Numerical implementation of some reweighted path integral methods

Details Numerical implementation of some reweighted path integral methods Numerical implementation of some reweighted path integral methods

2003-05-19

arxiv.org/abs/cond-mat/0305436v1

J. Chem. Phys. 119, 4641 (2003)

Physics

Condensed Matter

Statistical Mechanics

15 pages, 10 figures, submitted to JCP

Scientific paper

10.1063/1.1595640

The reweighted random series techniques provide finite-dimensional approximations to the quantum density matrix of a physical system that have fast asymptotic convergence. We study two special reweighted techniques that are based upon the Levy-Ciesielski and Wiener-Fourier series, respectively. In agreement with the theoretical predictions, we demonstrate by numerical examples that the asymptotic convergence of the two reweighted methods is cubic for smooth enough potentials. For each reweighted technique, we propose some minimalist quadrature techniques for the computation of the path averages. These quadrature techniques are designed to preserve the asymptotic convergence of the original methods.

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