http://arxiv.org/abs/1910.01436
We derive an effective evolution equation for a coarse-grained distribution function in the case of long-range-interacting systems by performing a coarse graining that preserves the symplectic structure of the collisionless Boltzmann, or Vlasov, equation obeyed by the fine-grained distribution function. We first derive a general form of such an equation based on symmetry considerations and very general assumptions only. We then restrict ourselves to the case of one-dimensional systems, performing the coarse-graining and obtaining an explicit version of the equation. Finally, we use such an equation to predict the dependence of the damping times on the coarse-graining scale and check them against numerical results for the Hamiltonian Mean Field (HMF) model.
G. Giachetti, A. Santini and L. Casetti
Fri, 4 Oct 19
39/61
Comments: 5 pages main paper + 9 pages of supplemental material, 1 figure in the main paper + 3 figures in the supplemental material
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