Origin of chaos in soft interactions and signatures of
non-ergodicity
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 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 point-like collisions for
specific mass ratios $\gamma=m_2/m_1$ 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 can be obtained. While the largest finite-time
Lyapunov exponent changes smoothly with $\gamma$, 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 most probable Lyapunov exponents suggest 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.