Complex statistics and diffusion in nonlinear disordered particle chains

Ch. G. Antonopoulos; T. Bountis; Ch. Skokos; L. Drossos

doi:10.1063/1.4871477

Complex statistics and diffusion in nonlinear disordered particle chains

Ch. G. Antonopoulos^*, T. Bountis, Ch. Skokos, L. Drossos

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

8 Downloads (Pure)

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 Kolmogorov-Arnold-Moser torus and that diffusion continues to spread chaotically for arbitrarily long times. (C) 2014 AIP Publishing LLC.

Original language	English
Article number	024405
Number of pages	7
Journal	Chaos
Volume	24
Issue number	2
DOIs	https://doi.org/10.1063/1.4871477
Publication status	Published - Jun 2014

Bibliographical note

We 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.

Keywords

area-preserving maps
Kam Tori
chaos
model
lattices
systems
absence

Access to Document

10.1063/1.4871477

Chaos_2014_vol24_p024045
Copyright (2014) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in (citation of published article) and may be found at http://dx.doi.org/10.1063/1.4871477
Final published version, 556 KB
code_for_all_figures_paper.tarSubmitted manuscript, 75.9 KB

Cite this

@article{b42b1c8cd950417b9ee8e872af3523e5,

title = "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 Kolmogorov-Arnold-Moser torus and that diffusion continues to spread chaotically for arbitrarily long times. (C) 2014 AIP Publishing LLC.",

keywords = "area-preserving maps, Kam Tori, chaos, model, lattices, systems, absence",

author = "Antonopoulos, {Ch. G.} and T. Bountis and Ch. Skokos and L. Drossos",

note = "We 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.",

year = "2014",

month = jun,

doi = "10.1063/1.4871477",

language = "English",

volume = "24",

journal = "Chaos",

issn = "1054-1500",

publisher = "American Institute of Physics",

number = "2",

}

TY - JOUR

T1 - Complex statistics and diffusion in nonlinear disordered particle chains

AU - Antonopoulos, Ch. G.

AU - Bountis, T.

AU - Skokos, Ch.

AU - Drossos, L.

N1 - We 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.

PY - 2014/6

Y1 - 2014/6

N2 - 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.

AB - 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.

KW - area-preserving maps

KW - Kam Tori

KW - chaos

KW - model

KW - lattices

KW - systems

KW - absence

U2 - 10.1063/1.4871477

DO - 10.1063/1.4871477

M3 - Article

SN - 1054-1500

VL - 24

JO - Chaos

JF - Chaos

IS - 2

M1 - 024405

ER -

Complex statistics and diffusion in nonlinear disordered particle chains

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this