Analyzing chaos in higher order disordered quartic-sextic Klein-Gordon lattices using q-statistics

Abstract

In the study of subdiffusive wave-packet spreading in disordered Klein–Gordon (KG) nonlinear lattices, a central open question is whether the motion continues to be chaotic despite decreasing densities, or tends to become quasi-periodic as nonlinear terms become negligible. In a recent study of such KG parti- cle chains with quartic (4th order) anharmonicity in the on-site potential it was shown that q −Gaussian probability distribution functions of sums of position observables with q > 1 always approach pure Gaus- sians ( q = 1 ) in the long time limit and hence the motion of the full system is ultimately “strongly chaotic”. In the present paper, we show that these results continue to hold even when a sextic (6th order) term is gradually added to the potential and ultimately prevails over the 4th order anharmonic- ity, despite expectations that the dynamics is more “regular”, at least in the regime of small oscillations. Analyzing this system in the subdiffusive energy domain using q -statistics, we demonstrate that groups of oscillators centered around the initially excited one (as well as the full chain) possess strongly chaotic dynamics and are thus far from any quasi-periodic torus, for times as long as t = 10 9 . © 2017 Elsevier Ltd. All rights reserved.