SLOW DECAY OF TEMPORAL CORRELATIONS IN QUANTUM-SYSTEMS WITH CANTOR SPECTRA

We prove that the temporal autocorrelation function C(t) for quantum systems with Cantor spectra has an algebraic decay C(t) approximately t(-delta), where 8 equals the generalized dimension D2 of the spectral measure and is bounded by the Hausdorff dimension D0 greater-than-or-equal-to delta. We study various incommensurate systems with singular continuous and absolutely continuous Cantor spectra and find extremely slow correlation decays in singular continuous cases (delta = 0.14 for the critical Harper model and 0 < delta less-than-or-equal-to 0.84 for the Fibonacci chains). In the kicked Harper model we demonstrate that the quantum mechanical decay is unrelated to the existence of classical chaos.