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arXiv · 1403.2692

Destruction of Anderson localization by nonlinearity in kicked rotator at different effective dimensions

Leonardo Ermann·Dima L. Shepelyansky
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Abstract

We study numerically the frequency modulated kicked nonlinear rotator with effective dimension $d=1,2,3,4$. We follow the time evolution of the model up to $10^9$ kicks and determine the exponent $α$ of subdiffusive spreading which changes from $0.35$ to $0.5$ when the dimension changes from $d=1$ to $4$. All results are obtained in a regime of relatively strong Anderson localization well below the Anderson transition point existing for $d=3,4$. We explain that this variation of the exponent is different from the usual $d-$dimensional Anderson models with local nonlinearity where $α$ drops with increasing $d$. We also argue that the renormalization arguments proposed by Cherroret N et al. arXiv:1401.1038 are not valid.

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Leonardo Ermann, Dima L. Shepelyansky. 2014-03-11. Destruction of Anderson localization by nonlinearity in kicked rotator at different effective dimensions. https://doi.org/10.1088/1751-8113%2F47%2F33%2F335101

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