Random Lindblad equations from complex environments

Budini, Adrián A.

doi:10.1103/physreve.72.056106

Cited by 76Quantum Mechanics and ApplicationsAdvanced Thermodynamics and Statistical MechanicsQuantum chaos and dynamical systems

Random Lindblad equations from complex environments

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Budini, Adrián A.·2005·Physical Review E

DOI 10.1103/physreve.72.056106

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Abstract

In this paper we demonstrate that Lindblad equations characterized by a random rate variable arise after tracing out a complex structured reservoir. Our results follows from a generalization of the Born-Markov approximation, which relies on the possibility of splitting the complex environment into a direct sum of subreservoirs, each one being able to induce by itself a Markovian system evolution. Strong non-Markovian effects, which microscopically originate from the entanglement with the different subreservoirs, characterize the average system decay dynamics. As an example, we study the anomalous irreversible behavior of a quantum tunneling system described in an effective two-level approximation. Stretched exponential and power law decay behaviors arise from the interplay between the dissipative and unitary hopping dynamics.

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The converse of the statement that non-Markovian processes are non-divisible is not true: there exist non-divisible dynamical processes which are Markovian in the sense of the paper's definition.
“However, it is important to note that the converse of this statement is not true, i.e., there exist non-divisible dynamical processes which are Markovian in the sense of the above definition.”
From Foundations and measures of quantum non-Markovianity (2012) · cites this paper as [35]

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Authors: Budini, A. A.
Affiliations: Max Planck Institute for the Physics of Complex Systems (DE)
Corresponding author: Budini, Adrián A.
ORCID: Budini, Adrián A.
Venue: Physical Review E
Publisher: American Physical Society (APS)
Published: 2005-11-07
Volume: 72
Issue: 5
Pages: 056106-056106
ISSN: 1539-3755 (ISSN-L)
1550-2376
DOI: 10.1103/physreve.72.056106
OpenAlex: W2022532881
Cited by: 75
References: 52
Citations by year: 2026: 2 · 2025: 2 · 2024: 2 · 2023: 1 · 2022: 1 · 2021: 1 · 2020: 3 · 2019: 4 · 2018: 3 · 2017: 5 · 2016: 1 · 2015: 3 · 2014: 3 · 2013: 3 · 2012: 5
FWCI: 3.27
Type: journal article
Language: en
Open access: green
arxiv.org
Licence: link.aps.org/licenses/aps-default-license (vor)
Locations: Physical Review E (publishedVersion)
PubMed (publishedVersion)
arXiv (Cornell University) (submittedVersion)
CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
Max Planck Institute for Plasma Physics (submittedVersion)
MPG.PuRe (Max Planck Society) (submittedVersion)
arXiv (Cornell University)
Topics: Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
Keywords: Lindblad master equation, complex reservoirs, Born-Markov approximation, non-Markovian dynamics, quantum tunneling, two-level system, stretched exponential decay, power-law decay, open quantum systems, entanglement with environment

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