Critical statistics in a KAM system
CE Creffield, G. Hur, T S Monteiro · arXiv (Cornell University) · 2005
We report a theoretical study of a chaotic KAM system, in a regime where the eigenstates have generic localization properties resulting from transport though classical cantori. We find eigenvalue statistics of a form analogous to the critical statistics of a Metal-Insulator Transition in a disordered system: the variances have a linear form $\\Sigma_2(L) \\simeq {1/2}(1-D_2) L$, where $D_2$ is a fractal dimension which characterizes the wavefunctions. The nearest-neighbour statistics assume an invariant form which, despite a fully chaotic classical phase-space, is far from GOE.