A finite-time exponent for random Ehrenfest gas
Abstract
We consider the motion of a system of free particles moving on a plane with regular hard polygonal scatterers arranged in a random manner. Calling this the Ehrenfest gas, which is known to have a zero Lyapunov exponent, we propose a finite-time exponent to characterize its dynamics. As the number of sides of the polygon goes to infinity, when polygon tends to a circle, we recover the usual Lyapunov exponent for the Lorentz gas from the exponent proposed here. To obtain this result, we generalize the reflection law of a beam of rays incident on a polygonal scatterer in a way that the formula for the circular scatterer is recovered in the limit of infinite number of vertices. Thus, chaos emerges from pseudochaos in an appropriate limit.
Keywords
Cite
@article{arxiv.1409.1488,
title = {A finite-time exponent for random Ehrenfest gas},
author = {Sanjay Moudgalya and Sarthak Chandra and Sudhir R. Jain},
journal= {arXiv preprint arXiv:1409.1488},
year = {2015}
}
Comments
15 pages, 8 figures; Accepted for publication at Annals of Physics