Lyapunov instability and finite size effects in a system with long-range forces
Lyapunov instability and finite size effects in a system with long-range forces
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DOI：
10.1103/physrevlett.80.692
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发表时间：
1998-01-26
影响因子：
8.6
通讯作者：
Ruffo, S
中科院分区：
文献类型：
--
作者：
Latora, V;Rapisarda, A;Ruffo, S
研究了N个完全耦合的经典粒子系统的最大李雅普诺夫指数A和有限尺寸效应，该系统表现出二级相变。略低于临界能量密度U-c，λ显示出对于非常大的N值（N = 20 000）持续存在的峰值。我们表明，无论是数值和分析，混沌是强烈相关的动能波动。在小能量的极限下，λ以N独立的幂律趋于零：λ类似于根U。在连续极限下，系统在整个高温阶段都是可积的。更准确地说，行为λ类似于N-1/3的数值发现U > U-c和证明的基础上的随机矩阵近似。[S0031-9007（97）05121-1]。
We study the largest Lyapunov exponent A 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 = 20 000). 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 an N-independent power law: lambda similar to root U. In the continuum limit the system is integrable in the whole high temperature phase. More precisely, the behavior lambda similar to N-1/3 is found numerically for U > U-c and justified on the basis of a random matrix approximation. [S0031-9007(97)05121-1].