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 Kolmogorov-Arnold-Moser torus and that diffusion continues to spread chaotically for arbitrarily long times. (C) 2014 AIP Publishing LLC.
Bibliographical noteWe would like to thank the referees for their constructive criticism and many useful suggestions that helped us considerably improve the presentation of our results. One of the authors (T. B.) gratefully acknowledges the hospitality of the New Zealand Institute of Advanced Study during the period of February 20–April 15, 2013, when some of this work was carried out. He is thankful for many useful conversations he had during his stay with Professor Sergej Flach on topics related to the content of the present paper. This research has been co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: THALES—Investing in knowledge society through the European Social Fund. Ch. S. was also supported by the Research Committees of the University of Cape Town (Start-Up Grant, Fund No. 459221) and of the Aristotle University of Thessaloniki (Prog. No. 89317). Computer simulations were performed in the facilities offered by the HPCS Lab of the Technological Educational Institute of Western Greece.
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