Markovian master equations for quantum-classical hybrid systems
| Autor: | Barchielli, Alberto |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Phys. Lett. A 492 (2023) 129230 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.physleta.2023.129230 |
| Popis: | The problem of constructing a consistent quantum-classical hybrid dynamics is afforded in the case of a quantum component in a separable Hilbert space and a continuous, finite-dimensional classical component. In the Markovian case, the problem is formalized by the notion of hybrid dynamical semigroup. A classical component can be observed without perturbing the system and information on the quantum component can be extracted, thanks to the quantum-classical interaction. This point is formalized by showing how to introduce positive operator valued measures and operations compatible with the hybrid dynamical semigroup; in this way the notion of hybrid dynamics is connected to quantum measurements in continuous time. Then, the case of the most general quasi-free generator is presented and the various quantum-classical interaction terms are discussed. To bee quasi-free means to send, in the Heisenberg description, hybrid Weyl operators into multiples of Weyl operators; the results on the structure of quasi-free semigroups were proved in the article arXiv:2307.02611. Even in the pure quantum case, a quasi-free semigroup is not restricted to have only a Gaussian structure, but also jump-type terms are allowed. An important result is that, to have interactions producing a flow of information from the quantum component to the classical one, suitable dissipative terms must be present in the generator. Finally, some possibilities are discussed to go beyond the quasi-free case. Comment: 12 pages. Section 2.1 has been reformulated. Some typos have been corrected |
| Databáze: | arXiv |
| Externí odkaz: |
|