Universal Behavior of Lyapunov Exponents in Unstable Systems

Abstract

We calculate the Lyapunov exponents in a classical molecular dynamics framework. The system is composed of few hundreds particles interacting either through Yukawa (Nuclear) or Slater-Kirkwood (Atomic) forces. The forces are chosen to give an Equation of State that resembles the nuclear and the atomic ${}^{4}He$ Equation Of State respectively near the critical point for liquid-gas phase transition. We find the largest fluctuations for an initial "critical temperature". The largest Lyapunov exponents $\lambda$ are always positive and can be very well fitted near this "critical temperature" with a functional form $\lambda \propto |T-T_c{|}^{-\omega }$, where the exponent $\omega =0.15$ is independent of the system and mass number. At smaller temperatures we find that $\lambda \propto T{}^{0.4498}$, a universal behavior characteristic of an order to chaos transition.

Comments: 11 pages, RevTeX, 3 figures not included available upon request