E Bogomolny and C Schmit 2007 J. Phys. A: Math. Theor. 40 14033 doi:10.1088/1751-8113/40/47/001
E Bogomolny and C Schmit
Show affiliationsRecently it was conjectured that nodal domains of random wavefunctions are adequately described by critical percolation theory. In this paper we strengthen this conjecture in two respects. First, we show that, though wavefunction correlations decay slowly, a careful use of Harris' criterion confirms that these correlations are unessential and nodal domains of random wavefunctions belong to the same universality class as non-correlated critical percolation. Second, we argue that level domains of random wavefunctions are described by the non-critical percolation model.
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
82B43 Percolation (See also 60K35)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 47 (23 November 2007)
Received 4 September 2007, in final form 10 October 2007
Published 6 November 2007
E Bogomolny and C Schmit 2007 J. Phys. A: Math. Theor. 40 14033
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