Volume 89, Number 5, March 2010
|Number of page(s)||6|
|Published online||26 March 2010|
Stationary states and fractional dynamics in systems with long-range interactions
IM2NP, Aix-Marseille Universit, Centre de Saint Jérôme - Case 142, F-13397 Marseille Cedex 20, France, EU
2 Dipartimento di Energetica Sergio Stecco, Università di Firenze - via s. Marta 3, I-50139 Firenze, Italy, EU
3 Centro interdipartimentale per lo Studio delle Dinamiche Complesse (CSDC) - via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy, EU
4 INFN, sezione di Firenze - via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy, EU
5 Centre de Physique Théorique (Unité Mixte de Recherche (UMR 6207) du CNRS, et des universités Aix-Marseille I, Aix-Marseille II et du Sud Toulon-Var. Laboratoire affilié la FRUMAM (FR 2291).) , Aix-Marseille Université, CNRS, Luminy - Case 907, F-13288 Marseille cedex 9, France, EU
Corresponding author: firstname.lastname@example.org
Accepted: 26 February 2010
The dynamics of many-body Hamiltonian systems with long-range interactions is studied, in the context of the so-called α-HMF model. Building on the analogy with the related mean-field model, we construct stationary states of the α-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.
PACS: 05.20.-y – Classical statistical mechanics / 05.45.-a – Nonlinear dynamics and chaos
© EPLA, 2010
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