Stationary states and fractional dynamics in systems with long range interactions

TL;DR

This paper investigates the stationary states and fractional dynamics in long-range interacting many-body systems, revealing a balance between microscopic regularity and spatial complexity through fractional equations.

Contribution

It introduces a novel class of stationary states in the $ ext{alpha}$-HMF model characterized by fractional spatial equations, linking microscopic regularity with complex spatial organization.

Findings

Stationary states satisfy fractional equations.

Microscopic dynamics are regular and explicitly known.

Spatial organization exhibits scale invariance.

Abstract

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.