Origin of chaos in soft interactions and signatures of nonergodicity

Simple item page
dc.creatorBeims, Marcus W.
dc.creatorManchein, Cesar
dc.creatorRost, Jan M.
dc.date2009-03-23
dc.date.accessioned2026-07-07T12:56:00Z
dc.date.available2026-07-07T12:56:00Z
dc.descriptionThe 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.
dc.description8 pages, 15 figures
dc.identifierhttps://arxiv.org/abs/0903.3956
dc.identifierhttp://arxiv.org/abs/0903.3956
dc.identifierPhys. Rev. E 76, 056203 (2007)
dc.identifierdoi:10.1103/PhysRevE.76.056203
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224441
dc.subjectChaotic Dynamics
dc.titleOrigin of chaos in soft interactions and signatures of nonergodicity
dc.typetext

Files

Collections

arXiv