Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces

TL;DR

This paper investigates the slow, subdiffusive dynamics of a non-Hamiltonian long-range force system, revealing how macroscopic evolution and single-particle behavior lead to nonlinear diffusion phenomena.

Contribution

It introduces a Vlasov-based approximation for non-Hamiltonian long-range systems and demonstrates subdiffusive momentum behavior through analytical and numerical analysis.

Findings

Macroscopic dynamics are slow and diverge with system size.

Single-particle momentum exhibits subdiffusive behavior.

Nonlinear Fokker-Planck equation describes the diffusion process.

Abstract

Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the thermodynamic limit by a Vlasov equation that does possess stable stationary solutions. This implies that on a macroscopic scale, the molecular dynamics evolves on a slow timescale that diverges with the system size. At the single-particle level, the evolution is driven by incoherent interaction between the particles, which may be effectively modeled by a noise, leading to a Brownian-like dynamics of the momentum. Because this self-generated diffusion process depends on the particle distribution, the associated Fokker-Planck equation is nonlinear, and a subdiffusive behavior of the momentum fluctuation emerges, in agreement with numerics.