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Article: An eulerian surface hopping method for the schrödinger equation with conical crossings

TitleAn eulerian surface hopping method for the schrödinger equation with conical crossings
Authors
KeywordsInterface condition
Liouville equation
Landau-Zener formula
Surface hopping method
Conical crossings
High resolution scheme
Issue Date2011
Citation
Multiscale Modeling and Simulation, 2011, v. 9, n. 1, p. 258-281 How to Cite?
AbstractIn a nucleonic propagation through conical crossings of electronic energy levels, the codimension two conical crossings are the simplest energy level crossings, which affect the Born- Oppenheimer approximation in the zeroth order term. The purpose of this paper is to develop the surface hopping method for the Schrödinger equation with conical crossings in the Eulerian formulation. The approach is based on the semiclassical approximation governed by the Liouville equations, which are valid away from the conical crossing manifold. At the crossing manifold, electrons hop to another energy level with the probability determined by the Landau-Zener formula. This hopping mechanics is formulated as an interface condition, which is then built into the numerical flux for solving the underlying Liouville equation for each energy level. While a Lagrangian particle method requires the increase in time of the particle numbers, or a large number of statistical samples in a Monte Carlo setting, the advantage of an Eulerian method is that it relies on fixed number of partial differential equations with a uniform in time computational accuracy. We prove the positivity and l1-stability and illustrate by several numerical examples the validity and accuracy of the proposed method. © 2011 Society for Industrial and Applied Mathematics.
Persistent Identifierhttp://hdl.handle.net/10722/219651
ISSN
2015 Impact Factor: 1.585
2015 SCImago Journal Rankings: 1.062

 

DC FieldValueLanguage
dc.contributor.authorJin, Shi-
dc.contributor.authorQi, Peng-
dc.contributor.authorZhang, Zhiwen-
dc.date.accessioned2015-09-23T02:57:37Z-
dc.date.available2015-09-23T02:57:37Z-
dc.date.issued2011-
dc.identifier.citationMultiscale Modeling and Simulation, 2011, v. 9, n. 1, p. 258-281-
dc.identifier.issn1540-3459-
dc.identifier.urihttp://hdl.handle.net/10722/219651-
dc.description.abstractIn a nucleonic propagation through conical crossings of electronic energy levels, the codimension two conical crossings are the simplest energy level crossings, which affect the Born- Oppenheimer approximation in the zeroth order term. The purpose of this paper is to develop the surface hopping method for the Schrödinger equation with conical crossings in the Eulerian formulation. The approach is based on the semiclassical approximation governed by the Liouville equations, which are valid away from the conical crossing manifold. At the crossing manifold, electrons hop to another energy level with the probability determined by the Landau-Zener formula. This hopping mechanics is formulated as an interface condition, which is then built into the numerical flux for solving the underlying Liouville equation for each energy level. While a Lagrangian particle method requires the increase in time of the particle numbers, or a large number of statistical samples in a Monte Carlo setting, the advantage of an Eulerian method is that it relies on fixed number of partial differential equations with a uniform in time computational accuracy. We prove the positivity and l1-stability and illustrate by several numerical examples the validity and accuracy of the proposed method. © 2011 Society for Industrial and Applied Mathematics.-
dc.languageeng-
dc.relation.ispartofMultiscale Modeling and Simulation-
dc.subjectInterface condition-
dc.subjectLiouville equation-
dc.subjectLandau-Zener formula-
dc.subjectSurface hopping method-
dc.subjectConical crossings-
dc.subjectHigh resolution scheme-
dc.titleAn eulerian surface hopping method for the schrödinger equation with conical crossings-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1137/090774185-
dc.identifier.scopuseid_2-s2.0-79955918897-
dc.identifier.volume9-
dc.identifier.issue1-
dc.identifier.spage258-
dc.identifier.epage281-
dc.identifier.eissn1540-3467-

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