Origin of chaos in soft interactions and signatures of nonergodicity

M. W. Beims, C. Manchein, and J. M. Rost
Phys. Rev. E 76, 056203 – Published 2 November 2007

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=m2m1 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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  • Received 13 February 2006

DOI:https://doi.org/10.1103/PhysRevE.76.056203

©2007 American Physical Society

Authors & Affiliations

M. W. Beims1,2, C. Manchein1, and J. M. Rost2

  • 1Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, PR, Brazil
  • 2Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany

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Issue

Vol. 76, Iss. 5 — November 2007

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