Stationary states and fractional dynamics in systems with long range interactions

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.

References in corpus (8)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Out-of-equilibrium tricritical point in a system with long-range interactions
• Abundance of regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit for long-range systems
• Lynden-Bell and Tsallis distributions for the HMF model
• Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos
• Out of Equilibrium Solutions in the $XY$-Hamiltonian Mean Field model
• Out of equilibrium phase transitions in mean field Hamiltonian dynamics
• Stabilizing the intensity of a wave amplified by a beam of particles

Cited by in corpus (10)

• Review of Some Promising Fractional Physical Models
• Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs
• Critical behaviour of the XY -rotors model on regular and small world networks
• Vlasov equation for long-range interactions on a lattice
• Existence of Quasi-stationary states at the Long Range threshold
• Action diffusion and lifetimes of quasistationary states in the Hamiltonian Mean Field model
• Emergence of a non trivial fluctuating phase in the XY model on regular networks
• Crafting networks to achieve, or not achieve, chaotic states
• Emergence of a collective crystal in a classical system with long-range interactions
• Full Self-Consistent Vlasov-Maxwell Solution