Scaling of the dynamics of homogeneous states of one-dimensional long-range interacting systems

Abstract

Quasi-Stationary States of long-range interacting systems have been studied at length over the last fifteen years. It is known that the collisional terms of the Balescu-Lenard and Landau equations vanish for one-dimensional systems in homogeneous states, thus requiring a new kinetic equation with a proper dependence on the number of particles. Here we show that previous scalings described in the literature are due either to small size effects or the use of improper variables to describe the dynamics. The correct scaling is proportional to the square of the number of particles and deduce the kinetic equation valid for the homogeneous regime and numerical evidence is given for the Hamiltonian Mean Field and ring models.

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Cited by in corpus (20)

• Role of the range of the interactions in thermal conduction
• Dissipation-assisted prethermalization in long-range interacting atomic ensembles
• Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
• Many-body synchronisation in a classical Hamiltonian system
• Controlling the Range of Interactions in the Classical Inertial Ferromagnetic Heisenberg Model: Analysis of Metastable States
• Secular dynamics of long-range interacting particles on a sphere in the axisymmetric limit
• Kinetic theory of $1D$ homogeneous long-range interacting systems sourced by $1/N^2$ effects
• Kinetic theory of one-dimensional homogeneous long-range interacting systems with an arbitrary potential of interaction
• Environment induced pre-thermalization in the Mott-Hubbard model
• Attractor non-equilibrium stationary states in perturbed long-range interacting systems
• Ergodicity in a two-dimensional self gravitating many body system
• Lyapunov Exponent and Criticality in the Hamiltonian Mean Field Model
• Kinetic theory of one-dimensional inhomogeneous long-range interacting $N$-body systems at order $1/N^2$ without collective effects
• Ensemble Inequivalence and Maxwell Construction in the Self-Gravitating Ring Model
• Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces
• Relaxation Processes in Long-Range Lattices
• Critical Exponent for the Lyapunov Exponent and Phase Transitions -- The Generalized Hamiltonian Mean-Field Model
• Classical Goldstone modes in Long-Range Interacting Systems
• Hard-core collisional dynamics in the hamiltonian mean-field model
• A convergent kinetic equation for gravitational and Coulomb systems