Localization in Strongly Chaotic Systems

Abstract

We show that, in the semiclassical limit and whenever the elements of the Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic time-independent systems in ordered bases can on average be exponentially localized across the energy shell and decay faster than exponentially outside the energy shell. Typically however, matrix elements are strongly correlated leading to deviations from such behavior.

RevTeX, 5 pages + 3 postscript figures, submitted to Phys. Rev. Lett