On the distribution of local extrema in quantum chaos Journal Article

Author(s): Pausinger, Florian; Steinerberger, Stefan
Article Title: On the distribution of local extrema in quantum chaos
Affiliation IST Austria
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 Z2.
Keywords: Laplacian eigenfunctions; Local extrema; Quantum chaos; Universality phenomena
Journal Title: Physics Letters, Section A: General, Atomic and Solid State Physics
Volume: 379
Issue 6
ISSN: 03759601
Publisher: Elsevier  
Date Published: 2015-03-06
Start Page: 535
End Page: 541
Sponsor: F.P. was supported by the Graduate School of IST Austria. S.S. was partially supported by CRC1060 of the DFG
DOI: 10.1016/j.physleta.2014.12.010
Notes: The authors thank Olga Symonova and Michael Kerber for sharing their implementation of the persistence algorithm.
Open access: no
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