Coarse-grained collisionless dynamics with long-range interactions

Abstract

We present an effective evolution equation for a coarse-grained distribution function of a long-range-interacting system preserving the symplectic structure of the non-collisional Boltzmann, or Vlasov, equation. We first derive a general form of such an equation based on symmetry considerations only. Then, we explicitly derive the equation for one-dimensional systems, finding that it has the form predicted on general grounds. Finally, we use such an equation to predict the dependence of the damping times on the coarse-graining scale and numerically check it for some one-dimensional models, including the Hamiltonian Mean Field (HMF) model, a scalar field with quartic interaction, a 1-d self-gravitating system, and the Self-Gravitating Ring (SGR).

17 pages, 7 figures. Accepted for publication in Physical Review Research

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Cited by in corpus (4)

• Symplectic coarse graining approach to the dynamics of spherical self-gravitating systems
• Violent relaxation in the Hamiltonian mean field model: II. Non-equilibrium phase diagrams
• Spreading of a local excitation in a Quantum Hierarchical Model
• On the Conditions for a Quantum Violent Relaxation