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Quasi-stationary states in low-dimensional Hamiltonian systems. (English) Zbl 1065.82014

Summary: We address a simple connection between results of Hamiltonian non-linear 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 non-extensive statistical mechanics one.

MSC:

82C03 Foundations of time-dependent statistical mechanics
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
70H05 Hamilton’s equations

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