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arXiv · 2206.02509

Spectral determinant of the two-photon quantum Rabi model

Daniel Braak
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Abstract

The various generalized spectral determinants (G-functions) of the two-photon quantum Rabi model are analyzed with emphasis on the qualitative aspects of the regular spectrum. Whereas all of them yield at least a subset of the exact regular eigenvalues, only the G-function proposed by Chen et al. in 2012 exhibits an explicitly known pole structure which dictates the approach to the collapse point. We derive this function rigorously employing the $\mathbb{Z}_4$-symmetry of the model and show that its zeros correspond to the complete regular spectrum.

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Daniel Braak. 2022-06-06. Spectral determinant of the two-photon quantum Rabi model. https://doi.org/10.1002/andp.202200519

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