Complex Statistics and Diffusion in Nonlinear Disordered Particle Chains

Abstract

We investigate dynamically and statistically diffusive motion in a Klein-Gordon particle chain in the presence of disorder. In particular, we examine a low energy (subdiffusive) and a higher energy (self-trapping) case and verify that subdiffusive spreading is always observed. We then carry out a statistical analysis of the motion in both cases in the sense of the Central Limit Theorem and present evidence of different chaos behaviors, for various groups of particles. Integrating the equations of motion for times as long as $10^9$, our probability distribution functions always tend to Gaussians and show that the dynamics does not relax onto a quasi-periodic KAM torus and that diffusion continues to spread chaotically for arbitrarily long times.

16 pages, 4 figures, accepted for publication in "Chaos: An Interdisciplinary Journal of Nonlinear Science" journal

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Cited by in corpus (9)

• Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices
• Computational efficiency of symplectic integration schemes: Application to multidimensional disordered Klein-Gordon lattices
• Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method
• Analyzing Chaos in Higher Order Disordered Quartic-Sextic Klein-Gordon Lattices Using $q$-Statistics
• Polydispersed Granular Chains: From Long-lived Chaotic Anderson-like Localization to Energy Equipartition
• Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems
• Frequency map analysis of spatiotemporal chaos in the nonlinear disordered Klein-Gordon lattice
• Chaotic behaviour of disordered nonlinear lattices