Domain decomposition strategies for the two-dimensional Wigner Monte Carlo Method

Weinbub, Josef; Ellinghaus, Paul; Nedjalkov, Mihail

doi:10.1007/s10825-015-0730-0

Cited by 8 publications

(5 citation statements)

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“…More recent advancements concern, for example, an extension of the theoretical framework for Monte Carlo, accessible descriptions of general electromagnetic fields [98], handling of boundary conditions [99], and an operator splitting spectral method for a Wigner-Poisson system [100]. A 1D/2D signed-particle Wigner transport simulator is available via ViennaWD [101,102]. For non-trivial interaction mechanisms a closure problem exists in the Wigner formalism [78, p 98].…”

Section: Wigner Functionmentioning

confidence: 99%

“…In follow-up work, Ballicchia et al applied parts of this theoretical framework (by utilizing the Wigner signed-particle formulation provided in the ViennaWD simulator [101,102]) to investigate the effect of a uniform magnetic field on the electron state interference pattern which arises in a focusing double-well potential structure [173]. The authors analyzed the electron density and the negativity of the Wigner function and showed how the magnetic field controls the electron state but also destroys the coherence of the evolution dynamics.…”

Section: Waveguides and Electron Dynamicsmentioning

confidence: 99%

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Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

Weinbub

Kosik

2022

J. Phys.: Condens. Matter

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Quantum electronics has significantly evolved over the last decades. Where initially the clear focus was on light-matter interactions, nowadays approaches based on the electron's wave nature have solidified themselves as additional focus areas. This development is largely driven by continuous advances in electron quantum optics, electron based quantum information processing, electronic materials, and nanoelectronic devices and systems. The pace of research in all of these areas is astonishing and is accompanied by substantial theoretical and experimental advancements. What is particularly exciting is the fact that the computational methods, together with broadly available large-scale computing resources, have matured to such a degree so as to be essential enabling technologies themselves. These methods allow to predict, analyze, and design not only individual physical processes but also entire devices and systems, which would otherwise be very challenging or sometimes even out of reach with conventional experimental capabilities. This review is thus a testament to the increasingly towering importance of computational methods for advancing the expanding field of quantum electronics. To that end, computational aspects of a representative selection of recent research in quantum electronics are highlighted where a major focus is on the electron's wave nature. By categorizing the research into concrete technological applications, researchers and engineers will be able to use this review as a source for inspiration regarding problem-specific computational methods.

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Section: Wigner Functionmentioning

confidence: 99%

Section: Waveguides and Electron Dynamicsmentioning

confidence: 99%

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

Weinbub

Kosik

2022

J. Phys.: Condens. Matter

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“…This greatly reduces the memory requirements in the implementation of the model. The first two-dimensional Wigner function based simulations could only be realized thanks to this approach but also due to novel parallelization strategies [ 52 , 53 ]. Because of both accomplishments, the number of particles can be significantly increased while still retaining feasible simulation times.…”

Section: Wigner Functionsmentioning

confidence: 99%

Complex Systems in Phase Space

Ferry

Nedjalkov

Weinbub

et al. 2020

Entropy

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The continued reduction of semiconductor device feature sizes towards the single-digit nanometer regime involves a variety of quantum effects. Modeling quantum effects in phase space in terms of the Wigner transport equation has evolved to be a very effective approach to describe such scaled down complex systems, accounting from full quantum processes to dissipation dominated transport regimes including transients. Here, we discuss the challanges, myths, and opportunities that arise in the study of these complex systems, and particularly the advantages of using phase space notions. The development of particle-based techniques for solving the transport equation and obtaining the Wigner function has led to efficient simulation approaches that couple well to the corresponding classical dynamics. One particular advantage is the ability to clearly illuminate the entanglement that can arise in the quantum system, thus allowing the direct observation of many quantum phenomena.

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“…In this paper, we propose a deterministic method to solve the Wigner equation by exploiting the analogy with the classical Boltzmann transport equation without, however, invoking the classical limit. In contrast to the highly optimized numerical techniques that have been outlined above [6,[10][11][12][13][15][16][17], our main focus is on the development of a different, but equivalent form of the Wigner function that allows for a natural, direct implementation. To this end, we recast the Wigner equation into a form that employs the force field rather than the potential energy from which one would conventionally proceed in quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

“…In line with the solution of the Boltzmann equation, there have been significant efforts in solving the Wigner equation using Monte-Carlo, or particle based techniques [6,[10][11][12][13]. Even though all Monte-Carlo approaches rely on the stochastic solution of the Wigner function, the differences between various Monte-Carlo approaches are significant, from relying on signed particles [10] and Fourier transforms [11] to using spatial decomposition approaches [12,13]. In contrast to the former, the deterministic approaches feature a more direct treatment, which we have adopted in this paper.…”

Section: Introductionmentioning

confidence: 99%

Efficient solution of the Wigner–Liouville equation using a spectral decomposition of the force field

Put

Sorée

Magnus

2017

Journal of Computational Physics

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The Wigner-Liouville equation is reformulated using a spectral decomposition of the classical force field instead of the potential energy. The latter is shown to simplify the Wigner-Liouville kernel both conceptually and numerically as the spectral force Wigner-Liouville equation avoids the numerical evaluation of the highly oscillatory Wigner kernel which is nonlocal in both position and momentum. The quantum mechanical evolution is instead governed by a term local in space and non-local in momentum, where the non-locality in momentum has only a limited range. An interpretation of the time evolution in terms of two processes is presented; a classical evolution under the influence of the averaged driving field, and a probability-preserving quantum-mechanical generation and annihilation term. Using the inherent stability and reduced complexity, a direct deterministic numerical implementation using Chebyshev and Fourier pseudo-spectral methods is detailed. For the purpose of illustration, we present results for the time-evolution of a onedimensional resonant tunneling diode driven out of equilibrium.

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Domain decomposition strategies for the two-dimensional Wigner Monte Carlo Method

Cited by 8 publications

References 8 publications

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

Complex Systems in Phase Space

Efficient solution of the Wigner–Liouville equation using a spectral decomposition of the force field

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