Journal
NEW JOURNAL OF PHYSICS
Volume 22, Issue 8, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1367-2630/ab9f6b
Keywords
open quantum systems; master equations; memory kernels; quantum Markovianity
Categories
Funding
- Alexander von Humboldt Foundation
- FFABR project of MIUR
- Joint Project 'Quantum Information Processing in Non-Markovian Quantum Complex Systems' - FRIAS, University of Freiburg
- IAR, Nagoya University
- UniMi Transition Grant H2020
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Master equations are a useful tool to describe the evolution of open quantum systems. In order to characterize the mathematical features and the physical origin of the dynamics, it is often useful to consider different kinds of master equations for the same system. Here, we derive an exact connection between the time-local and the integro-differential descriptions, focusing on the class of commutative dynamics. The use of the damping-basis formalism allows us to devise a general procedure to go from one master equation to the other and vice versa, by working with functions of time and their Laplace transforms only. We further analyze the Lindbladian form of the time-local and the integro-differential master equations, where we account for the appearance of different sets of Lindbladian operators. In addition, we investigate a Redfield-like approximation, that transforms the exact integro-differential equation into a time-local one by means of a coarse graining in time. Besides relating the structure of the resulting master equation to those associated with the exact dynamics, we study the effects of the approximation on Markovianity. In particular, we show that, against expectation, the coarse graining in time can possibly introduce memory effects, leading to a violation of a divisibility property of the dynamics.
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