QUANTUM SIGNATURES OF CLASSICAL CHAOS - SENSITIVITY OF WAVE-FUNCTIONSTO PERTURBATIONS

We compare the influence of perturbations of classically regular respe ctively chaotic Hamiltonians on their eigenfunctions. A generic measur e of the perturbation strength is given by the average spreading width , which semiclassically is a phase-space integral. Thus, contrary to c ommon assumption, the spreading width cannot be an indicator of regula rity or chaos. The distribution of expansion coefficients of perturbed eigenfunctions in terms of unperturbed ones is markedly different for the two cases and may serve as a quantum signature of chaos referring to states rather than to spectra.