无规洛仑兹气体中渗流与玻璃化的相互作用
Interplay between percolation and glassiness in the random Lorentz gas
摘要：
随机洛仑兹气体（RLG）是非均匀介质中输运的一种极小模型。它还模拟了玻璃态系统中示踪剂的动力学。然而，这两种观点从根本上是不一致的。前者的阻滞与渗透有关，因此是连续的，而玻璃状阻滞是不连续的。为了阐明RLG中的渗流和玻璃化之间的相互作用，我们考虑其在无限维$d\rightarrow\infty$极限下的精确解，以及在$d=2\ldots 20$中的数值解。我们发现，平均场的解决方案的RLG和玻璃属于相同的普适性类，并在有限维的玻璃化转变的瞬间修正有关罕见的笼逃逸破坏。这一进展表明，激光陀螺可以作为一个玩具模型，以发展的第一原理描述跳跃的结构玻璃。
英文摘要：
The random Lorentz gas (RLG) is a minimal model of transport in heterogeneous media. It also models the dynamics of a tracer in a glassy system. These two perspectives, however, are fundamentally inconsistent. Arrest in the former is related to percolation, and hence continuous, while glass-like arrest is discontinuous. In order to clarify the interplay between percolation and glassiness in the RLG, we consider its exact solution in the infinite-dimensional $d\rightarrow\infty$ limit, as well as numerics in $d=2\ldots 20$. We find that the mean field solutions of the RLG and glasses fall in the same universality class, and that instantonic corrections related to rare cage escapes destroy the glass transition in finite dimensions. This advance suggests that the RLG can be used as a toy model to develop a first-principle description of hopping in structural glasses.
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