We present numerical results for the tagged-particle dynamics by solving the mode-coupling theory in confined geometry for colloidal liquids (cMCT). We show that neither the microscopic dynamics nor the type of intermediate scattering function qualitatively changes the asymptotic dynamics in vicinity of the glass transition. In particular, we find similar characteristics of confinement in the low-frequency susceptibility spectrum which we interpret as footprints of parallel relaxation. We derive predictions for the localization length and the scaling of the diffusion coefficient in the supercooled regime and discover a pronounced nonmonotonic dependence on the confinement length. For dilute liquids in the hydrodynamic limit we calculate an analytical expression for the intermediate scattering functions, which is in perfect agreement with event-driven Brownian dynamics simulations. From this, we derive an expression for persistent anticorrelations in the velocity autocorrelation function (VACF) for confined motion. Using numerical results of the cMCT equations for the VACF we also identify a crossover between different scalings corresponding to a transition from unconfined to confined behavior.

中文翻译：

---

受限胶体液体中的标记颗粒动力学

我们通过解决胶体液体（cMCT）的受限几何中的模式耦合理论，给出了标记粒子动力学的数值结果。我们表明，无论是微观动力学还是中间散射函数的类型都没有定性地改变玻璃化转变附近的渐近动力学。特别是，我们在低频磁化谱中发现了类似的局限性特征，我们将其解释为平行弛豫的足迹。我们推导了过冷状态下的局部长度和扩散系数比例的预测，并发现了对约束长度的明显非单调依赖性。对于流体动力极限中的稀液体，我们计算出中间散射函数的解析表达式，与事件驱动的布朗动力学仿真完全吻合。由此，我们得出了用于受限运动的速度自相关函数（VACF）中持久反相关的表达式。使用VACF的cMCT方程的数值结果，我们还确定了不同标度之间的交叉，这与从无约束行为到受限行为的转变相对应。