The Monte Carlo Method for Wigner and Boltzmann Transport Equations

Dollfus, Philippe; Querlioz, Damien; Martin, Jérôme Saint

doi:10.1002/9781118761793.ch8

Cited by 3 publications

(2 citation statements)

References 113 publications

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“…At this time, nearly 90 years after the original paper appeared, there is a resurgence of interest 2 in the Wigner equation due to the relevance of phase space quantum mechanics to new algorithms in quantum computing 3 , and quantum electronics 4,5 . In quantum chemical dynamics the Wigner equation is rarely solved directly 6 but partial Wignerization plays an important role in mixed quantum-classical methods [7][8][9][10] and the Wigner function is sometimes used for improving sampling in quantum molecular dynamics simulations 11,12 .…”

Section: Introductionmentioning

confidence: 99%

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Solving the Wigner Equation with Signed Particles Monte Carlo for Chemically Relevant Potentials

Wang¹,

Simine

2021

Preprint

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Section: Introductionmentioning

confidence: 99%

“…3 nm in space and 0.05h nm −1 in momentum. The initial wave-packet is a Gaussian and placed on the left side of the barrier ψ 0 (x) =4 where x 0 = −15 nm, p 0 = 0.7h nm −1 , and σ 0 = 2.852 nm. The mass of the particle is set to be 0.32.…”

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confidence: 99%

Solving the Wigner Equation with Signed Particles Monte Carlo for Chemically Relevant Potentials

Wang¹,

Simine

2021

Preprint

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Recent advances in Wigner function approaches

Weinbub

Ferry

2018

Applied Physics Reviews

241

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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Solving the Wigner equation with signed particle Monte Carlo for chemically relevant potentials

Wang

Simine

2021

The Journal of Chemical Physics

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Expanding the set of stable, accurate, and scalable methods for simulating molecular quantum dynamics is important for accelerating the computational exploration of molecular processes. In this paper, we adapt the signed particles Monte Carlo algorithm for solving the transient Wigner equation to scenarios of chemical interest. This approach was used in the past to study electronic processes in semi-conductors, but to the best of our knowledge, it had never been applied to molecular modeling. We present the algorithm and demonstrate its excellent performance on harmonic and double well potentials for electronic and nuclear systems. We explore the stability of the algorithm, discuss the choice of hyper-parameters, and cautiously speculate that it may be used in quantum molecular dynamics simulations.

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The Monte Carlo Method for Wigner and Boltzmann Transport Equations

Cited by 3 publications

References 113 publications

Solving the Wigner Equation with Signed Particles Monte Carlo for Chemically Relevant Potentials

Solving the Wigner Equation with Signed Particles Monte Carlo for Chemically Relevant Potentials

Recent advances in Wigner function approaches

Solving the Wigner equation with signed particle Monte Carlo for chemically relevant potentials

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