Reply to the Comment on `` Moving glass phase of driven lattices ''

TL;DR

This paper defends the idea that the moving glass phase's unique properties stem from transverse periodicity, asserting their robustness against structural details along the motion direction despite claims to the contrary.

Contribution

It clarifies that the moving glass phase's properties are due solely to transverse periodicity, countering claims that they depend on structure along the motion direction.

Findings

Transverse periodicity causes the glassy properties.

Properties are robust to structural variations along the motion.

Existence of random forces in both directions confirmed.

Abstract

It was shown in our Letter that the novel glassy property of the moving lattice (transverse critical force and pinned channels) originate {\it only} from the periodicity in the {\it transverse} direction, i.e the underlying smectic density modes of the structure. Thus, contrarily to the claim of the Comment, these properties should be robust to the details of the structure along the direction of motion, even in the presence of a random force (we have demonstrated the existence of a random force in both directions) or dislocations between layers.