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arXiv · 2510.25034

Cluster formation for weakly interacting kinetic Langevin dynamics

Benedict Leimkuhler·René Lohmann·Grigorios A. Pavliotis·Peter A. Whalley
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Abstract

In this paper, we study the formation of clusters for stochastic interacting particle systems (IPS) that interact through short-range attractive potentials in a periodic domain. We consider kinetic (underdamped) Langevin dynamics and focus on the low-friction regime. Employing a linear stability analysis for the kinetic McKean-Vlasov equation, we show that, at sufficiently low temperatures, and for sufficiently short-ranged interactions, the particles form clusters that correspond to metastable states of the mean-field dynamics. We derive the friction and particle-count dependent cluster-formation time and numerically measure the friction-dependent times to reach a stationary state (given by a state in which all particles are bound in a single cluster). By providing both theory and numerical methods in the inertial stochastic setting, this work acts as a bridge between cluster formation studies in overdamped Langevin dynamics and the Hamiltonian (microcanonical) limit.

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Benedict Leimkuhler, René Lohmann, Grigorios A. Pavliotis, Peter A. Whalley. 2025-10-28. Cluster formation for weakly interacting kinetic Langevin dynamics. https://arxiv.org/abs/2510.25034

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