Lyapunov Instability and Finite Size Effects in a System with Long-Range Forces

Vito Latora, Andrea Rapisarda, Stefano Ruffo
1998 Physical Review Letters  
We study the largest Lyapunov exponent $\lambda$ and the finite size effects of a system of N fully-coupled classical particles, which shows a second order phase transition. Slightly below the critical energy density $U_c$, $\lambda$ shows a peak which persists for very large N-values (N=20000). We show, both numerically and analytically, that chaoticity is strongly related to kinetic energy fluctuations. In the limit of small energy, $\lambda$ goes to zero with a N-independent power law:
more » ... nt power law: $\lambda \sim \sqrt{U}$. In the continuum limit the system is integrable in the whole high temperature phase. More precisely, the behavior $\lambda \sim N^{-1/3}$ is found numerically for $U > U_c$ and justified on the basis of a random matrix approximation.
doi:10.1103/physrevlett.80.692 fatcat:24q5nfcif5hdbfq4mz3ydnd53u