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Wavepacket dynamics of the nonlinear Harper model

Gim Seng Ng·Tsampikos Kottos
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Abstract

The destruction of anomalous diffusion of the Harper model at criticality, due to weak nonlinearity $χ$, is analyzed. It is shown that the second moment grows subdiffusively as $ \sim t^α$ up to time $t^*\sim χ^γ$. The exponents $α$ and $γ$ 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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Gim Seng Ng, Tsampikos Kottos. 2007-05-23. Wavepacket dynamics of the nonlinear Harper model. https://doi.org/10.1103/physrevb.75.205120

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