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.

The interplay between local and non-local master equations: exact and approximated dynamics / N. Megier, A. Smirne, B.M. Vacchini. - In: NEW JOURNAL OF PHYSICS. - ISSN 1367-2630. - 22:8(2020 Aug), pp. 083011.1-083011.19. [10.1088/1367-2630/ab9f6b]

The interplay between local and non-local master equations: exact and approximated dynamics

A. Smirne
Secondo
;
B.M. Vacchini
Ultimo
2020

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.
open quantum systems; master equations; memory kernels; quantum Markovianity;
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
Settore FIS/03 - Fisica della Materia
PIANO DI SOSTEGNO ALLA RICERCA 2015-2017 - TRANSITION GRANT LINEA 1A PROGETTO "UNIMI PARTENARIATI H2020"
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/761036
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