Sufficient conditions for memory kernel master equation

TL;DR

This paper establishes sufficient conditions for memory kernels that ensure valid quantum dynamical maps, generalizing Markovian semigroups and encompassing most known quantum evolution models.

Contribution

It provides a natural parameterization of dynamical maps that guarantees complete positivity and trace preservation, extending the class of Markovian and semi-Markov evolutions.

Findings

Conditions guarantee legitimate dynamical maps

Class covers Markovian, semi-Markov, and collision models

Generalizes known quantum evolution frameworks

Abstract

We derive sufficient conditions for the memory kernel which guarantee legitimate (completely positive and trace-preserving) dynamical map. It turns out that these conditions provide a natural parameterizations of the dynamical map being a generalization of Markovian semigroup. It is shown that this class of maps cover almost all known examples -- from Markovian semigroup, semi-Markov evolution up to collision models and their generalization.