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- W3098933484 abstract "We study transport properties of Schrodinger operators depending on one or more parameters. Examples include the kicked rotor and operators with quasi-periodic potentials. We show that the mean growth exponent of the kinetic energy in the kicked rotor and of the mean square displacement in quasi-periodic potentials is generically equal to 2: this means that the motion remains ballistic, at least in a weak sense, even away from the resonances of the models. Stronger results are obtained for a class of tight-binding Hamiltonians with an electric field $E(t)= E_0 + E_1cosomega t$. For $$ H=sum a_{n-k}(mid n-k><nmid + mid n>< n-kmid) + E(t)mid n><nmid $$ with $a_nsimmid nmid^{-nu} (nu>3/2)$ we show that the mean square displacement satisfies $bar{<psi_t, N^2psi_t>}geq C_epsilon t^{2/(nu+1/2)-epsilon}$ for suitable choices of $omega, E_0$ and $E_1$. We relate this behaviour to the spectral properties of the Floquet operator of the problem." @default.
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- W3098933484 doi "https://doi.org/10.1023/a:1023227327494" @default.
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