Equivalence between non-commutative harmonic oscillators and two-photon quantum Rabi models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917969300291584 |
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| author | Nakahama, Ryosuke |
| author_facet | Nakahama, Ryosuke |
| contents | We prove that the non-commutative harmonic oscillator on $L^2(\mathbb{R})\otimes\mathbb{C}^2$ introduced by Parmeggiani and Wakayama is equivalent to the two-photon quantum Rabi model, and they are also equivalent to a holomorphic differential equation on the unit disk. The confluence process of this differential equation and the relation with the one-photon quantum Rabi model are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19814 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivalence between non-commutative harmonic oscillators and two-photon quantum Rabi models Nakahama, Ryosuke Mathematical Physics Classical Analysis and ODEs Representation Theory Spectral Theory 81Q10, 35P05, 34M46 We prove that the non-commutative harmonic oscillator on $L^2(\mathbb{R})\otimes\mathbb{C}^2$ introduced by Parmeggiani and Wakayama is equivalent to the two-photon quantum Rabi model, and they are also equivalent to a holomorphic differential equation on the unit disk. The confluence process of this differential equation and the relation with the one-photon quantum Rabi model are also discussed. |
| title | Equivalence between non-commutative harmonic oscillators and two-photon quantum Rabi models |
| topic | Mathematical Physics Classical Analysis and ODEs Representation Theory Spectral Theory 81Q10, 35P05, 34M46 |
| url | https://arxiv.org/abs/2405.19814 |