Stationary states and fractional dynamics in systems with long range interactions

Details Stationary states and fractional dynamics in systems with long range interactions Stationary states and fractional dynamics in systems with long range interactions

2009-12-16

arxiv.org/abs/0912.3060v2

T. L. Van Den Berg, D. Fanelli and X. Leoncini, EPL, 89 (2010) 50010

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1209/0295-5075/89/50010

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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