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arXiv · 2510.20201

Strong-coupling asymptotics for anisotropic Rabi model

Masao Hirokawa·Fumio Hiroshima·DongYun Lee
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Abstract

The anisotropic quantum Rabi model provides a continuous interpolation between the quantum Rabi model and the Jaynes-Cummings model obtained via the rotating-wave approximation. In this paper, we investigate the limit as the coupling constant tends to infinity from an operator-theoretic viewpoint. After an explicit quadratic renormalization and a suitable unitary transformation, we identify an effective limiting Hamiltonian and establish the strong resolvent convergence to it. The limiting Hamiltonian determines the asymptotic spectral structure of the anisotropic Rabi model. It provides a unified operator-theoretic description connecting the rotating-wave approximation and the full quantum Rabi model through the strong-coupling limit, thereby revealing the dominant role of the counter-rotating interaction.

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Masao Hirokawa, Fumio Hiroshima, DongYun Lee. 2025-10-23. Strong-coupling asymptotics for anisotropic Rabi model. https://arxiv.org/abs/2510.20201

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