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

  • 30 July 1997
Abstract
We study the largest Lyapunov exponent $\lambda$ and finite size effects for a system of N fully-coupled classical particles. The system shows a phase transition (PT) from a clustering phase to a homogeneous one as the energy per particle U is increased. Around the PT region, $\lambda$ 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. At small energy, $\lambda$ goes to zero with a N-independent power law behavior: $\lambda \sim \sqrt{U}$. The system is integrable above the PT region and $\lambda$ goes slowly to zero as N is increased. At very large energy U, the behavior $\lambda \sim N^{-1/3}$ as $N \to \infty$ is found numerically and justified on the basis of a random matrix approximation. Finally, we find an interesting discrepancy between the canonical and the microcanonical ensemble predictions in the PT region, which is strongly reduced for $N < 500$. This is of particular relevance in nuclear physics for the multifragmentation phase transition.

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