Weak mixing and anomalous kinetics along filamented surfaces

Area of Science:

• * Physics
• * Dynamical Systems
• * Statistical Mechanics

Background:

• * Investigates chaotic properties of a particle within a square billiard system featuring a central horizontal bar.
• * Models field-line windings in merged surfaces, presenting an intermediate case between integrability and strong mixing.
• * Characterizes systems with weak-mixing properties, including zero Lyapunov exponent and entropy.

Purpose of the Study:

• * To analyze the chaotic dynamics and transport properties of particles in a square billiard with a central bar.
• * To connect the system's transport behavior to the ergodic properties of continued fractions.
• * To investigate the distribution of Poincare recurrences and displacements, including truncated moments.

Main Methods:

• * Analysis of chaotic properties within the defined billiard system.
• * Calculation of Poincare recurrence distributions and displacement distributions.
• * Examination of truncated moments of displacement distributions and their temporal evolution.

Main Results:

• * Demonstrated anomalous transport properties within the square billiard system.
• * Established a link between transport characteristics and the ergodic properties of continued fractions.
• * Identified log-periodic oscillations in the distribution function of displacements and truncated moments, with a universal period T(log)=pi(2)/12 ln 2.
• * Found similar results applicable to other billiard systems, such as square-in-square geometries.

Conclusions:

• * The square billiard with a central bar exhibits intermediate chaotic properties and anomalous transport.
• * The system's behavior is strongly related to ergodic properties of continued fractions.
• * Log-periodic oscillations in displacement distributions are a universal feature in such systems.