SLE description of the nodal lines of random wavefunctions

The nodal lines of random wavefunctions 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 additional support to the recent conjecture that the nodal domains of
random (and chaotic) wavefunctions 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.