Deterministic Diffusion
L. Nizhnik, I. Nizhnik
TL;DR
This paper explores the concept of deterministic diffusion within Lifting Dynamical Systems, providing definitions, properties, and mechanisms, including applications to billiard channels, and deriving formulas for diffusion coefficients.
Contribution
It introduces a formal framework for deterministic diffusion in LDS and analyzes anomalous diffusion in periodic billiard channels, offering new theoretical insights and formulas.
Findings
Derived expressions for deterministic diffusion coefficients.
Explained mechanisms behind deterministic and anomalous diffusion.
Applied theory to long billiard channels with periodic structures.
Abstract
In the present paper, we give a series of definitions and properties of Lifting Dynamical Systems (LDS) corresponding to the notion of deterministic diffusion. We present heuristic explanations of the mechanism of formation of deterministic diffusion in LDS and the anomalous deterministic diffusion in the case of transportation in long billiard channels with spatially periodic structures. The expressions for the coefficient of deterministic diffusion are obtained.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems · Mathematical Dynamics and Fractals