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

LEONARDO ERMANN; DIMA L. SHEPELYANSKY

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

IOP PUBLISHING LTD

Lugar: Londres; Año: 2014 vol. 47 p. 335101 - 335110

1751-8113

We study numerically the frequency modulated kicked nonlinear rotator witheffective dimension d = 1, 2, 3, 4 . We follow the time evolution of the modelup to 10 9 kicks and determine the exponent α of subdiffusive spreading whichchanges from 0.35 to 0.5 when the dimension changes from d = 1 to 4. Allresults are obtained in a regime of relatively strong Anderson localization wellbelow the Anderson transition point existing for d = 3, 4. We explain that thisvariation of the exponent is different from the usual d − dimensional Andersonmodels with local nonlinearity where α drops with increasing d. We also arguethat the renormalization arguments proposed by Cherroret N et al(arXiv:1401.1038) are not valid for this model and the Anderson model withlocal nonlinearity in d = 3