Collision models in open system dynamics: A versatile tool for deeper insights?

Abstract

Understanding and simulating how a quantum system interacts and exchanges information or energy with its surroundings is a ubiquitous problem, one which must be carefully addressed in order to establish a coherent framework to describe the dynamics and thermodynamics of quantum systems. Significant effort has been invested in developing various methods for tackling this issue and in this Perspective paper we focus on one such technique, namely collision models, which have emerged as a remarkably flexible approach. We discuss their application to understanding non-Markovian dynamics and to studying the thermodynamics of quantum systems, two areas in which collision models have proven to be particularly insightful. Their simple structure endows them with extremely broad applicability which has spurred their recent experimental demonstrations. By focusing on these areas, our aim is to provide a succinct entry point to this remarkable framework.

Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes

“…Sketch of the information backflow in open quantum system dynamics, which is at the basis of the notion of quantum non-Markovianity used in this paper: initially the reduced states ρ, σ approach each other since the information is flowing out of the reduced system to the environment or to the correlations between the system and the environment (left); on the other hand, an information backflow makes the two states diverge from each other at a later time (right), as can be witnessed via proper state distinguishability quantifiers. This behaviour was observed in fundamental open system models[27,[62][63][64] as well as in general classes of dynamics arising by repeated random interactions as those that are considered in this paper[27,60].…”

“…Note that, even though the definition of non-Markovianity used here has an interpretation in terms of information flow between the system and environment as explained above, it can be directly used at the level of the reduced evolution without the necessity to specify an underlying microscopical model. With this, it can also be applied to our phenomenological approach, where we construct the proper dynamical maps without directly starting from the total Hamiltonian, although realisations-for example, with collisional models-are possible [60,61]. approach each other since the information is flowing out of the reduced system to the environment or to the correlations between the system and the environment (left); on the other hand, an information backflow makes the two states diverge from each other at a later time (right), as can be witnessed via proper state distinguishability quantifiers.…”

Periodically refreshed baths to simulate open quantum many-body dynamics

“…The PReB process may be thought of as a collisional or repeated-interaction model [35][36][37][38][39], where the system repeatedly interacts with multiple finite-sized chains. Collisional or repeated-interaction models have provided valuable insight in a diverse range of settings, with quantum thermodynamics [40][41][42][43] and non-Markovian dynamics [44][45][46][47][48][49] being particularly elegant examples.…”

“…Obtaining the numerically exact dynamics of interacting quantum many-body chains in such two-terminal setups has been an outstanding problem, despite its relevance in a wide range of contexts, such as quantum transport, localization, integrability breaking [24][25][26][27][28][29][30][31][32][33][34], quantum heat engines, and refrigerators [2]. Further, we discuss the relationship between our formalism and collisional (or repeated interaction) models [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], highlighting how our results extend these notions, significantly advancing this highly active field of research. Finally, to demonstrate that our formalism can be combined with not one but any of the existing techniques for numerically exact non-Markovian dynamics [10][11][12][13][14][15][16][17][18][19][20][21][22][23], we also apply our formalism to a spin-boson model employing a completely different numerical technique [17] compared to the one used for the many...…”

Heat Modulation on Target Thermal Bath via Coherent Auxiliary Bath

“…We, in the framework of collision model (or repeated interaction model), will investigate the behaviors of steady heat current between the system and the TTB (also named target heat current-THC, hereafter) and thermal functions of the system with a CAB. Here, it is pointed out that the collision model has become a convenient and powerful tool for studying the dynamics of open quantum system [74], especially for the situations of non-equilibrium bath with quantum effects [75][76][77]. Thus, so far, the general thermodynamic framework of collision models has been explored deeply and established [35,[78][79][80].…”