How Quantum Evolution with Memory is Generated in a Time-Local Way

Two widely used but distinct approaches to the dynamics of open quantum systems are the Nakajima-Zwanzig and time-convolutionless quantum master equation, respectively. Although both describe identical quantum evolutions with strong memory effects, the first uses a time-nonlocal memory kernel K, whe...

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Autores principales:	K. Nestmann, V. Bruch, M. R. Wegewijs
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/a9e899d5eedd4de1a0d9f2bb7f25833a
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spelling	oai:doaj.org-article:a9e899d5eedd4de1a0d9f2bb7f25833a2021-12-02T14:57:19ZHow Quantum Evolution with Memory is Generated in a Time-Local Way10.1103/PhysRevX.11.0210412160-3308https://doaj.org/article/a9e899d5eedd4de1a0d9f2bb7f25833a2021-05-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.021041http://doi.org/10.1103/PhysRevX.11.021041https://doaj.org/toc/2160-3308Two widely used but distinct approaches to the dynamics of open quantum systems are the Nakajima-Zwanzig and time-convolutionless quantum master equation, respectively. Although both describe identical quantum evolutions with strong memory effects, the first uses a time-nonlocal memory kernel K, whereas the second achieves the same using a time-local generator G. Here we show that the two are connected by a simple yet general fixed-point relation: G=K[over ^][G]. This allows one to extract nontrivial relations between the two completely different ways of computing the time evolution and combine their strengths. We first discuss the stationary generator, which enables a Markov approximation that is both nonperturbative and completely positive for a large class of evolutions. We show that this generator is not equal to the low-frequency limit of the memory kernel, but additionally “samples” it at nonzero characteristic frequencies. This clarifies the subtle roles of frequency dependence and semigroup factorization in existing Markov approximation strategies. Second, we prove that the fixed-point equation sums up the time-domain gradient or Moyal expansion for the time-nonlocal quantum master equation, providing nonperturbative insight into the generation of memory effects. Finally, we show that the fixed-point relation enables a direct iterative numerical computation of both the stationary and the transient generator from a given memory kernel. For the transient generator this produces nonsemigroup approximations which are constrained to be both initially and asymptotically accurate at each iteration step.K. NestmannV. BruchM. R. WegewijsAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 2, p 021041 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 K. Nestmann V. Bruch M. R. Wegewijs How Quantum Evolution with Memory is Generated in a Time-Local Way
description	Two widely used but distinct approaches to the dynamics of open quantum systems are the Nakajima-Zwanzig and time-convolutionless quantum master equation, respectively. Although both describe identical quantum evolutions with strong memory effects, the first uses a time-nonlocal memory kernel K, whereas the second achieves the same using a time-local generator G. Here we show that the two are connected by a simple yet general fixed-point relation: G=K[over ^][G]. This allows one to extract nontrivial relations between the two completely different ways of computing the time evolution and combine their strengths. We first discuss the stationary generator, which enables a Markov approximation that is both nonperturbative and completely positive for a large class of evolutions. We show that this generator is not equal to the low-frequency limit of the memory kernel, but additionally “samples” it at nonzero characteristic frequencies. This clarifies the subtle roles of frequency dependence and semigroup factorization in existing Markov approximation strategies. Second, we prove that the fixed-point equation sums up the time-domain gradient or Moyal expansion for the time-nonlocal quantum master equation, providing nonperturbative insight into the generation of memory effects. Finally, we show that the fixed-point relation enables a direct iterative numerical computation of both the stationary and the transient generator from a given memory kernel. For the transient generator this produces nonsemigroup approximations which are constrained to be both initially and asymptotically accurate at each iteration step.
format	article
author	K. Nestmann V. Bruch M. R. Wegewijs
author_facet	K. Nestmann V. Bruch M. R. Wegewijs
author_sort	K. Nestmann
title	How Quantum Evolution with Memory is Generated in a Time-Local Way
title_short	How Quantum Evolution with Memory is Generated in a Time-Local Way
title_full	How Quantum Evolution with Memory is Generated in a Time-Local Way
title_fullStr	How Quantum Evolution with Memory is Generated in a Time-Local Way
title_full_unstemmed	How Quantum Evolution with Memory is Generated in a Time-Local Way
title_sort	how quantum evolution with memory is generated in a time-local way
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/a9e899d5eedd4de1a0d9f2bb7f25833a
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How Quantum Evolution with Memory is Generated in a Time-Local Way

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