Quantum corrections of the truncated Wigner approximation applied to an exciton transport model

Ivanov, A.P.; Breuer, Heinz‐Peter

doi:10.1103/physreve.95.042115

Cited by 5 publications

(2 citation statements)

References 41 publications

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“…Various numerical schemes for the WDF, including implementation of boundary conditions, such as inflow, outflow, or absorbing boundary conditions [25][26][27], and a Fourier based treatment of potential operators have been developed [1,3]. Varieties of application for quantum electronic devices [28][29][30][31][32][33][34][35], most notably the RTD [36][37][38][39][40][41][42][43][44][45][46] that includes the results from the QHFPE approach [22][23][24], quantum ratchet [47][48][49], chemical reaction [13,14], multi-state nonadiabatic electron transfer dynamics [50][51][52][53][54][55], photo-isomerization through a conical intersection [56], molecular motor [57], linear and nonlinear spectroscopies [58][59][60], in which the quantum entanglement between the system and bath plays an essential role, have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Open quantum dynamics theory on the basis of periodical system-bath model for discrete Wigner function

Iwamoto

Tanimura

2021

J Comput Electron

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Discretizing distribution function in a phase space for an efficient quantum dynamics simulation is non-trivial challenge, in particular for a case that a system is further coupled to environmental degrees of freedom. Such open quantum dynamics is described by a reduced equation of motion (REOM) most notably by a quantum Fokker-Planck equation (QFPE) for a Wigner distribution function (WDF). To develop a discretization scheme that is stable for numerical simulations from the REOM approach, we find that a twodimensional (2D) periodically invariant system-bath (PISB) model with two heat baths is an ideal platform not only for a periodical system but also for a system confined by a potential. We then derive the numerically "exact" hierarchical equations of motion (HEOM) for a discrete WDF in terms of periodically invariant operators in both coordinate and momentum spaces. The obtained equations can treat non-Markovian heat-bath in a non-perturbative manner at finite temperatures regardless of the mesh size. The stability of the present scheme is demonstrated in a high-temperature Markovian case by numerically integrating the discrete QFPE with by a coarse mesh for a 2D free rotor and harmonic potential systems for an initial condition that involves singularity.

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Section: Introductionmentioning

confidence: 99%

Open quantum dynamics theory on the basis of periodical system-bath model for discrete Wigner function

Iwamoto

Tanimura

2021

J Comput Electron

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“…Various numerical schemes for the WDF, including the implementation of boundary conditions, for example inflow, outflow, or absorbing boundary conditions [25,26,27], and a Fourier based treatment of potential operators [1,3], have been developed. Varieties of application for quantum electronic devices [28,29,30,31,32,33,34,35], most notably the RTD [36,37,38,39,40,41,42,43,44,45,46] that includes the results from the QHFPE approach [22,23,24], quantum ratchet [47,48,49], chemical reaction [13,14], multi-state nonadiabatic electron transfer dynamics [50,51,52,53,54,55], photo-isomerization through a conical intersection [56], molecular motor [57], linear and nonlinear spectroscopies [58,59,60], in which the quantum entanglement between the system and bath plays an essential role, have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Open quantum dynamics theory on the basis of periodical system-bath model for discrete Wigner function

Iwamoto,

Tanimura

2021

Preprint

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Discretizing a distribution function in a phase space for an efficient quantum dynamics simulation is a non-trivial challenge, in particular for a case that a system is further coupled to environmental degrees of freedom. Such open quantum dynamics is described by a reduced equation of motion (REOM) most notably by a quantum Fokker-Planck equation (QFPE) for a Wigner distribution function (WDF). To develop a discretization scheme that is stable for numerical simulations from the REOM approach, we employ a two-dimensional (2D) periodically invariant system-bath (PISB) model with two heat baths. This model is an ideal platform not only for a periodic system but also for a non-periodic system confined by a potential. We then derive the numerically "exact" hierarchical equations of motion (HEOM) for a discrete WDF in terms of periodically invariant operators in both coordinate and momentum spaces. The obtained equations can treat non-Markovian heat-bath in a non-perturbative manner at finite temperatures regardless of the mesh size. As demonstrations, we numerically integrate the discrete QFPE for a 2D free rotor and harmonic potential systems in a high-temperature Markovian case using a coarse mesh with initial conditions that involve singularity.

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Recent advances in Wigner function approaches

Weinbub

Ferry

2018

Applied Physics Reviews

237

174

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The Wigner function was formulated in 1932 by Eugene Paul Wigner, at a time when quantum mechanics was in its infancy. In doing so, he brought phase space representations into quantum mechanics. However, its unique nature also made it very interesting for classical approaches and for identifying the deviations from classical behavior and the entanglement that can occur in quantum systems. What stands out, though, is the feature to experimentally reconstruct the Wigner function, which provides far more information on the system than can be obtained by any other quantum approach. This feature is particularly important for the field of quantum information processing and quantum physics. However, the Wigner function finds wide-ranging use cases in other dominant and highly active fields as well, such as in quantum electronics—to model the electron transport, in quantum chemistry—to calculate the static and dynamical properties of many-body quantum systems, and in signal processing—to investigate waves passing through certain media. What is peculiar in recent years is a strong increase in applying it: Although originally formulated 86 years ago, only today the full potential of the Wigner function—both in ability and diversity—begins to surface. This review, as well as a growing, dedicated Wigner community, is a testament to this development and gives a broad and concise overview of recent advancements in different fields.

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Quantum corrections of the truncated Wigner approximation applied to an exciton transport model

Cited by 5 publications

References 41 publications

Open quantum dynamics theory on the basis of periodical system-bath model for discrete Wigner function

Open quantum dynamics theory on the basis of periodical system-bath model for discrete Wigner function

Open quantum dynamics theory on the basis of periodical system-bath model for discrete Wigner function

Recent advances in Wigner function approaches

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