dorsal/arxiv
View SchemaOptimal series representations for numerical path integral simulations
| Authors | Cristian Predescu, J. D. Doll |
|---|---|
| Categories | |
| ArXiv ID | physics/0209073 |
| URL | https://arxiv.org/abs/physics/0209073 |
| DOI | 10.1063/1.1509058 |
| Journal | J. Chem. Phys. 117, 7448 (2002) |
Abstract
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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"abstract": "By means of the Ito-Nisio theorem, we introduce and discuss a general\napproach to series representations of path integrals. We then argue that the\noptimal basis for both ``primitive\u0027\u0027 and partial averaged approaches is the\nWiener sine-Fourier basis. The present analysis also suggests a new approach to\nimproving the convergence of primitive path integral methods. Current work\nindicates that this new technique, the ``reweighted\u0027\u0027 method, converges as the\ncube of the number of path variables for ``smooth\u0027\u0027 potentials. The technique\nis based on a special way of approximating the Brownian bridge which enters the\nFeynman-Kac formula and it does not require the Gaussian transform of the\npotential for its implementation.",
"arxiv_id": "physics/0209073",
"authors": [
"Cristian Predescu",
"J. D. Doll"
],
"categories": [
"physics.chem-ph",
"cond-mat.stat-mech"
],
"doi": "10.1063/1.1509058",
"journal_ref": "J. Chem. Phys. 117, 7448 (2002)",
"title": "Optimal series representations for numerical path integral simulations",
"url": "https://arxiv.org/abs/physics/0209073"
},
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