# Analyzing Chaos in Higher Order Disordered Quartic-Sextic Klein-Gordon Lattices Using $q$-Statistics

## TL;DR

This paper investigates the chaotic behavior of disordered Klein-Gordon lattices with quartic and sextic anharmonicities, showing that the system remains strongly chaotic over long times even with higher-order terms.

## Contribution

It extends previous work by demonstrating that adding a sextic term does not diminish chaos, confirming persistent strong chaos in higher-order disordered Klein-Gordon lattices.

## Key findings

- $q$-Gaussian distributions approach Gaussian in long time limit
- System remains strongly chaotic for times up to 10^9
- Chaos persists despite higher-order anharmonicity

## 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 $t=10^9$.