The breakdown of the Stokes–Einstein relation in supercooled liquids, which is the increase in the ratio $\frac{{\tau }_{\alpha }}{{\tau }_D}$ between the two macroscopic times for structural relaxation and diffusion on decreasing the temperature, is commonly ascribed to dynamic heterogeneities, but a clear-cut microscopic interpretation is still lacking. Here, we tackle this issue exploiting the single-particle cage-jump framework to analyze molecular dynamics simulations of soft disk assemblies and supercooled water. We find that $\frac{{\tau }_{\alpha }}{{\tau }_D}\propto \frac{⟨t_p⟩}{⟨t_c⟩}$, where ⟨t_p⟩ and ⟨t_c⟩ are the cage-jump times characterizing slow and fast particles, respectively. We further clarify that this scaling does not arise from a simple term-by-term proportionality; rather, the relations ${\tau }_{\alpha }\propto \frac{⟨t_p⟩}{⟨\mathrm{\Delta }{r}_J^2⟩}$ and ${\tau }_D\propto \frac{⟨t_c⟩}{⟨\mathrm{\Delta }{r}_J^2⟩}$ effectively connect the macroscopic and microscopic timescales, with the mean square jump length $⟨\mathrm{\Delta }{r}_J^2⟩$ shrinking on cooling. Our work provides a microscopic perspective on the Stokes–Einstein breakdown and generalizes previous results on lattice models to the case of more realistic glass-formers.

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过冷液体中斯托克斯-爱因斯坦关系的分解：笼式跳跃视角

过冷液体中斯托克斯-爱因斯坦关系的破坏，即比率的增加 $\frac{{\tau }_{\alpha }}{{\tau }_D}$在温度降低时结构松弛和扩散的两个宏观时间之间，通常归因于动态异质性，但仍然缺乏明确的微观解释。在这里，我们利用单粒子笼跳跃框架来分析软盘组件和过冷水的分子动力学模拟来解决这个问题。我们发现$\frac{{\tau }_{\alpha }}{{\tau }_D}\propto \frac{⟨{吨}_{磷}⟩}{⟨{吨}_C⟩}$，其中 ⟨ t _p ⟩ 和 ⟨ t _c ⟩ 分别是表征慢粒子和快粒子的笼子跳跃时间。我们进一步澄清，这种缩放不是由简单的逐项比例引起的；相反，关系${\tau }_{\alpha }\propto \frac{⟨{吨}_{磷}⟩}{⟨\mathrm{\Delta }{r}_J^2⟩}$ 和 ${\tau }_D\propto \frac{⟨{吨}_C⟩}{⟨\mathrm{\Delta }{r}_J^2⟩}$ 有效连接宏观和微观时间尺度，均方跳跃长度 $⟨\mathrm{\Delta }{r}_J^2⟩$冷却时收缩。我们的工作提供了斯托克斯-爱因斯坦击穿的微观视角，并将先前关于晶格模型的结果推广到更真实的玻璃形成体的情况。