TRANSPORT-PROPERTIES OF KICKED AND QUASI-PERIODIC HAMILTONIANS

We study transport properties of Schrodinger operators depending on on e or more parameters. Examples include the kicked rotor and operators with quasiperiodic potentials. We show that the mean growth exponent o f the kinetic energy in the kicked rotor and of the mean square displa cement in quasiperiodic potentials is generically equal to 2: this mea ns that the motion remains ballistic, at least in a weak sense, even a way from the resonances of the models. Stronger results are obtained f or a class of tight-binding Hamiltonians with an electric field E(t) = E-0 + E-1 cos omega t. For H= Sigma a(n-k)(/n -k)(n/ + /n>(n -k/)+ E( t) /n>(n/ with a(n) similar to/n/(-v) (v > 3/2) we show that the mean square displacement satisfies <(psi(t),N-2 psi(t))over bar> greater th an or equal to C(epsilon)t(2/(v+1/2)-epsilon) for suitable choices of omega, E-0, and E-1. We relate this behavior to the spectral propertie s of the Floquet operator of the problem.