# 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}
}
• Published 2016
• Physics, Mathematics
• Journal of Statistical Physics
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