Wavepacket dynamics of the nonlinear Harper model

Abstract

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 $<m_2>\sim t^{\alpha }$ up to time $t^{\ast }\sim {\chi }^{\gamma }$. The exponents $\alpha$ and $\gamma$ reflect the multifractal properties of the spectra and the eigenfunctions of the linear model. For $t>t^{\ast }$, 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.

6 pages, 5 figures. Revised and published in Phys. Rev. B