On the distribution of local extrema in Quantum Chaos

Florian Pausinger, Stefan Steinerberger*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)535-541
Number of pages7
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number6
Early online date10 Dec 2014
Publication statusPublished - 06 Mar 2015


  • Laplacian eigenfunctions
  • Local extrema
  • Quantum chaos
  • Universality phenomena

ASJC Scopus subject areas

  • General Physics and Astronomy


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