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

IF 1.3 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2024-10-18 DOI:10.1007/s00023-024-01495-2

Anne Boutet de Monvel, Mirna Charif, Lech Zielinski

引用次数: 0

Abstract

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 \(O(m^{-1/2}\ln m)\) when m tends to infinity.

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具有共振偏置的量子Rabi模型大特征值的三项渐近公式

研究了具有整数静态偏置的非对称量子Rabi模型大特征值的渐近分布。对于这个模型，我们考虑了广义旋转波近似的一个变体，对应于双特征值的扰动。利用这一思想，我们得到了当m趋于无穷时的第m个特征值的3项渐近公式，其馀估计为\(O(m^{-1/2}\ln m)\)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.