Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces
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.
Keywords
Cite
@article{arxiv.1807.09093,
title = {Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces},
author = {Romain Bachelard and Nicola Piovella and Shamik Gupta},
journal= {arXiv preprint arXiv:1807.09093},
year = {2019}
}