Quantum-classical hybrid dynamics: coupling mechanisms and diffusive approximation

• URL: http://arxiv.org/abs/2409.09861v1
• Date: Sun, 15 Sep 2024 20:51:19 GMT
• Title: Quantum-classical hybrid dynamics: coupling mechanisms and diffusive approximation
• Authors: Adrián A. Budini,
• Abstract summary: We show 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. A broader class of diffusive evolutions is obtained when positivity is only granted after a transient time.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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