On the local nature and scaling of chaos in weakly nonlinear disordered chains
Disordered Systems and Neural Networks
2015-06-05 v3 Chaotic Dynamics
Abstract
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 presentwork it is argued that at weak nonlinearity chaos is nucleated locally on rare resonant segments of the chain. Based on this picture, the probability of chaos is evaluated analytically. The same probability is also evaluated by direct numerical sampling of disorder realizations and quantitative agreement between the two results is found.
Keywords
Cite
@article{arxiv.1206.1149,
title = {On the local nature and scaling of chaos in weakly nonlinear disordered chains},
author = {D. M. Basko},
journal= {arXiv preprint arXiv:1206.1149},
year = {2015}
}