Wavepacket dynamics of the nonlinear Harper model

Details Wavepacket dynamics of the nonlinear Harper model Wavepacket dynamics of the nonlinear Harper model

2007-02-21

arxiv.org/abs/cond-mat/0702506v2

Phys. Rev. B 75, 205120 (2007)

Physics

Condensed Matter

Other Condensed Matter

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

Scientific paper

10.1103/PhysRevB.75.205120

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