Quasi-stationary states in low-dimensional Hamiltonian systems

Abstract

We address a simple connection between results of Hamiltonian nonlinear dynamical theory and thermostatistics. Using a properly defined dynamical temperature in low-dimensional symplectic maps, we display and characterize long-standing quasi-stationary states that eventually cross over to a Boltzmann-Gibbs-like regime. As time evolves, the geometrical properties (e.g., fractal dimension) of the phase space change sensibly, and the duration of the anomalous regime diverges with decreasing chaoticity. The scenario that emerges is consistent with the nonextensive statistical mechanics one.