平均场系统中有限N效应的随机处理及其在相干结构寿命中的应用
Stochastic treatment of finite-N effects in mean-field systems and its application to the lifetimes of coherent structures
摘要：
本文提出了一种由一般Fokker-Planck方程推导出的随机处理方法，用以模拟由于有限N效应而导致的平均场系统向平衡态缓慢收敛的现象。热化过程涉及到可能维持非平衡准稳态的相干结构的瓦解。分析计算了接近平均场势谷的粒子分数随时间的演化。该指标能够估计平均场系统中相干结构的寿命和热化时间尺度。
英文摘要：
A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence towards equilibrium of mean-field systems due to finite-N effects. The thermalization process involves notably the disintegration of coherent structures that may sustain out-of-equilibrium quasistationary states. The time evolution of the fraction of particles remaining close to a mean-field potential trough is analytically computed. This indicator enables to estimate the lifetime of coherent structures and thermalization timescale in mean-field systems.
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