Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2002-12-03
J. Phys. A: Math. Gen., Vol. 36 (2003), L53-L59
Nonlinear Sciences
Chaotic Dynamics
7 pages, 2 figures. Second version: minor corrections
Scientific paper
10.1088/0305-4470/36/3/102
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. (Phys. Rev. Lett., Vol. 88 (2002), 114101) and by Bogomolny and Schmit (Phys. Rev. Lett., Vol. 88 (2002), 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.
Keating Jon P.
Mezzadri Francesco
Monastra Alejandro G.
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