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Propagation through conical crossings: An asymptotic semigroup
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UNSPECIFIED (2005) Propagation through conical crossings: An asymptotic semigroup. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 58 (9). pp. 1188-1230. ISSN 0010-3640.
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Abstract
We consider the standard model problem for a conical intersection of electronic surfaces in molecular dynamics. Our main result is the construction of a semigroup in order to approximate the Wigner function associated with the solution of the Schrodinger 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 Gerard [10] for the propagation of two-scale Wigner measures through conical crossings. (c) 2005 Wiley Periodicals, Inc.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | ||||
Publisher: | JOHN WILEY & SONS INC | ||||
ISSN: | 0010-3640 | ||||
Official Date: | September 2005 | ||||
Dates: |
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Volume: | 58 | ||||
Number: | 9 | ||||
Number of Pages: | 43 | ||||
Page Range: | pp. 1188-1230 | ||||
Publication Status: | Published |
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