In this paper, we study the formation of clusters for stochastic interacting particle systems (SIPS) 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.

翻译：本文研究了在周期域中通过短程吸引势相互作用的随机相互作用粒子系统（SIPS）的团簇形成过程。我们考虑动力学（欠阻尼）朗之万方程，并重点关注低摩擦区域。通过对动力学McKean-Vlasov方程进行线性稳定性分析，我们证明在足够低的温度下，对于足够短程的相互作用，粒子会形成对应于平均场动力学亚稳态的团簇。我们推导了依赖于摩擦系数和粒子数量的团簇形成时间，并通过数值方法测量了达到稳态（即所有粒子结合为单一团簇的状态）所需的摩擦相关时间。通过在惯性随机框架中提供理论与数值方法，本研究在过阻尼朗之万动力学与哈密顿（微正则）极限的团簇形成研究之间建立了桥梁。