Speaker
Description
The Lorentz mirror model provides a clean setting to study macroscopic transport generated solely by quenched environmental randomness. We introduce a hierarchical version whose distribution of left--right crossings satisfies an exact recursion. In dimensions d>=3, we prove normal transport: the mean conductance scales as (cross-section)/(length) on all length scales. A Gaussian closure, supported by numerics, predicts that the variance-to-mean ratio of the conductance converges to the universal value 2/3 for all d>=2 (the ``2/3 law''). We provide numerical evidence for the 2/3 law in the original (non-hierarchical) Lorentz mirror model in d=3, and conjecture that it is a universal signature of normal transport induced by random current matching. In the marginal case d=2, our hierarchical recursion reproduces the known scaling of the mean conductance and its variance. The talk is based on my joint work with Raphael Lefevere