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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
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Complex statistics and diffusion in nonlinear disordered particle chains.
Ch G Antonopoulos1, T Bountis2, Ch Skokos3
1Institute for Complex Systems and Mathematical Biology (ICSMB), Department of Physics, University of Aberdeen, AB24 3UE Aberdeen, United Kingdom.
Chaos (Woodbury, N.Y.)
|July 3, 2014
Summary
This study shows that disordered Klein-Gordon particle chains exhibit chaotic diffusion. Even at high energies, particle motion spreads diffusively over long times, defying typical relaxation patterns.
Area of Science:
- Physics
- Nonlinear Dynamics
- Statistical Mechanics
Background:
- Disorder in physical systems can lead to complex emergent behaviors.
- Understanding particle motion in nonlinear chains is crucial for condensed matter physics.
Purpose of the Study:
- To investigate diffusive motion in a Klein-Gordon particle chain with disorder.
- To analyze the statistical properties and chaotic behavior of particle dynamics.
Main Methods:
- Simulating particle motion in a disordered Klein-Gordon chain at low (subdiffusive) and high (self-trapping) energies.
- Applying statistical analysis based on the Central Limit Theorem.
- Integrating equations of motion for extended time scales (up to 10^9).
Main Results:
- Subdiffusive spreading is consistently observed across different energy regimes.
- Probability distribution functions evolve towards Gaussian distributions.
- Evidence of distinct chaotic behaviors in particle groups was found.
Conclusions:
- The dynamics do not relax onto a Kolmogorov-Arnold-Moser torus.
- Chaotic diffusion persists indefinitely in these systems.
- Disordered Klein-Gordon chains exhibit long-term chaotic spreading.
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