Wavepacket dynamics of the nonlinear Harper model

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.