Log-periodic drift oscillations in self-similar billiards

TL;DR

This paper investigates a particle's movement in a self-similar Lorentz billiard channel with exponentially growing cells, revealing logarithmic periodicity in drift corrections through numerical analysis.

Contribution

It demonstrates the logarithmic periodicity of drift correction in a self-similar billiard, a novel insight into such dynamical systems.

Findings

Drift term computed numerically.

Logarithmic periodicity established.

Self-similar structure influences drift behavior.

Abstract

We study a particle moving at unit speed in a self-similar Lorentz billiard channel; the latter consists of an infinite sequence of cells which are identical in shape but growing exponentially in size, from left to right. We present numerical computation of the drift term in this system and establish the logarithmic periodicity of the corrections to the average drift.