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

Abstract

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.

arXiv comment11 pages including 6 figures

References in corpus (20)

• Non-Gaussian equilibrium in a long-range Hamiltonian system
• Geometric approach to Hamiltonian dynamics and statistical mechanics
• Superdiffusion and Out-of-equilibrium Chaotic Dynamics with Many Degrees of Freedoms
• Lyapunov instability and finite size effects in a system with long-range forces
• Riemannian theory of Hamiltonian chaos and Lyapunov exponents
• Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system
• Analytic estimation of Lyapunov exponent in a mean-field model undergoing a phase transition
• Chaos and Statistical Mechanics in the Hamiltonian Mean Field Model
• Statistics of finite-time Lyapunov exponents in a random time-dependent potential
• Violation of ensemble equivalence in the antiferromagnetic mean-field XY model
• Chaotic dynamics and superdiffusion in a Hamiltonian system with many degrees of freedom
• Scaling laws for the largest Lyapunov exponent in long-range systems: A random matrix approach
• Slow Relaxation at Critical Point of Second Order Phase Transition in a Highly Chaotic Hamiltonian System
• Chaos, ergodicity, and the thermodynamics of lower-dimensional Hamiltonian systems
• Theoretical estimates for the largest Lyapunov exponent of many-particle systems
• Clustering in a model with repulsive long-range interactions
• Chaos in the thermodynamic limit
• Dynamical Quasi-Stationary States in a system with long-range forces
• Comment on ``Lyapunov Exponent of a Many Body System and Its Transport Coefficients''
• Semi-Analytic Estimates of Lyapunov Exponents in Lower-Dimensional Systems

Cited by in corpus (6)

• Scaling with system size of the Lyapunov exponents for the Hamiltonian Mean Field model
• Lyapunov instabilities in lattices of interacting classical spins at infinite temperature
• Quasi-stationary trajectories of the HMF model: a topological perspective
• Largest Lyapunov exponent of long-range XY systems
• Generalized Lyapunov exponents of the random harmonic oscillator: cumulant expansion approach
• Lyapunov exponent of the random frequency oscillator: cumulant expansion approach