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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

CiteScore 2017: 0.67

SCImago Journal Rank (SJR) 2017: 0.417
Source Normalized Impact per Paper (SNIP) 2017: 0.860

Mathematical Citation Quotient (MCQ) 2017: 0.25

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Volume 20, Issue 1


A benchmark study of the Wigner Monte Carlo method

Jean Michel Sellier / Mihail Nedjalkov / Ivan Dimov / Siegfried Selberherr
Published Online: 2014-02-18 | DOI: https://doi.org/10.1515/mcma-2013-0018


The Wigner equation is a promising full quantum model for the simulation of nanodevices. It is also a challenging numerical problem. Two basic Monte Carlo approaches to this model exist exploiting, in the time-dependent case, the so-called particle affinity and, in the stationary case, integer particle signs. In this paper we extend the second approach for time-dependent simulations and present a validation against a well-known benchmark model, the Schrödinger equation. Excellent quantitative agreement is demonstrated by the compared results despite the very different numerical properties of the utilized stochastic and deterministic approaches.

Keywords: Wigner equation; Monte Carlo methods; quantum mechanics; Schrödinger equation

MSC: 81S30; 65C05; 45K05

About the article

Received: 2013-07-26

Accepted: 2014-02-14

Published Online: 2014-02-18

Published in Print: 2014-03-01

Funding Source: AComIn

Award identifier / Grant number: FP7-REGPOT-2012-2013-1

Funding Source: Bulgarian NSF

Award identifier / Grant number: SuperCA++

Funding Source: Austrian Science Fund Project

Award identifier / Grant number: FWF-P21685-N22

Citation Information: Monte Carlo Methods and Applications, Volume 20, Issue 1, Pages 43–51, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma-2013-0018.

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