Nodal domain statistics for quantum maps, percolation, and stochastic Loewner evolution

JP Keating, J Marklof, IG Williams

Research output: Contribution to journalArticle (Academic Journal)peer-review

28 Citations (Scopus)

Abstract

We develop a percolation model for nodal domains in the eigenvectors of quantum chaotic torus maps. Our model follows directly from the assumption that the quantum maps are described by random matrix theory. Its accuracy in predicting statistical properties of the nodal domains is demonstrated for perturbed cat maps and supports the use of percolation theory to describe the wave functions of general Hamiltonian systems. We also demonstrate that the nodal domains of the perturbed cat maps obey the Cardy crossing formula and find evidence that the boundaries of the nodal domains are described by stochastic Loewner evolution with diffusion constant kappa close to the expected value of 6, suggesting that quantum chaotic wave functions may exhibit conformal invariance in the semiclassical limit.
Translated title of the contributionNodal domain statistics for quantum maps, percolation, and stochastic Loewner evolution
Original languageEnglish
Article numberArt no. 034101
Pages (from-to)034101-1 - 034101-4
Number of pages4
JournalPhysical Review Letters
Volume97 (3)
DOIs
Publication statusPublished - Jul 2006

Bibliographical note

Publisher: Americal Physical Soc
Other identifier: IDS number 065QS
Other: PACS numbers: 05.45.Mt, 03.65.Sq, 11.25.Hf, 64.60.Ak

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