Fermanian Kammerer, C. and Lasser, C. (2008) Propagation through Generic Level Crossings: A Surface Hopping Semigroup. J. Math. Anal., 40 (1). pp. 103133.

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Official URL: http://dx.doi.org/10.1137/070686810
Abstract
We construct a surface hopping semigroup, which asymptotically describes nuclear propagation through crossings of electron energy levels. The underlying timedependent Schrödinger equation has a matrixvalued potential, whose eigenvalue surfaces have a generic intersection of codimension two, three, or five in Hagedorn's classification. Using microlocal normal forms reminiscent of the Landau–Zener problem, we prove convergence to the true solution with an error of the order $\varepsilon^{1/8}$, where $\varepsilon$ is the semiclassical parameter. We present numerical experiments for an algorithmic realization of the semigroup illustrating the convergence of the algorithm.
Item Type:  Article 

Subjects:  Physical Sciences > Physics > Mathematical & Theoretical Physics > Quantum Mechanics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  903 
Deposited By:  Burkhard Schmidt 
Deposited On:  29 Apr 2010 08:02 
Last Modified:  03 Mar 2017 14:40 
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