On the distribution of local extrema in quantum chaos Pausinger, Florian ; https://orcid.org/0000-0002-8379-3768 Steinerberger, Stefan 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 Z2. Elsevier 2015 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/1938 Pausinger F, Steinerberger S. On the distribution of local extrema in quantum chaos. <i>Physics Letters, Section A</i>. 2015;379(6):535-541. doi:<a href="https://doi.org/10.1016/j.physleta.2014.12.010">10.1016/j.physleta.2014.12.010</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physleta.2014.12.010 info:eu-repo/semantics/altIdentifier/wos/000349586000006 info:eu-repo/semantics/closedAccess