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Book Sections Year : 2021

Asymptotic behavior of large eigenvalues of the two-photon Rabi model

Abstract

We investigate the asymptotic behavior of large eigenvalues for the two-photon Rabi Hamiltonian, i.e., for the two-photon Jaynes-Cummings model without the rotating wave approximation. We prove that the spectrum of this Hamiltonian consists of two eigenvalues sequences, satisfying the same two-term asymptotic formula with remainder O(n^{−1/3}) when n tends to infinity. We also propose a conjecture on a three-term asymptotic formula modeled on the GRWA for the one-photon Rabi model.
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hal-04147636 , version 1 (04-07-2023)

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Anne Boutet de Monvel, Lech Zielinski. Asymptotic behavior of large eigenvalues of the two-photon Rabi model. Albeverio, Sergio; Balslev, Anindita; Weder, Ricardo. Schrödinger Operators, Spectral Analysis and Number Theory, 348, Springer, pp.89-115, 2021, Springer Proceedings in Mathematics & Statistics, 978-3-030-68492-1. ⟨10.1007/978-3-030-68490-7_5⟩. ⟨hal-04147636⟩
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