The morphology of nodal lines-random waves versus percolation

Abstract

In this paper we investigate the properties of nodal structures in random wave fields, and in particular we scrutinize their recently proposed connection with short-range percolation models. We propose a measure which shows the difference between monochromatic random waves, which are characterized by long-range correlations, and Gaussian fields with short-range correlations, which are naturally assumed to be better modelled by percolation theory. We also study the relevance of the quantities which we compute to the probability that nodal lines are in the vicinity of a given reference line.

arXiv comment10 pages, 5 figures (incl. one coloured figure), published version

References in corpus (6)

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• Percolation model for nodal domains of chaotic wave functions
• Simple strong glass forming models: mean-field solution with activation
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• Local and global analysis of eigenfunctions
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• Geometric characterization of nodal domains: the area-to-perimeter ratio
• The Statistics of the Points Where Nodal Lines Intersect a Reference Curve
• Eigenfunctions and Nodal Sets
• Nodal Domain Distribution for a Nonintegrable Two-Dimensional Anharmonic Oscillator
• Short and Long Range Screening of Optical Singularities
• On the Nodal Count Statistics for Separable Systems in any Dimension
• Singularities in Speckled Speckle: Screening
• Level sets percolation on chaotic graphs
• On the connection between Random Waves and Quantum Fields. Duality between nodal lines statistic and the Casimir energy