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首页> 外文期刊>The journal of physical chemistry, B. Condensed matter, materials, surfaces, interfaces & biophysical >Mean-Field Caging in a Random Lorentz Gas
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Mean-Field Caging in a Random Lorentz Gas

机译：随机洛伦兹气体的平均场持续

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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. 8 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 finited perturbative and nonperturbative (instantonic) corrections [Biroli et al. Phys. Rev. E 2021, 103, L030104]. Here, we expand on the d -> infinity 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 ->infinity RLG. These insights help chart a path toward a complete description of finite-dimensional glasses.
机译：随机洛伦兹气体（RLG）是渗流和玻璃质的最小模型，这导致了无限维d.8极限中的悖论：因此，前者的局部化跃迁预计是连续的，后者是不连续的。作为一个推定的解决方案，我们最近提出，随着D的增加，RLG的行为收敛到玻璃的描述，渗流物理恢复由于有限微扰和非微扰（瞬时）校正[BiROLi等人，Pys.Rev E 2021, 103，L030104]。在这里，我们通过考虑RLG的一个更简单的静态解和动力学解来扩展d->无穷大物理。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无法达到现有的理论描述。将动力学解与模式耦合理论（MCT）的结果进行比较，进一步表明，尽管MCT的关键定量特征远远没有达到标准，但它确实很好地捕捉到了d->无穷大RLG的不连续性。这些见解有助于绘制出一条通向有限维眼镜完整描述的道路。

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