Nodal domain distributions for quantum maps

JP Keating, F Mezzadri, AG Monastra

Research output: Contribution to journalArticle (Academic Journal)

8 Citations (Scopus)

Abstract

The statistics of the nodal lines and nodal domains of the eigenfunctions of quantum billiards have recently been observed to be fingerprints of the chaoticity of the underlying classical motion by Blum et al (2002 Phys. Rev. Lett. 88 114101) and by Bogomolny and Schmit (2002 Phys. Rev. Lett. 88 114102). These statistics were shown to be computable from the random wave model of the eigenfunctions. We here study the analogous problem for chaotic maps whose phase space is the two-torus. We show that the distributions of the numbers of nodal points and nodal domains of the eigenvectors of the corresponding quantum maps can be computed straightforwardly and exactly using random matrix theory. We compare the predictions with the results of numerical computations involving quantum perturbed cat maps.
Translated title of the contributionNodal domain distributions for quantum maps
Original languageEnglish
Pages (from-to)L53 - L59
JournalJournal of Physics A: Mathematical and General
Volume36 (3)
Publication statusPublished - 24 Jan 2003

Bibliographical note

Publisher: IOP PUblishing Ltd

Fingerprint Dive into the research topics of 'Nodal domain distributions for quantum maps'. Together they form a unique fingerprint.

Cite this