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Pré-Publication, Document De Travail Année : 2009

Stationary states and fractional dynamics in systems with long range interactions

Résumé

Dynamics of many-body Hamiltonian systems with long range interactions is studied, in the context of the so called $\alpha-$HMF model. Building on the analogy with the related mean field model, we construct stationary states of the $\alpha-$HMF model for which the spatial organization satisfies a fractional equation. At variance, the microscopic dynamics turns out to be regular and explicitly known. As a consequence, dynamical regularity is achieved at the price of strong spatial complexity, namely a microscopic inhomogeneity which locally displays scale invariance.
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Dates et versions

hal-00441021 , version 1 (14-12-2009)
hal-00441021 , version 2 (29-03-2010)

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Citer

Tineke L. van den Berg, Duccio Fanelli, Xavier Leoncini. Stationary states and fractional dynamics in systems with long range interactions. 2009. ⟨hal-00441021v1⟩
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