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Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics

Please always quote using this URN: urn:nbn:de:0297-zib-9604
  • Wigner transformation provides a one-to-one correspondence between functions on position space (wave functions) and functions on phase space (Wigner functions). Weighted integrals of Wigner functions yield quadratic quantities of wave functions like position and momentum densities or expectation values. For molecular quantum systems, suitably modified classical transport of Wigner functions provides an asymptotic approximation of the dynamics in the high energy regime. The article addresses the computation of Wigner functions by Monte Carlo quadrature. An ad aption of the Metropolis algorithm for the approximation of signed measures with disconnected support is systematically tested in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The numerical experiments give expectation values and level populations with an error of two to three percent, which agrees with the theoretically expected accuracy.

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Author:Susanna Kube, Caroline Lasser, Marcus Weber
Document Type:ZIB-Report
Tag:Metropolis Monte Carlo; approximation; oscillating functions; quadrature
MSC-Classification:62-XX STATISTICS / 62Dxx Sampling theory, sample surveys / 62D05 Sampling theory, sample surveys
65-XX NUMERICAL ANALYSIS / 65Dxx Numerical approximation and computational geometry (primarily algorithms) (For theory, see 41-XX and 68Uxx) / 65D30 Numerical integration
Date of first Publication:2007/07/23
Series (Serial Number):ZIB-Report (07-17)
Published in:A rev. vers. appeared in: Journal of Computational Physics 228 (2009) pp. 1947-1962. doi:10.1016/j.jcp.2008.11.016
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