Abstract
We prove that the temporal autocorrelation function C(t) for quantum systems with Cantor spectra has an algebraic decay C(t)∼, where δ equals the generalized dimension of the spectral measure and is bounded by the Hausdorff dimension ≥δ. We study various incommensurate systems with singular continuous and absolutely continuous Cantor spectra and find extremely slow correlation decays in singular continuous cases (δ=0.14 for the critical Harper model and 0<δ≤0.84 for the Fibonacci chains). In the kicked Harper model we deomonstrate that the quantum mechanical decay is unrelated to the existence of classical chaos.
- Received 5 September 1991
DOI:https://doi.org/10.1103/PhysRevLett.69.695
©1992 American Physical Society