标题： 热平衡中由空间相关噪声引起的示踪粒子水动力捕获 显示英文标题

标题： Hydrodynamic Trapping of Tracer Particles Induced by Spatially Correlated Noise in Thermal Equilibrium

摘要： 我们研究在存在空间相关噪声（由单一长度尺度表征）的情况下波动的斯托克斯方程，同时通过相应的涨落-耗散关系保持热平衡。 数值模拟显示，示踪粒子的均方位移（MSD）随比值$\ell/r$的变化而非单调地变化，其中相关长度$\ell$与粒子半径$r$的比值：当$\ell$接近$r$时，MSD 减小，在$\ell\simeq r$附近达到最小值，之后对于$\ell > r$又上升。 初始抑制源于瞬时捕获，其中短波长处缓慢的动量扩散限制了粒子的运动。 当$\ell>r$时，粒子在陷阱之间跳跃并最终恢复正常的扩散（$\text{MSD}\propto t$），这与动量扩散在长波长下过渡到标准拉普拉斯扩散的事实一致。我们进一步说明，空间相关性在流体力学方程中引入了非局部动量扩散，类似于玻璃态和其他无序系统中的缓慢动力学。 显示英文摘要

摘要： We investigate the fluctuating Stokes equation in the presence of spatially correlated noise -- characterized by a single length scale -- while preserving thermal equilibrium through the corresponding fluctuation-dissipation relation. Numerical simulations reveal that a tracer particle's mean-squared displacement (MSD) depends nonmonotonically on the ratio $\ell/r$ between the correlation length $\ell$ and the particle radius $r$: the MSD decreases as $\ell$ approaches $r$, reaches a minimum near $\ell\simeq r$, and rises again for $\ell > r$. The initial suppression stems from transient trapping, where sluggish momentum diffusion at short wavelengths confines the particle. When $\ell>r$, the particle hops between traps and eventually recovers normal diffusion ($\text{MSD}\propto t$) consistent with the fact that momentum diffusion crosses over to the standard Laplacian at long wavelengths. We further illustrate that spatial correlation introduces nonlocal momentum diffusion in the hydrodynamic equations, reminiscent of the slow dynamics in glassy and other disordered systems.