On the distribution of local extrema in quantum chaos

F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541.

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Journal Article | Published | English
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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.
Publishing Year
Date Published
2015-03-06
Journal Title
Physics Letters, Section A
Acknowledgement
F.P. was supported by the Graduate School of IST Austria. S.S. was partially supported by CRC1060 of the DFG The authors thank Olga Symonova and Michael Kerber for sharing their implementation of the persistence algorithm.
Volume
379
Issue
6
Page
535 - 541
IST-REx-ID

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Pausinger F, Steinerberger S. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 2015;379(6):535-541. doi:10.1016/j.physleta.2014.12.010
Pausinger, F., & Steinerberger, S. (2015). On the distribution of local extrema in quantum chaos. Physics Letters, Section A, 379(6), 535–541. https://doi.org/10.1016/j.physleta.2014.12.010
Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A 379, no. 6 (2015): 535–41. https://doi.org/10.1016/j.physleta.2014.12.010.
F. Pausinger and S. Steinerberger, “On the distribution of local extrema in quantum chaos,” Physics Letters, Section A, vol. 379, no. 6, pp. 535–541, 2015.
Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in quantum chaos. Physics Letters, Section A. 379(6), 535–541.
Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local Extrema in Quantum Chaos.” Physics Letters, Section A, vol. 379, no. 6, Elsevier, 2015, pp. 535–41, doi:10.1016/j.physleta.2014.12.010.

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