An efficient numerical scheme for the discrete Wigner transport equation via the momentum domain narrowing

Kim, Kyoung-Youm; Kim, Jungho; Kim, Saehwa

doi:10.1063/1.4954237

Cited by 8 publications

(6 citation statements)

References 30 publications

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“…In the case if there is onlyVy = ℏ sin(xdp/ℏ)/dp interaction in the PISB model, (i.e.Vx = 0), we encounter the divergent term iℏηδ(0)[(Vy) 2 ,ρ(t)] that arises from the second term in the RHS of Eq. (34). BecauseVy reduce to the linear operator of the coordinateVy ≈x in the large N limit, the PISB model in this condition corresponds to the Caldeira-Leggett model without a counter term: Divergent term arises because we exclude the counter term in the bath Hamiltonian, Eq.…”

Section: B Qme For 2d Pisb Model and Counter Termmentioning

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 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 two-dimensional (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: B Qme For 2d Pisb Model and Counter Termmentioning

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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“…These distributions arose owing to the finite difference operator of the potential term in Eq. (34), which created the positive and negative populations W (p N +1 , q k ) and −W (p −(N +1) , q k ) from W (p 0 , q k ). The sign of these distributions changed at q = q 0 , because of the presence of the prefactor sin (x k dp/ ).…”

Section: P(p)mentioning

confidence: 99%

“…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

View full text Add to dashboard Cite

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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“…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

View full text Add to dashboard Cite

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.

show abstract

An efficient numerical scheme for the discrete Wigner transport equation via the momentum domain narrowing

Cited by 8 publications

References 30 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

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

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