论文标题
Riesz气体的动力波动
Dynamical fluctuations in the Riesz gas
论文作者
论文摘要
我们考虑在线上执行相同布朗运动并通过$ | x-y |^{ - s} $ riesz电位相互作用的无限系统，从而导致颗粒的过度抑制运动。我们研究了综合电流的波动和标记粒子的位置。我们表明，对于$ 0 <s <1 $，两个数量的标准偏差随着$ t^{\ frac {s} {2（1+s）}} $的增长而生长。当$ s> 1 $时，交互实际上是短距离的，并且通用亚脱水$ t^\ frac {1} {4} $增长仅根据指数而出现。我们还表明，标记的粒子位置的两次相关性具有与分数布朗运动相同的形式。
We consider an infinite system of particles on a line performing identical Brownian motions and interacting through the $|x-y|^{-s}$ Riesz potential, causing the over-damped motion of particles. We investigate fluctuations of the integrated current and the position of a tagged particle. We show that for $0 < s < 1$, the standard deviations of both quantities grow as $t^{\frac{s}{2(1+s)}}$. When $s>1$, the interactions are effectively short-ranged, and the universal sub-diffusive $t^\frac{1}{4}$ growth emerges with only amplitude depending on the exponent. We also show that the two-time correlations of the tagged-particle position have the same form as for fractional Brownian motion.
