On dynamical semigroup for damped driven Jaynes-Cummings equations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917351498186752 |
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| author | Komech, A. I. Kopylova, E. A. |
| author_facet | Komech, A. I. Kopylova, E. A. |
| contents | The article addresses the damped driven Jaynes-Cummings for quantised one-mode Maxwell field coupled to a two-level molecule. We consider a broad class of damping and pumping which are polynomial in the creation and annihilation operators.
Our main result is the construction of a contraction dynamical semigroup in the Hilbert space of Hermitian Hilbert-Schmidt operators in the case of a nonpositive dissipation operator and time-independent pumping. All trajectories of the semigroup are generalised solutions to the Jaynes-Cummings equations. As a key example, we prove nonpositivity for the basic dissipation operator of Quantum Optics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_17553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On dynamical semigroup for damped driven Jaynes-Cummings equations Komech, A. I. Kopylova, E. A. Mathematical Physics Quantum Physics 81V80, 81S05, 81S08 37K06, 37K40, 37K45, 78A40, 78A60 The article addresses the damped driven Jaynes-Cummings for quantised one-mode Maxwell field coupled to a two-level molecule. We consider a broad class of damping and pumping which are polynomial in the creation and annihilation operators. Our main result is the construction of a contraction dynamical semigroup in the Hilbert space of Hermitian Hilbert-Schmidt operators in the case of a nonpositive dissipation operator and time-independent pumping. All trajectories of the semigroup are generalised solutions to the Jaynes-Cummings equations. As a key example, we prove nonpositivity for the basic dissipation operator of Quantum Optics. |
| title | On dynamical semigroup for damped driven Jaynes-Cummings equations |
| topic | Mathematical Physics Quantum Physics 81V80, 81S05, 81S08 37K06, 37K40, 37K45, 78A40, 78A60 |
| url | https://arxiv.org/abs/2603.17553 |