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

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 $\alpha$ 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.

arXiv comment8 pages, 3 figures

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• Chaos and subdiffusion in the infinite-range coupled quantum kicked rotors
• Barrier induced chaos in kicked rotor : classical sub-diffusion and quantum localization
• Bogoliubov excitations in the quasiperiodic kicked rotor: stability of a kicked condensate and the quasi-insulator-metal transition
• Dynamical many-body delocalization transition of a Tonks gas in a quasi-periodic driving potential
• Prethermalization and wave condensation in a nonlinear disordered Floquet system
• Many-Body Anderson Metal-Insulator Transition using Kicked Quantum Gases
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems
• Chaotic behaviour of disordered nonlinear lattices
• Deconfinement of classical Yang-Mills color fields in a disorder potential