Journal
PHYSICAL REVIEW B
Volume 75, Issue 20, Pages -Publisher
AMERICAN PHYSICAL SOC
DOI: 10.1103/PhysRevB.75.205120
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The destruction of anomalous diffusion of the Harper model at criticality, due to weak nonlinearity chi, is analyzed. It is shown that the second moment grows subdiffusively as < m(2)>similar to t(alpha) up to time t(*)similar to chi(gamma). The exponents alpha and gamma reflect the multifractal properties of the spectra and the eigenfunctions of the linear model. For t > t(*), the anomalous diffusion law is recovered, although the evolving profile has a different shape than in the linear case. These results are applicable in wave propagation through nonlinear waveguide arrays and transport of Bose-Einstein condensates in optical lattices.
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