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Uni-directional transport properties of a serpent billiard

Martin Horvat·Tomaz Prosen
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Abstract

We present a dynamical analysis of a classical billiard chain -- a channel with parallel semi-circular walls, which can serve as a model for a bended optical fiber. An interesting feature of this model is the fact that the phase space separates into two disjoint invariant components corresponding to the left and right uni-directional motions. Dynamics is decomposed into the jump map -- a Poincare map between the two ends of a basic cell, and the time function -- traveling time across a basic cell of a point on a surface of section. The jump map has a mixed phase space where the relative sizes of the regular and chaotic components depend on the width of the channel. For a suitable value of this parameter we can have almost fully chaotic phase space. We have studied numerically the Lyapunov exponents, time auto-correlation functions and diffusion of particles along the chain. As a result of a singularity of the time function we obtain marginally-normal diffusion after we subtract the average drift. The last result is also supported by some analytical arguments.

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Martin Horvat, Tomaz Prosen. 2006-01-25. Uni-directional transport properties of a serpent billiard. https://doi.org/10.1088/0305-4470%2F37%2F9%2F006

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