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arXiv · 1409.1488

A finite-time exponent for random Ehrenfest gas

Sanjay Moudgalya·Sarthak Chandra·Sudhir R. Jain
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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.

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Sanjay Moudgalya, Sarthak Chandra, Sudhir R. Jain. 2014-09-04. A finite-time exponent for random Ehrenfest gas. https://doi.org/10.1016/j.aop.2015.05.033

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