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arXiv · 1807.09093

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

Romain Bachelard·Nicola Piovella·Shamik Gupta
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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.

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Romain Bachelard, Nicola Piovella, Shamik Gupta. 2018-07-24. Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces. https://doi.org/10.1103/physreve.99.010104

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