Instabilities in the Mean Field Limit

@article{HanKwan2016InstabilitiesIT,
  title={Instabilities in the Mean Field Limit},
  author={Daniel Han-Kwan and T. Nguyen},
  journal={Journal of Statistical Physics},
  year={2016},
  volume={162},
  pages={1639-1653}
}
Consider a system of N particles interacting through Newton’s second law with Coulomb interaction potential in one spatial dimension or a $$\mathcal {C}^2$$C2 smooth potential in any dimension. We prove that in the mean field limit $$N \rightarrow + \infty $$N→+∞, the N particles system displays instabilities in times of order $$\log N$$logN, for some configurations approximately distributed according to unstable homogeneous equilibria. 
4 Citations
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