随机Lorentz气体中的平均场囚禁
Mean-field caging in a random Lorentz gas
摘要：
随机洛仑兹气体（RLG）是一个极小模型的渗流和glassiness，这导致了一个悖论的无限维，$d\rightarrow\infty$限制：本地化过渡，然后预计是连续的，后者的不连续。作为一个假定的解决方案，我们最近提出，随着$d$的增加，RLG的行为收敛到玻璃态描述，并且由于有限- $d$微扰和非微扰（瞬时）校正，渗流物理被恢复[Biroli等人arXiv：2003.11179]。在这里，我们扩大了$d\rightarrow\infty$物理考虑一个简单的静态解决方案，以及动态解决方案的RLG。将该解的$1/d$修正与数值结果进行比较，发现即使是微扰修正也超出了现有理论描述的范围。将动力学解与模式耦合理论（MCT）结果进行比较，进一步揭示了尽管MCT的关键定量特征与实际相差甚远，但它确实正确地捕捉到了$d\rightarrow\infty$ RLG的不连续性质。这些见解有助于绘制一条完整描述有限维眼镜的道路。
英文摘要：
The random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional, $d\rightarrow\infty$ limit: the localization transition is then expected to be continuous for the former and discontinuous for the latter. As a putative resolution, we have recently suggested that as $d$ increases the behavior of the RLG converges to the glassy description, and that percolation physics is recovered thanks to finite-$d$ perturbative and non-perturbative (instantonic) corrections [Biroli et al. arXiv:2003.11179]. Here, we expand on the $d\rightarrow\infty$ physics by considering a simpler static solution as well as the dynamical solution of the RLG. Comparing the $1/d$ correction of this solution with numerical results reveals that even perturbative corrections fall out of reach of existing theoretical descriptions. Comparing the dynamical solution with the mode-coupling theory (MCT) results further reveals that although key quantitative features of MCT are far off the mark, it does properly capture the discontinuous nature of the $d\rightarrow\infty$ RLG. These insights help chart a path toward a complete description of finite-dimensional glasses.
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