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

Antonopoulos, CG and Skokos, C and Bountis, T and Flach, S (2017) 'Analyzing chaos in higher order disordered quartic-sextic Klein-Gordon lattices using q-statistics.' Chaos, Solitons and Fractals, 104. pp. 129-134. ISSN 0960-0779

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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 particle 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 Gaussians ($q=1$) 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 anharmonicity, 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 $t=10^9$.

Item Type: Article
Additional Information: 13 pages, 4 figures
Uncontrolled Keywords: Klein–Gordon; Wave packet spreading; Chaotic dynamics; Quasi-periodic motion; Subdiffusive regime; q-Gaussian; q-statistics; Tsallis entropy
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 06 Oct 2017 15:50
Last Modified: 06 Jan 2022 14:49
URI: http://repository.essex.ac.uk/id/eprint/20472

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