ISSN:
1572-9613
Keywords:
Anomalous transport
;
singular spectra
;
kicked Hamiltonians
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We study transport properties of Schrödinger 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 quasiperiodic 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 1cos ωt. For $$H = \sum {a_{n - k} (|n - k\rangle \langle n| + |n\rangle \langle n - k|) + E(t)|n\rangle \langle n|} $$ with $$a_n\sim|n|^{-\nu}(\nu〉3/2)$$ we show that the mean square displacement satisfies $$\overline {\langle\psi_{t,}N^2\psi_1\rangle}\geqslant C_\varepsilon t^{2/(\nu+1/2)-\varepsilon} $$ for suitable choices of ω, E 0, and E 1. We relate this behavior to the spectral properties of the Floquet operator of the problem.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1023227327494
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