Kinetic theory of $1D$ homogeneous long-range interacting systems sourced by $1/N^2$ effects

Jean-Baptiste Fouvry, Ben Bar-Or, Pierre-Henri Chavanis

The long-term dynamics of long-range interacting $N$-body systems can generically be described by the Balescu-Lenard kinetic equation. However, for $1D$ homogeneous systems, this…