Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1866841 | Physics Letters A | 2015 | 7 Pages |
Abstract
We numerically investigate the distribution of extrema of ‘chaotic’ Laplacian eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a) we count extrema on grid graphs with a small number of randomly added edges and show the behavior to coincide with the 1957 prediction of Longuet-Higgins for the continuous case and (b) we compute the regularity of their spatial distribution using discrepancy , which is a classical measure from the theory of Monte Carlo integration. The first part suggests that grid graphs with randomly added edges should behave like two-dimensional surfaces with ergodic geodesic flow; in the second part we show that the extrema are more regularly distributed in space than the grid Z2Z2.
Keywords
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Physical Sciences and Engineering
Physics and Astronomy
Physics and Astronomy (General)
Authors
Florian Pausinger, Stefan Steinerberger,