Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Journal of Computational Physics
Numerical Analysis in Modern Scientific Computing: An Introduction
Numerical Analysis in Modern Scientific Computing: An Introduction
Quasi-Monte Carlo algorithms for unbounded, weighted integration problems
Journal of Complexity
Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics
Journal of Computational Physics
Computing Semiclassical Quantum Dynamics with Hagedorn Wavepackets
SIAM Journal on Scientific Computing
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We compute expectation values for the solution of the nuclear Schrödinger equation. The proposed particle method consists of three steps: sampling of the initial Wigner function, classical transport of the sampling points, and weighted phase space summation for the final computation of the expectation values. The Egorov theorem guarantees that the algorithm is second order accurate with respect to the semiclassical parameter. We present numerical experiments for a two-dimensional torsional potential with three different sets of initial data and for a six-dimensional Henon-Heiles potential. By construction, the computing times scale linearly with the number of initial sampling points and range between three seconds and one hour.