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.
From: Peter Archibald Whalley [view email]
[v1]
Tue, 28 Oct 2025 23:28:15 UTC (7,838 KB)
[v2]
Fri, 26 Jun 2026 16:41:23 UTC (7,817 KB)
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