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Systems with long-range interactions have interaction potentials that decay slower than 1/r^d at large distances r in d dimensions. Common examples are self-gravitating systems, non-neutral plasmas, dipolar ferroelectrics and ferromagnets, etc. Long-range interacting systems are non-additive. This leads to unusual properties, both thermodynamic (e.g., negative microcanonical specific heat, ensemble inequivalence) and dynamic (e.g., slow relaxation, breaking of ergodicity). After a brief review, I will discuss a paradigmatic example, the Hamiltonian Mean-Field model, involving XY spins with mean-field interactions. For this model, relaxation of some initial states towards equilibrium proceeds through intermediate quasistationary states characterized by a slow variation of macroscopic observables over time. The life time of these states diverges with the system size. These states are observed in deterministic microcanonical evolution within a certain energy interval. Our recent study suggests that in presence of noise, quasistationary states occur only as a crossover phenomenon depending on the relative magnitudes of two timescales set by the system size and the level of noise in the evolution. Our proposed scaling form for the relaxation time to equilibrium is verified in simulations by a scheme of piecewise deterministic evolution for the model.

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Dr. Shamik Gupta, ENS Lyon
Konferenzraum Theoretische Physik
Contact: not specified