Optimal series representations for numerical path integral simulations

Details Optimal series representations for numerical path integral simulations Optimal series representations for numerical path integral simulations

2002-09-19

arxiv.org/abs/physics/0209073v2

J. Chem. Phys. 117, 7448 (2002)

Physics

Chemical Physics

19 pages, 6 figures. Minor changes

Scientific paper

10.1063/1.1509058

By means of the Ito-Nisio theorem, we introduce and discuss a general approach to series representations of path integrals. We then argue that the optimal basis for both ``primitive'' and partial averaged approaches is the Wiener sine-Fourier basis. The present analysis also suggests a new approach to improving the convergence of primitive path integral methods. Current work indicates that this new technique, the ``reweighted'' method, converges as the cube of the number of path variables for ``smooth'' potentials. The technique is based on a special way of approximating the Brownian bridge which enters the Feynman-Kac formula and it does not require the Gaussian transform of the potential for its implementation.

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