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 a 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 a drops with increasing d. We also argue that the renormalization arguments proposed by Cherroret N et al (arXiv: 1401.1038) are not valid for this model and the Anderson model with local nonlinearity in d = 3.