Quasi-stationary states in low-dimensional Hamiltonian systems

TL;DR

This paper investigates long-lasting quasi-stationary states in low-dimensional Hamiltonian systems, linking nonlinear dynamics with thermostatistics and showing how these states evolve over time and relate to nonextensive statistical mechanics.

Contribution

It introduces a dynamical temperature for symplectic maps and characterizes quasi-stationary states, connecting dynamical properties with nonextensive statistical mechanics.

Findings

Quasi-stationary states can persist for long times before crossing over to Boltzmann-Gibbs regimes.

The duration of anomalous regimes increases as chaoticity decreases.

Phase space geometry changes significantly during the evolution of these states.

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.