A finite-time exponent for random Ehrenfest gas
- Indian Institute of Technology, Kanpur 208016 (India)
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. - Highlights: • 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.
- OSTI ID:
- 22451232
- Journal Information:
- Annals of Physics, Journal Name: Annals of Physics Vol. 361; ISSN 0003-4916; ISSN APNYA6
- Country of Publication:
- United States
- Language:
- English
Similar Records
Lyapunov exponent as a signature of dissipative many-body quantum chaos
Curvature fluctuations and the Lyapunov exponent at melting