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Title
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Efficient solution of the Wigner-Liouville equation using a spectral decomposition of the force field
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Author
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Abstract
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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 one-dimensional resonant tunneling diode driven out of equilibrium. (C) 2017 Elsevier Inc. All rights reserved. |
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Language
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English
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Source (journal)
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Journal of computational physics. - New York
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Publication
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New York
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2017
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ISSN
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0021-9991
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DOI
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10.1016/J.JCP.2017.08.059
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Volume/pages
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350
(2017)
, p. 314-325
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ISI
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000413379000016
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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