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

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 $t=10^9$.