Open Access
December 2007 Construction and validation of a rigorous surface hopping algorithm for conical crossings
Caroline Lasser, Torben Swart, Stefan Teufel
Commun. Math. Sci. 5(4): 789-814 (December 2007).


This article presents and evaluates a surface hopping algorithm for time-dependent two-level Schrödinger systems with conically intersecting eigenvalues. The algorithm implements an asymptotic semigroup for approximating the solution’s Wigner function, which was rigorously defined and derived from the Schrödinger equation by two of the authors in previous work. It is applied to two-dimensional isotropic systems, which include linear Jahn-Teller Hamiltonians and Gaussian initial data. It reproduces energy level populations and expectation values with an accuracy of two to three percent.


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Caroline Lasser. Torben Swart. Stefan Teufel. "Construction and validation of a rigorous surface hopping algorithm for conical crossings." Commun. Math. Sci. 5 (4) 789 - 814, December 2007.


Published: December 2007
First available in Project Euclid: 3 January 2008

zbMATH: 1136.65094
MathSciNet: MR2375047

Primary: 65Z05 , 81-04

Keywords: eigenvalue crossing , time-dependent Schrödinger system , trajectory surface hopping algorithm

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 4 • December 2007
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