Discrete memory kernel for multitime correlations in non-Markovian quantum processes

Jørgensen, Mathias R.; Pollock, Felix A.

doi:10.1103/physreva.102.052206

Cited by 20 publications

(10 citation statements)

References 34 publications

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“…The only information kept about the environment is its correlation function, or equivalently its spectral density. The evolution of the system's density matrix can then be described, for example, by an approximate weak-coupling master equation [1] or exactly using a process tensor [17] or a tensor network representation of the influence functional as in the time-evolving matrix product operator (TEMPO) method [18,19]. Indeed, a process tensor can be extracted from the TEMPO method [20] and this can lead to still more efficient calculations [21].…”

Section: Etmentioning

confidence: 99%

Unveiling non-Markovian spacetime signaling in open quantum systems with long-range tensor network dynamics

et al. 2021

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Nanoscale devices, either biological or artificial, operate in a regime where the usual assumptions of a structureless Markovian bath do not hold. Being able to predict and study the dynamics of such systems is crucial and is usually done by tracing out the bath degrees of freedom, which implies losing information about the environment. To go beyond these approaches we use a numerically exact method relying on a matrix product state representation of the quantum state of a system and its environment to keep track of the bath explicitly. This method is applied to a specific example of interaction that depends on the spatial structure of a system made of two sites. The result is that we predict a non-Markovian dynamics where long-range couplings induce correlations into the environment. The environment dynamics can be naturally extracted from our method and shine a light on long-time feedback effects that are responsible for the observed non-Markovian recurrences in the eigenpopulations of the system.

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Section: Etmentioning

confidence: 99%

Unveiling non-Markovian spacetime signaling in open quantum systems with long-range tensor network dynamics

et al. 2021

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“…This approach has been popular in the community of mixed quantum-classical dynamics, including problems of nonadiabatic quantum dynamics (beyond the Born-Oppenheimer approximation) and coupling classical and quantum degrees of freedom, where various approximations to the quantum-classical Liouville equation can also be derived [217]. Starting from generalized versions of the master equation, one has to construct an efficient procedure for calculating memory kernels, including non-Markovian cases [218]. Nonperturbative approaches [219][220][221][222] can provide here superior efficiency and accuracy improvements, see, e.g., [223] where they were tested on the Fenna-Matthews-Olson (FMO) light-harvesting complexes important in the analysis of photosynthetic systems [224][225][226][227].…”

Section: Modelling With Nonlocality In Data-driven Environmentsmentioning

confidence: 99%

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Sytnyk

Melnik

2021

MCA

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Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations.

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“…The only information kept about the environment is its correlation function -or equivalently its spectral density. The evolution of the system's density matrix can then be described for example, by an approximate weak coupling master equation [1], or exactly using a process tensor [17] or a tensor network representation of the influence functional as in the Time Evolving Matrix Product Operator (TEMPO) method [18,19]. Indeed, a process tensor can be extracted from the TEMPO method [20] and this can lead to still more efficient calculations [21].…”

Section: S S S S E E (A) (B)mentioning

confidence: 99%

Unveiling non-Markovian spacetime signalling in open quantum systems with long-range tensor network dynamics

Lacroix,

Dunnett,

Gribben

et al. 2021

Preprint

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Nanoscale devices -either biological or artificial -operate in a regime where the usual assumptions of a structureless, Markovian, bath do not hold. Being able to predict and study the dynamics of such systems is crucial and is usually done by tracing out the bath degrees of freedom, which implies losing information about the environment. To go beyond these approaches we use a numerically exact method relying on a Matrix Product State representation of the quantum state of a system and its environment to keep track of the bath explicitly. This method is applied to a specific example of interaction that depends on the spatial structure of the system. The result is that we predict a non-Markovian dynamics where long-range couplings induce correlations into the environment. The environment dynamics can be naturally extracted from our method and shine a light on long time feedback effects that are responsible for the observed non-Markovian recurrences in the eigenpopulations of the system.

show abstract

Discrete memory kernel for multitime correlations in non-Markovian quantum processes

Cited by 20 publications

References 34 publications

Unveiling non-Markovian spacetime signaling in open quantum systems with long-range tensor network dynamics

Unveiling non-Markovian spacetime signaling in open quantum systems with long-range tensor network dynamics

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Unveiling non-Markovian spacetime signalling in open quantum systems with long-range tensor network dynamics

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