Transition from non-Markovian to Markovian dynamics for generic environments

Garrido, Nephtalí; Gorin, T.; Pineda, Carlos

doi:10.1103/physreva.93.012113

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…Nakajima and Zwanzig independently derived exact memory kernel master equations using the so-called projection operator method. Since then there have an enormous number of studies of non-Markovian master and stochastic equations , spanning from exploring their mathematical structure, studying the transition between the Markovian and non-Markovian regime [135,136] and applying them chemistry or condensed matter systems. Here, we will not concern with these details and limit our discussion to the overarching structure of the master equation, and in particular how to tell Markovian ones apart from non-Markovian ones.…”

Section: Quantum Master Equationsmentioning

confidence: 99%

Quantum Stochastic Processes and Quantum non-Markovian Phenomena

2021

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The field of classical stochastic processes forms a major branch of mathematics. They are, of course, also very well studied in biology, chemistry, ecology, geology, finance, physics, and many more fields of natural and social sciences. When it comes to quantum stochastic processes, however, the topic is plagued with pathological issues that have led to fierce debates amongst researchers. Recent developments have begun to untangle these issues and paved the way for generalizing the theory of classical stochastic processes to the quantum domain without ambiguities. This tutorial details the structure of quantum stochastic processes, in terms of the modern language of quantum combs, and is aimed at students in quantum physics and quantum information theory. We begin with the basics of classical stochastic processes and generalize the same ideas to the quantum domain. Along the way, we discuss the subtle structure of quantum physics that has led to troubles in forming an overarching theory for quantum stochastic processes. We close the tutorial by laying out many exciting problems that lie ahead in this branch of science.

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Section: Quantum Master Equationsmentioning

confidence: 99%

Quantum Stochastic Processes and Quantum non-Markovian Phenomena

2021

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“…Owing to its diverse applications, various aspects of non-Markovianity are now being studied. Lately, researchers have been focusing on transition from non-Markovian to Markovian dynamics [14][15][16][17][18][19]. Some of them have dealt with bosonic bath of infinite or finite degrees of freedom, while some have considered a qudit system as the environment.…”

Section: Introductionmentioning

confidence: 99%

Non-Markovianity of qubit evolution under the action of spin environment

Chakraborty

Mallick

Mandal

et al. 2019

Sci Rep

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The question, whether an open system dynamics is Markovian or non-Markovian can be answered by studying the direction of the information flow in the dynamics. In Markovian dynamics, information must always flow from the system to the environment. If the environment is interacting with only one of the subsystems of a bipartite system, the dynamics of the entanglement in the bipartite system can be used to identify the direction of information flow. Here we study the dynamics of a two-level system interacting with an environment, which is also a heat bath, and consists of a large number of two-level quantum systems. Our model can be seen as a close approximation to the ‘spin bath’ model at low temperatures. We analyze the Markovian nature of the dynamics, as we change the coupling between the system and the environment. We find the Kraus operators of the dynamics for certain classes of couplings. We show that any form of time-independent or time-polynomial coupling gives rise to non-Markovianity. Also, we witness non-Markovianity for certain parameter values of time-exponential coupling. Moreover, we study the transition from non-Markovian to Markovian dynamics as we change the value of coupling strength.

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“…The transition from Markovian to non-Markovian dynamics via tuning of the system-environmental coupling in various quantum systems has been reported [ 27 , 28 , 29 , 30 , 31 ]. The aim of the present study is to provide an answer to the question of whether there is any connection between the non-Markovianity of classical noise and the non-Markovianity of quantum dynamics of a two-state system (TSS) driven by such a noise source.…”

Section: Introductionmentioning

confidence: 99%

Interplay between Non-Markovianity of Noise and Dynamics in Quantum Systems

Kurt

2023

Entropy

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The non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment, and it is thought to be a resource for various quantum information tasks. We have investigated the non-Markovianity of the dynamics of a two-state system driven by continuous time random walk-type noise, which can be Markovian or non-Markovian depending on its residence time distribution parameters. Exact analytical expressions for the distinguishability as well as the trace distance and entropy-based non-Markovianity measures are obtained and used to investigate the interplay between the non-Markovianity of the noise and that of dynamics. Our results show that, in many cases, the dynamics are also non-Markovian when the noise is non-Markovian. However, it is possible for Markovian noise to cause non-Markovian dynamics and for non-Markovian noise to cause Markovian dynamics but only for certain parameter values.

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Transition from non-Markovian to Markovian dynamics for generic environments

Cited by 3 publications

References 25 publications

Quantum Stochastic Processes and Quantum non-Markovian Phenomena

Quantum Stochastic Processes and Quantum non-Markovian Phenomena

Non-Markovianity of qubit evolution under the action of spin environment

Interplay between Non-Markovianity of Noise and Dynamics in Quantum Systems

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