Lyapunov instability and finite size effects in a system with long-range forces

الأصل · EN

We study the largest Lyapunov exponent λ 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 Uc, λ 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, λ goes to zero with a N-independent power law: λ √U. In the continuum limit the system is integrable in the whole high temperature phase. More precisely, the behavior λ N⁻¹/³ is found numerically for U > Uc and justified on the basis of a random matrix approximation.