论文标题
带有复位的布朗颗粒系统的波动和第一通道特性
Fluctuations and first-passage properties of systems of Brownian particles with reset
论文作者
论文摘要
我们在两个模型中研究固定的波动，涉及$ n $ brownian颗粒，经过随机重置为1d的起源。我们从粒子独立重置的基本重置模型开始（模型A）。然后，我们通过假设只有远离原点的粒子是重置的（B）来引入非局部粒子间相关性。长期以来，两种模型都接近非平衡稳态。在$ n \至\ infty $的极限中，模型A中的稳态粒子密度具有无限的支持，而在模型B中，它具有紧凑的支撑。当$ n $是有限的时，在$ \ ln n $中以$ \ ln n $的规模缩放为$ n $的有限系统半径。在这两个模型中，由于布朗运动的随机特征和重置事件的随机特征，我们研究了系统质量中心和系统半径的静止波动。在模型A中，我们确定了这两个数量的精确分布。两种型号的质量中心的差异为$ 1/n $。半径的差异独立于A型A中的$ N $，并且在模型B中表现出异常的缩放缩放$（\ ln n）/n $。后者的缩放与半径自相关中的$ 1/f $噪声密切相关。最后，我们将平均第一通道时间（MFPT）评估为模型A，M型B和BBM中的遥远目标。对于模型A，我们获得了MFPT的精确渐近表达式，该表达式为$ 1/n $。对于B模型，对于“ Brownian Bees”模型，我们为MFPT提出了一个锋利的上限。边界假设一个``蒸发''场景，其中第一个段落需要多次尝试从其他粒子到目标的粒子，才能达到目标。型号B和Brownian Bees模型的结果MFPT和Brownian Bees模型缩放量表，并通过$ \ sqrt {N} $验证了该模型。
We study stationary fluctuations in two models involving $N$ Brownian particles undergoing stochastic resetting to the origin in 1d. We start with the basic reset model where the particles reset independently (model A). Then we introduce nonlocal interparticle correlations by postulating that only the particle farthest from the origin is reset (model B). At long times both models approach nonequilibrium steady states. In the limit of $N\to \infty$, the steady-state particle density in model A has an infinite support, whereas in model B it has a compact support. A finite system radius, which scales at large $N$ as $\ln N$, appears in model A when $N$ is finite. In both models we study stationary fluctuations of the center of mass of the system and of the system's radius due to the random character of the Brownian motion and of the resetting events. In model A we determine exact distributions of these two quantities. The variance of the center of mass for both models scales as $1/N$. The variance of the radius is independent of $N$ in model A and exhibits an unusual scaling $(\ln N)/N$ in model B. The latter scaling is intimately related to the $1/f$ noise in the radius autocorrelations. Finally, we evaluate the mean first-passage time (MFPT) to a distant target in model A, model B, and the BBM. For model A we obtain an exact asymptotic expression for the MFPT which scales as $1/N$. For model B, and for the "Brownian bees" model, we propose a sharp upper bound for the MFPT. The bound assumes an ``evaporation" scenario, where the first passage requires multiple attempts of a single particle, which breaks away from the rest of the particles, to reach the target. The resulting MFPT for model B and the Brownian bees model scales exponentially with $\sqrt{N}$. We verify this bound by performing highly efficient weighted-ensemble simulations of the first passage in model B.
