Repository: Freie Universität Berlin, Math Department

Propagation through Generic Level Crossings: A Surface Hopping Semigroup

Fermanian Kammerer, C. and Lasser, C. (2008) Propagation through Generic Level Crossings: A Surface Hopping Semigroup. J. Math. Anal., 40 (1). pp. 103-133.


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We construct a surface hopping semigroup, which asymptotically describes nuclear propagation through crossings of electron energy levels. The underlying time-dependent Schrödinger equation has a matrix-valued 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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