Perturbation Theory and the Quantum Rabi-model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908837152292864 |
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| author | Malagutti, Marcello Parmeggiani, Alberto |
| author_facet | Malagutti, Marcello Parmeggiani, Alberto |
| contents | In the first part of the paper we study a perturbative model of the Rabi system of Quantum Optics. We are therefore able to describe, through Rellich's theory, an analytic expansion of finite families of eigenvalues, of arbitrary fixed length. In particular, we prove that for finite families of eigenvalues the Braak conjecture holds. In the second part we study the asymptotics of the Weyl spectral counting function of a class of systems that generalize the Quantum Rabi Model to an $N$-level atom ($N\geq3$) with $N-1$ cavity modes of the electromagnetic field. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_17924 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perturbation Theory and the Quantum Rabi-model Malagutti, Marcello Parmeggiani, Alberto Quantum Physics Analysis of PDEs Spectral Theory Primary 35P20, Secondary 35S05 81Q10 In the first part of the paper we study a perturbative model of the Rabi system of Quantum Optics. We are therefore able to describe, through Rellich's theory, an analytic expansion of finite families of eigenvalues, of arbitrary fixed length. In particular, we prove that for finite families of eigenvalues the Braak conjecture holds. In the second part we study the asymptotics of the Weyl spectral counting function of a class of systems that generalize the Quantum Rabi Model to an $N$-level atom ($N\geq3$) with $N-1$ cavity modes of the electromagnetic field. |
| title | Perturbation Theory and the Quantum Rabi-model |
| topic | Quantum Physics Analysis of PDEs Spectral Theory Primary 35P20, Secondary 35S05 81Q10 |
| url | https://arxiv.org/abs/2601.17924 |