On the connection between microscopic description and memory effects in open quantum system dynamics

Abstract

The exchange of information between an open quantum system and its environment allows us to discriminate among different kinds of dynamics, in particular detecting memory effects to characterize non-Markovianity. Here, we investigate the role played by the system-environment correlations and the environmental evolution in the flow of information. First, we derive general conditions ensuring that two generalized dephasing microscopic models of the global system-environment evolution result exactly in the same open-system dynamics, for any initial state of the system. Then, we use the trace distance to quantify the distinct contributions to the information inside and outside the open system in the two models. Our analysis clarifies how the interplay between system-environment correlations and environmental-state distinguishability can lead to the same information flow from and toward the open system, despite significant qualitative and quantitative differences at the level of the global evolution.

Correlations, Information Backflow, and Objectivity in a Class of Pure Dephasing Models

“…The existence of different environments equally affecting a given system has been studied in different contexts, with the purpose of allowing for more convenient numerical treatments [ 35 , 36 , 37 , 38 ]. The occurrence of the very same reduced evolution starting from different microscopic dynamics in a controlled setting was recently considered also in [ 21 ], in order to investigate the physical mechanism behind memory effects in quantum dynamics.…”

“…However, a given open system dynamics does not arise from a unique microscopic system–environment model, and rather, there are infinitely many system–environment models that result in the same system evolution [ 21 ]. Such an insight calls for a more careful analysis of the information exchanges between the system and its environment, allowing to more precisely pin down the relevant contributions which give rise to, for example, Markovian vs. non-Markovian dynamics [ 22 ], or establish the conditions for classical objectivity [ 23 , 24 , 25 ].…”

“…In this work, we attempt to unravel the contribution that various correlations play in the characterisation of an open system dynamics. To that end, we consider a spin-star dephasing model, where several different initial environmental states, which in turn lead to significantly different correlation profiles, nevertheless produce the same reduced dynamics for the system [ 21 ]. We employ recently developed tools for understanding the emergence of non-Markovianity in terms of the correlations established between the system and environment, as well as changes in the environmental state [ 22 , 27 ], to put into evidence the quite different role that these features play when characterising the dynamics, either in terms of its non-Markovian character or its ability to establish the conditions necessary for classical objectivity.…”

Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes

“…The tracedistance-based definition of non-Markovianity provides a clear-cut interpretation in terms of the information flow between the open quantum system and the environment as the key element, possibly leading to the occurrence of memory effects in the dynamics. In addition, this picture allows us to trace back the exchange of information between the open system and the environment to the correlations established by their mutual interaction [52][53][54][55][56][57]; see Figure 1. Initially, the whole information is contained in the reduced system; however, due to the system-environment interaction, some information gets transferred to external degrees of freedom over the course of the evolution.…”

Adapted projection operator technique for the treatment of initial correlations

“…While the absence of initial system-environment correlations is naturally expected if the interaction between the open system and the environment starts at a specific instant of time and it can be rigorously proven to be justified in the weak-coupling regime [4,5], it is by now clear that initial correlations can have instead a significant impact in many situations, including the interaction of a two-level system with bosonic modes [6][7][8][9], the damped harmonic oscillator [10][11][12][13], spin systems [14], and even many-body [15,16] and transport-related [17][18][19][20] open systems. In addition, a full understanding of the role of the correlations, and possibly of their quantum or classical nature, in the evolution of open quantum systems should indeed include the analysis of those correlations that are present between the system and the environment at the initial time, thus complementing the related studies on the correlations built up by the dynamics [21][22][23][24][25].…”