Lyapunov exponent of many-particle systems: testing the stochastic approach

The stochastic approach to the determination of the largest Lyapunov exponent of a many-particle system is tested in the so-called mean-field XY Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the Lyapunov exponent to a few statistical properties of the Hessian matrix of the...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2003-09, Vol.68 (3 Pt 2), p.036120-036120
Main Authors: Anteneodo, Celia, Maia, Raphael N P, Vallejos, Raúl O
Format: Article
Language:English
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The stochastic approach to the determination of the largest Lyapunov exponent of a many-particle system is tested in the so-called mean-field XY Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the Lyapunov exponent to a few statistical properties of the Hessian matrix of the interaction, which can be calculated as suitable thermal averages. We have verified that there is a satisfactory quantitative agreement between theory and simulations in the disordered phases of the XY models, either with attractive or repulsive interactions. Part of the success of the theory is due to the possibility of predicting the shape of the required correlation functions, because this permits the calculation of correlation times as thermal averages.
ISSN:1539-3755