Abstract
The destruction of anomalous diffusion of the Harper model at criticality, due to weak nonlinearity , is analyzed. It is shown that the second moment grows subdiffusively as up to time . The exponents and reflect the multifractal properties of the spectra and the eigenfunctions of the linear model. For , 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.
- Received 9 November 2006
DOI:https://doi.org/10.1103/PhysRevB.75.205120
©2007 American Physical Society