Repository: Freie Universität Berlin, Math Department

Propagation through conical crossings: An asymptotic semigroup

Lasser, C. and Teufel, St. (2005) Propagation through conical crossings: An asymptotic semigroup. Comm. Pure Appl. Math., 58 (9). pp. 1188-1230.


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We consider the standard model problem for a conical intersection of electronic surfaces in molecular dynamics. Our main result is the construction of a semi-group in order to approximate the Wigner function associated with the solution of the Schrödinger equation at leading order in the semiclassical parameter. The semigroup stems from an underlying Markov process that combines deterministic transport along classical trajectories within the electronic surfaces and random jumps between the surfaces near the crossing. Our semigroup can be viewed as a rigorous mathematical counterpart of so-called trajectory surface hopping algorithms, which are of major importance in molecular simulations in chemical physics. The key point of our analysis, the incorporation of the nonadiabatic transitions, is based on the Landau-Zener type formula of Fermanian-Kammerer and Gérard[10] for the propagation of two-scale Wigner measures through conical crossings.

Item Type:Article
Subjects:Physical Sciences > Physics > Mathematical & Theoretical Physics > Quantum Mechanics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:907
Deposited By: Burkhard Schmidt
Deposited On:29 Apr 2010 08:42
Last Modified:03 Mar 2017 14:40

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