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Deterministic diffusion in almost integrable systems.

J. L. Vega¹, T. Uzer, F. Borondo

¹School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430Departamento de Quimica, Universidad Autonoma de Madrid, Cantoblanco 28049, SpainSchool of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430.

Chaos (Woodbury, N.Y.)

|December 1, 1996

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Deterministic diffusion processes can occur in zero-entropy systems, mimicking chaos without true mathematical chaos. A random walk model predicts diffusion coefficient behavior in these non-random systems.

Area of Science:

Physics
Statistical Mechanics
Chaos Theory

Background:

Diffusion processes are typically characterized by randomness.
Understanding the underlying mechanisms of diffusion is crucial in various scientific fields.

Purpose of the Study:

To demonstrate the occurrence of deterministic diffusion processes in systems with zero entropy.
To show that these processes can mimic chaotic behavior without being mathematically chaotic.
To utilize a random walk model for predicting diffusion coefficient behavior.

Main Methods:

Development of a theoretical framework for deterministic diffusion.
Simulation of systems with zero entropy.
Application of a random walk model to analyze diffusion coefficients.

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Main Results:

Deterministic diffusion processes were observed in zero-entropy systems.
These processes exhibited characteristics that mimicked chaos.
The random walk model successfully predicted the behavior of the diffusion coefficient.

Conclusions:

Deterministic diffusion is possible in non-random, zero-entropy systems.
Such systems can exhibit apparent chaotic behavior.
The random walk model provides a valid approach for analyzing diffusion coefficients in these contexts.