Abstract
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.
Highlights
Any realistic physical system is unavoidably coupled to some external degrees of freedom and should be treated as an open system
The former situation refers to the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equation [7, 8], which is associated to quantum dynamical semigroups; the latter is based on more general time-local master equations or on integro-differential master equations, fixed by a memory kernel
We investigated the connection between the time-local and the memory-kernel master equations associated with the dynamics of an open quantum system
Summary
Keywords: open quantum systems, master equations, memory kernels, quantum Markovianity Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
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