Asymptotic formula for large eigenvalues of the two-photon quantum Rabi model
We prove that the spectrum of the two-photon quantum Rabi Hamiltonian consists of two eigenvalue sequences $(E_m^+)_{m=0}^\infty $, $(E_m^-)_{m=0}^\infty $ satisfying a three-term asymptotic formula with the remainder estimate $O(m^{-1}\ln m)$ when $m$ tends to infinity. By analogy to the one-photon...
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Académie des sciences
2023-12-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.515/ |
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| author | Boutet de Monvel, Anne Zielinski, Lech |
| author_facet | Boutet de Monvel, Anne Zielinski, Lech |
| author_sort | Boutet de Monvel, Anne |
| collection | DOAJ |
| description | We prove that the spectrum of the two-photon quantum Rabi Hamiltonian consists of two eigenvalue sequences $(E_m^+)_{m=0}^\infty $, $(E_m^-)_{m=0}^\infty $ satisfying a three-term asymptotic formula with the remainder estimate $O(m^{-1}\ln m)$ when $m$ tends to infinity. By analogy to the one-photon quantum Rabi model, the leading three terms of this asymptotic formula, describe a generalized rotating-wave approximation for large eigenvalues of the two-photon quantum Rabi model. |
| format | Article |
| id | doaj-art-45157a17b3974e9bb2db94ddc8e7704b |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-45157a17b3974e9bb2db94ddc8e7704b2025-02-07T11:12:14ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-12-01361G111761176610.5802/crmath.51510.5802/crmath.515Asymptotic formula for large eigenvalues of the two-photon quantum Rabi modelBoutet de Monvel, Anne0Zielinski, Lech1Institut de Mathématiques de Jusieu, Université Paris Cité, 8 place Aurélie Nemours, 75013 Paris, FranceLaboratoire de Mathématiques Pures et Appliquées Joseph Liouville UR 2597, Université du Littoral Côte d’Opale, 62228 Calais, FranceWe prove that the spectrum of the two-photon quantum Rabi Hamiltonian consists of two eigenvalue sequences $(E_m^+)_{m=0}^\infty $, $(E_m^-)_{m=0}^\infty $ satisfying a three-term asymptotic formula with the remainder estimate $O(m^{-1}\ln m)$ when $m$ tends to infinity. By analogy to the one-photon quantum Rabi model, the leading three terms of this asymptotic formula, describe a generalized rotating-wave approximation for large eigenvalues of the two-photon quantum Rabi model.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.515/ |
| spellingShingle | Boutet de Monvel, Anne Zielinski, Lech Asymptotic formula for large eigenvalues of the two-photon quantum Rabi model Comptes Rendus. Mathématique |
| title | Asymptotic formula for large eigenvalues of the two-photon quantum Rabi model |
| title_full | Asymptotic formula for large eigenvalues of the two-photon quantum Rabi model |
| title_fullStr | Asymptotic formula for large eigenvalues of the two-photon quantum Rabi model |
| title_full_unstemmed | Asymptotic formula for large eigenvalues of the two-photon quantum Rabi model |
| title_short | Asymptotic formula for large eigenvalues of the two-photon quantum Rabi model |
| title_sort | asymptotic formula for large eigenvalues of the two photon quantum rabi model |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.515/ |
| work_keys_str_mv | AT boutetdemonvelanne asymptoticformulaforlargeeigenvaluesofthetwophotonquantumrabimodel AT zielinskilech asymptoticformulaforlargeeigenvaluesofthetwophotonquantumrabimodel |