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Article Dans Une Revue Journal of Physics A: Mathematical and General (1975 - 2006) Année : 2001

Mean-field treatment of the many-body Fokker–Planck equation

Résumé

We review some properties of the stationary states of the Fokker–Planck equation for N interacting particles within a mean-field approximation, which yields a non-linear integrodifferential equation for the particle density. Analytical results show that for attractive long-range potentials the steady state is always a precipitate containing one or several clusters of small size. For arbitrary potential, linear stability analysis allows the statement of the conditions under which the uniform equilibrium state is unstable against small perturbations and, via the Einstein relation, definition of a critical temperature Tc separating the two phases, uniform and precipitate. The corresponding phase diagram turns out to be strongly dependent on the pair-potential. In addition, numerical calculations reveal that the transition is hysteretic. We finally discuss the dynamics of relaxation for the uniform state suddenly cooled below Tc.

Dates et versions

hal-03942772 , version 1 (17-01-2023)

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Citer

Nicolas Martzel, Claude Aslangul. Mean-field treatment of the many-body Fokker–Planck equation. Journal of Physics A: Mathematical and General (1975 - 2006), 2001, 34 (50), pp.11225-11240. ⟨10.1088/0305-4470/34/50/305⟩. ⟨hal-03942772⟩
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