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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2409.09861 |
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| _version_ | 1866916395712774144 |
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| author | Budini, Adrián A. |
| author_facet | Budini, Adrián A. |
| contents | In this paper we demonstrate that any Markovian master equation defining a completely positive evolution for a quantum-classical hybrid state can always be written in terms of four basic coupling mechanisms. Each of them is characterized by a different "backaction" on each subsystem. On this basis, for each case, we find the conditions under which a diffusive limit is approached, that is, the time evolution can be approximated in terms of the first and second derivatives of the hybrid state with respect to a classical coordinate. In this limit, the restricted class of evolutions that guaranty the positivity of the hybrid state at all times (quantum Fokker-Planck master equations) emerges when the coupling mechanisms lead to infinitesimal (non-finite) changes in both the quantum and classical subsystems. A broader class of diffusive evolutions is obtained when positivity is only granted after a transient time or alternatively is granted after imposing an initial finite width on the state of the classical subsystem. A set of representative examples support these results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09861 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum-classical hybrid dynamics: coupling mechanisms and diffusive approximation Budini, Adrián A. Quantum Physics In this paper we demonstrate that any Markovian master equation defining a completely positive evolution for a quantum-classical hybrid state can always be written in terms of four basic coupling mechanisms. Each of them is characterized by a different "backaction" on each subsystem. On this basis, for each case, we find the conditions under which a diffusive limit is approached, that is, the time evolution can be approximated in terms of the first and second derivatives of the hybrid state with respect to a classical coordinate. In this limit, the restricted class of evolutions that guaranty the positivity of the hybrid state at all times (quantum Fokker-Planck master equations) emerges when the coupling mechanisms lead to infinitesimal (non-finite) changes in both the quantum and classical subsystems. A broader class of diffusive evolutions is obtained when positivity is only granted after a transient time or alternatively is granted after imposing an initial finite width on the state of the classical subsystem. A set of representative examples support these results. |
| title | Quantum-classical hybrid dynamics: coupling mechanisms and diffusive approximation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2409.09861 |