A novel approach to the spectral problem in the two photon Rabi model
arXiv:1911.01965 · doi:10.1088/1751-8121/aa6fb8
Abstract
We explore the spectral problem of the two photon Rabi model from the point of view of complex differential equations in the Bargmann representation. The wave-functions are automatically entire but to ensure finite norm one has to effectively construct asymptotic expansions. This is achieved by means of the Mellin transformation and convergent factorial series, which allow direct computation of the spectral determinant. By further analysing the differential equation satisfied by the Mellin transform, we obtain a new form of the spectral conditions -- in terms of holonomy matrices and contour integrals.
arXiv comment28 pages, 3 figures (including color)
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Cited by in corpus (9)
- Polaron picture of the two-photon quantum Rabi model
- Generalized quantum Rabi model with both one- and two-photon terms: A concise analytical study
- Two-photon-interaction effects in the bad-cavity limit
- Spectral determinant of the two-photon quantum Rabi model
- The mixed quantum Rabi model
- Two-photon Rabi-Stark model
- Level crossings and new exact solutions of the two-photon Rabi model
- Critical spectrum of the anisotropic two-photon quantum Rabi model
- Loss of integrability in a system with two-photon interactions