Asymptotic formula for large eigenvalues of the two-photon quantum Rabi model

被引：1

作者：

de Monvel, Anne Boutet ^{[1
]}

Zielinski, Lech ^{[2
]}

机构：

[1] Univ Paris Cite, Inst Math Jusieu, 8 Pl Aurelie Nemours, F-75013 Paris, France

[2] Univ Littoral Cote dOpale, Lab Math Pures & Appl Joseph Liouville UR 2597, F-62228 Calais, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2023年 / 361卷 / 01期

关键词：

JAYNES-CUMMINGS MODEL;

D O I：

10.5802/crmath.515

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the spectrum of the two-photon quantum Rabi Hamiltonian consists of two eigenvalue sequences (E-m(+))(infinity)(m=0), (E-m(-))(infinity)(m=0) 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.

引用

页码：1761 / 1766

页数：6

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