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arXiv · 0903.3956

Origin of chaos in soft interactions and signatures of nonergodicity

Marcus W. Beims·Cesar Manchein·Jan M. Rost
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Abstract

The emergence of chaotic motion is discussed for hard-point like and soft collisions between two particles in a one-dimensional box. It is known that ergodicity may be obtained in hard-point like collisions for specific mass ratios $γ=m2/m1$ of the two particles and that Lyapunov exponents are zero. However, if a Yukawa interaction between the particles is introduced, we show analytically that positive Lyapunov exponents are generated due to double collisions close to the walls. While the largest finite-time Lyapunov exponent changes smoothly with $γ$, the number of occurrences of the most probable one, extracted from the distribution of finite-time Lyapunov exponents over initial conditions, reveals details about the phase-space dynamics. In particular, the influence of the integrable and pseudointegrable dynamics without Yukawa interaction for specific mass ratios can be clearly identified and demonstrates the sensitivity of the finite-time Lyapunov exponents as a phase-space probe. Being not restricted to two-dimensional problems such as Poincaré sections, the number of occurrences of the most probable Lyapunov exponents suggests itself as a suitable tool to characterize phase-space dynamics in higher dimensions. This is shown for the problem of two interacting particles in a circular billiard.

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Marcus W. Beims, Cesar Manchein, Jan M. Rost. 2009-03-23. Origin of chaos in soft interactions and signatures of nonergodicity. https://doi.org/10.1103/physreve.76.056203

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