Jaggedness of Path Integral Trajectories

Details Jaggedness of Path Integral Trajectories Jaggedness of Path Integral Trajectories

2005-09-10

arxiv.org/abs/cond-mat/0509266v1

Phys.Lett.A345:258,2005

Physics

Condensed Matter

Statistical Mechanics

11 pages, 7 figures, uses elsart.cls

Scientific paper

10.1016/j.physleta.2005.07.057

We define and investigate the properties of the jaggedness of path integral trajectories. The new quantity is shown to be scale invariant and to satisfy a self-averaging property. Jaggedness allows for a classification of path integral trajectories according to their relevance. We show that in the continuum limit the only paths that are not of measure zero are those with jaggedness 1/2, i.e. belonging to the same equivalence class as random walks. The set of relevant trajectories is thus narrowed down to a specific subset of non-differentiable paths. For numerical calculations, we show that jaggedness represents an important practical criterion for assessing the quality of trajectory generating algorithms. We illustrate the obtained results with Monte Carlo simulations of several different models.

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