A non-Markovian approach for two dissipative quantum walks

Cáceres, Manuel O.; Nizama, Marco

doi:10.1140/epjb/e2018-90387-x

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Interplay Between Classical Memory Kernel and Operator Co1

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2020

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“…More precisely the approximation

describes a CP divisible dynamics, since on general grounds

. This is true independently of the waiting time distribution

, since the integral over the memory kernel can be identified with the renewal density, also called sprinkling distribution and obeying the renewal equation [ 51 , 57 , 58 ]

…”

Section: Interplay Between Classical Memory Kernel and Operator Comentioning

confidence: 99%

Evolution Equations for Quantum Semi-Markov Dynamics

Megier

Smirne

Vacchini

2020

Entropy

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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.

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“…More precisely the approximation

describes a CP divisible dynamics, since on general grounds

. This is true independently of the waiting time distribution

, since the integral over the memory kernel can be identified with the renewal density, also called sprinkling distribution and obeying the renewal equation [ 51 , 57 , 58 ]

…”

Section: Interplay Between Classical Memory Kernel and Operator Comentioning

confidence: 99%