Complex Statistics and Diffusion in Nonlinear Disordered Particle Chains

2013/12/31 by Ch. G. Antonopoulos, T. Bountis, Ch. Skokos +1 · 2 citations
Physics and Astronomy · #nlin.CD

paper · pdf · doi:10.1063/1.4871477

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

arxiv created 2014/04/05 · arxiv updated 2015/06/18

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 10⁹, 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.

Cited by

• Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices
• On the dynamical and statistical properties of a quartic mean-field Hamiltonian model

Related

• Subdiffusion in the Nonlinear Schroedinger Equation with Disorder
• Microscopic chaos and diffusion
• Paradoxes of Subdiffusive Infiltration in Disordered Systems
• Effects of Dynamic Disorder on Diffusion in Rugged Energy Landscapes
• Chaotic behaviour of disordered nonlinear lattices