---
_id: '1938'
abstract:
- lang: eng
  text: '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.'
acknowledgement: "F.P. was supported by the Graduate School of IST Austria. S.S. was
  partially supported by CRC1060 of the DFG\r\nThe authors thank Olga Symonova and
  Michael Kerber for sharing their implementation of the persistence algorithm. "
article_processing_charge: No
author:
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
- first_name: Stefan
  full_name: Steinerberger, Stefan
  last_name: Steinerberger
citation:
  ama: 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>
  apa: Pausinger, F., &#38; Steinerberger, S. (2015). On the distribution of local
    extrema in quantum chaos. <i>Physics Letters, Section A</i>. Elsevier. <a href="https://doi.org/10.1016/j.physleta.2014.12.010">https://doi.org/10.1016/j.physleta.2014.12.010</a>
  chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local
    Extrema in Quantum Chaos.” <i>Physics Letters, Section A</i>. Elsevier, 2015.
    <a href="https://doi.org/10.1016/j.physleta.2014.12.010">https://doi.org/10.1016/j.physleta.2014.12.010</a>.
  ieee: F. Pausinger and S. Steinerberger, “On the distribution of local extrema in
    quantum chaos,” <i>Physics Letters, Section A</i>, vol. 379, no. 6. Elsevier,
    pp. 535–541, 2015.
  ista: Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in
    quantum chaos. Physics Letters, Section A. 379(6), 535–541.
  mla: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local
    Extrema in Quantum Chaos.” <i>Physics Letters, Section A</i>, vol. 379, no. 6,
    Elsevier, 2015, pp. 535–41, doi:<a href="https://doi.org/10.1016/j.physleta.2014.12.010">10.1016/j.physleta.2014.12.010</a>.
  short: F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541.
corr_author: '1'
date_created: 2018-12-11T11:54:49Z
date_published: 2015-03-06T00:00:00Z
date_updated: 2025-09-23T09:44:12Z
day: '06'
department:
- _id: HeEd
doi: 10.1016/j.physleta.2014.12.010
external_id:
  isi:
  - '000349586000006'
intvolume: '       379'
isi: 1
issue: '6'
language:
- iso: eng
month: '03'
oa_version: None
page: 535 - 541
publication: Physics Letters, Section A
publication_status: published
publisher: Elsevier
publist_id: '5152'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the distribution of local extrema in quantum chaos
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 379
year: '2015'
...