Analyzing Chaos in Higher Order Disordered Quartic-Sextic Klein-Gordon Lattices Using q-Statistics
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Date
2018-03-19
Authors
Antonopoulos, Chris G.
Skokos, Charalampos
Bountis, Tassos
Flach, Sergej
Journal Title
Journal ISSN
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Publisher
arXiv
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 distribu-
tion 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 sys-
tem 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
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Citation
Chris G. Antonopoulos, Charalampos Skokos, Tassos Bountis, Sergej Flach. 2018. Analyzing Chaos in Higher Order Disordered Quartic-Sextic Klein-Gordon Lattices Using q-Statistics. arXiv