Evolution Equations for Quantum Semi-Markov Dynamics

Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of quantum evolutions, which is a direct generalisation of the...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2020-07, Vol.22 (7), p.796
Main Authors: Megier, Nina, Smirne, Andrea, Vacchini, Bassano
Format: Article
Language:English
Subjects:
divisibility
Evolution
Generators
Granulation
Laplace transforms
Markov processes
master equations
Mathematical analysis
memory kernel
non-Markovianity
Numerical analysis
Quantum theory
Random processes
System dynamics
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Summary:Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of quantum evolutions, which is a direct generalisation of the corresponding classical concept, guarantees mathematically well-defined master equations, while accounting for a wide range of phenomena, possibly in the non-Markovian regime. In particular, we analyse the emergence of a dephasing term when moving from one type of master equation to the other, by means of several examples. We also investigate the corresponding Redfield-like approximated dynamics, which are obtained after a coarse graining in time. Relying on general properties of the associated classical random process, we conclude that such an approximation always leads to a Markovian evolution for the considered class of dynamics.
ISSN:1099-4300
1099-4300
DOI:10.3390/e22070796