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

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 $\alpha$ 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 $\alpha$ drops with increasing $d$. We also argue that the renormalization arguments proposed by Cherroret N et al. arXiv:1401.1038 are not valid.