Percolation model for nodal domains of chaotic wave functions

Abstract

Nodal domains are regions where a function has definite sign. In recent paper [nlin.CD/0109029] it is conjectured that the distribution of nodal domains for quantum eigenfunctions of chaotic systems is universal. We propose a percolation-like model for description of these nodal domains which permits to calculate all interesting quantities analytically, agrees well with numerical simulations, and due to the relation to percolation theory opens the way of deeper understanding of the structure of chaotic wave functions.