SLE description of the nodal lines of random wave functions

Abstract

The nodal lines of random wave functions are investigated. We demonstrate numerically that they are well approximated by the so-called SLE_6 curves which describe the continuum limit of the percolation cluster boundaries. This result gives an additional support to the recent conjecture that the nodal domains of random (and chaotic) wave functions in the semi classical limit are adequately described by the critical percolation theory. It is also shown that using the dipolar variant of SLE reduces significantly finite size effects.

17 pages, 13 figures

References in corpus (3)

• A Guide to Stochastic Loewner Evolution and its Applications
• Nodal Domain Statistics for Quantum Maps, Percolation and SLE
• Discrete Loewner evolution

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