Hybrid completely positive Markovian quantum-classical dynamics
- URL: http://arxiv.org/abs/2302.13418v2
- Date: Wed, 1 Nov 2023 11:31:48 GMT
- Title: Hybrid completely positive Markovian quantum-classical dynamics
- Authors: Lajos Di\'osi
- Abstract summary: derivation of hybrid quantum-classical dynamics is given in terms of Markovian master equations.
Goal is a brief introduction to state-of-the-art of hybrid dynamics.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A concise and self-contained derivation of hybrid quantum-classical dynamics
is given in terms of Markovian master equations. Many previously known results
are re-derived, revised, some of them completed or corrected. Using as simple
method as possible, our goal is a brief introduction to state-of-the-art of
hybrid dynamics, with a limited discussion of the implications for foundations.
and without discussion of further relevance in quantum-gravity, or chemistry,
numeric methods, etc. Hybrid dynamics is defined as special case of composite
quantum dynamics where the observables of one of the two subsystems are
restricted for the commuting set of diagonal operators in a fixed basis. With
this restriction, the derivation of hybrid dynamical equations is clear
conceptually and simple technically. Jump and diffusive dynamics follow in the
form of hybrid master equations. Their stochastic interpretation (called
unravellings) is derived. We discuss gauge-type ambiguities, problems of
uniqueness, and covariance of the diffusive master equation. Also conditions of
minimum noise and of monitoring the quantum trajectory are derived. We conclude
that hybrid formalism is equivalent with standard Markovian theory of
time-continuous quantum measurement (monitoring) on one hand, and is a
motivating alternative formalism on the other hand.
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