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Relaxation and diffusion in a globally coupled Hamiltonian system.
1Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606-8501, Japan. yyama@i.kyoto-u.ac.jp
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 3, 2004
Summary
Anomalous diffusion in globally coupled rotators occurs transiently during the approach to equilibrium. This non-stationary behavior is explained by stretched exponential correlations, not standard power-law diffusion.
Area of Science:
- Statistical Mechanics
- Nonlinear Dynamics
Background:
- Understanding relaxation and diffusion dynamics is crucial in complex systems.
- Hamiltonian systems of globally coupled rotators provide a model for studying collective behavior.
Purpose of the Study:
- To investigate the relationship between relaxation processes and diffusion in a Hamiltonian system.
- To characterize the nature of anomalous diffusion in this system.
Main Methods:
- Analysis of a Hamiltonian system of globally coupled rotators.
- Investigation of diffusion behavior during the approach to equilibrium.
- Characterization of correlation functions and their time evolution.
Main Results:
- Anomalous diffusion is observed if and only if the system is approaching equilibrium.
- The observed anomaly is transient and due to nonstationarity, not standard power-law anomalous diffusion.
- Diffusion in quasistationary states can be described by a stretched exponential correlation function.
Conclusions:
- The study clarifies the transient nature of anomalous diffusion in globally coupled rotators.
- Stretched exponential correlation functions with evolving parameters explain diffusion dynamics.
- System nonstationarity is key to understanding diffusion anomalies in this context.