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 $^4He$ 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 $λ$ are always positive and can be very well fitted near this "critical temperature" with a functional form $λ\propto |T-T_c|^{-ω}$, where the exponent $ω=0.15$ is independent of the system and mass number. At smaller temperatures we find that $λ\propto T~ ^{0.4498}$, a universal behavior characteristic of an order to chaos transition.