A finite-time exponent for random Ehrenfest gas

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...

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Veröffentlicht in:Annals of physics 2015-10, Vol.361, p.82-90
Hauptverfasser: Moudgalya, Sanjay, Chandra, Sarthak, Jain, Sudhir R.
Format: Artikel
Sprache:eng
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Zusammenfassung: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. •We present a finite-time exponent for particles moving in a plane containing polygonal scatterers.•The exponent found recovers the Lyapunov exponent in the limit of the polygon becoming a circle.•Our findings unify pseudointegrable and chaotic scattering via a generalized collision rule.•Stretch and fold:shuffle and cut :: Lyapunov:finite-time exponent :: fluid:granular mixing.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2015.05.033