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A Note on Local Refinement for Direction Splitting Methods Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Deterministic Solution of the Discrete Wigner Equation

Authors : Johann Cervenka, Paul Ellinghaus, Mihail Nedjalkov

Published in: Numerical Methods and Applications

Publisher: Springer International Publishing

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Abstract

The Wigner formalism provides a convenient formulation of quantum mechanics in the phase space. Deterministic solutions of the Wigner equation are especially needed for problems where phase space quantities vary over several orders of magnitude and thus can not be resolved by the existing stochastic approaches. However, finite difference schemes have been problematic due to the discretization of the diffusion term in this differential equation. A new approach, which uses an integral formulation of the Wigner equation that avoids the problematic differentiation, is shown here. The results of the deterministic method are compared and validated with solutions of the Schrödinger equation. Furthermore, certain numerical aspects pertaining to the demanded parallel implementation are discussed.

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previous chapter Isogeometric Analysis for Nonlinear Dynamics of Timoshenko Beams
next chapter Explicit-Implicit Splitting Schemes for Parabolic Equations and Systems
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Metadata
Title
Deterministic Solution of the Discrete Wigner Equation
Authors
Johann Cervenka
Paul Ellinghaus
Mihail Nedjalkov
Copyright Year
2015
Book
Numerical Methods and Applications

Print ISBN: 978-3-319-15584-5

Electronic ISBN: 978-3-319-15585-2

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-15585-2_17

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