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].

Lyapunov instability and finite size effects in a system with long-range forces / Latora, V.; Rapisarda, A.; Ruffo, S.. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 80:4(1998), pp. 692-695. [10.1103/PhysRevLett.80.692]

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

Ruffo, S.
1998-01-01

Abstract

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].
1998
80
4
692
695
Latora, V.; Rapisarda, A.; Ruffo, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/17265
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