Quasi-stationary distribution for Hamiltonian dynamics with singular potentials

Arnaud Guillin ♦ (1) , Boris Nectoux ♦ (1) , Liming Wu (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

In this work, we prove the existence and the uniqueness of a quasi-stationary distribution for hypoelliptic Hamiltonian dynamics for a system of N particles in R^d interacting with Lennard-Jones type potentials or with repulsive Coulomb potentials.

Mots clés: Lyapunov functions; Hypoelliptic Hamiltonian diffusions; Molecular dynamics; Lennard-Jones potential; Coulomb potential; Quasi-stationary distribution

Domaines: Mathématiques [math]; Probabilités [math.PR]; Physique mathématique [math-ph]

Arnaud Guillin ♦, Boris Nectoux ♦, Liming Wu. Quasi-stationary distribution for Hamiltonian dynamics with singular potentials. 2022. ⟨hal-03276880v2⟩