1206.1149 (D. M. Basko)

On the local nature and scaling of chaos in weakly nonlinear disordered
chains    [PDF]

D. M. Basko

The dynamics of a disordered nonlinear chain can be either regular or chaotic with a certain probability. The chaotic behavior is often associated with the destruction of Anderson localization by the nonlinearity. In the present work, it is argued that at weak nonlinearity chaos is nucleated locally on rare resonant segments of the chain. Based on this, the probability of chaos is evaluated analytically. This result is also confirmed by the direct numerical sampling. Our results, in combination with those of M. V. Ivanchenko, T. V. Laptyeva, and S. Flach, [Phys. Rev. Lett. 107, 240602 (2011)], indicate that chaos is not a necessary prerequisite for the spreading of an initially localized wave packet.

View original: http://arxiv.org/abs/1206.1149