LMPA Joseph Liouville, UR 2597, Université du Littoral Côte d’Opale, F-62228 Calais, France | [b] Faculty of Sciences, Department of Mathematics, Lebanese University, P.O. Box 826 Tripoli, Lebanon | [c] College of Engineering and Technology, American University of the Middle East, Kuwait

Correspondence: [*] Corresponding author. E-mail: Lech.Zielinski@univ-littoral.fr.

Abstract: We prove that the spectrum of the asymmetric quantum Rabi model consists of two eigenvalue sequences (Em+)m=0∞, (Em−)m=0∞, satisfying a two-term asymptotic formula with error estimate of the form O(m−1/4), when m tends to infinity.

Keywords: Quantum Rabi model, unbounded self-adjoint operators, discrete spectrum, asymtotic distribution of eigenvalues

DOI: 10.3233/ASY-231875

Journal: Asymptotic Analysis, vol. 136, no. 3-4, pp. 231-256, 2024