Generalization of Euler's Summation Formula to Path Integrals

Details Generalization of Euler's Summation Formula to Path Integrals Generalization of Euler's Summation Formula to Path Integrals

2005-08-29

arxiv.org/abs/cond-mat/0508710v2

Phys.Lett.A344:84-90,2005

Physics

Condensed Matter

Statistical Mechanics

12 pages, 1 figure, uses elsart.cls, ref. [15] resolved

Scientific paper

10.1016/J.PHYSLETA.2005.06.053

A recently developed analytical method for systematic improvement of the convergence of path integrals is used to derive a generalization of Euler's summation formula for path integrals. The first $p$ terms in this formula improve convergence of path integrals to the continuum limit from 1/N to $1/N^p$, where $N$ is the coarseness of the discretization. Monte Carlo simulations performed on several different models show that the analytically derived speedup holds.

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