Nonequilibrium Steady States of Driven Periodic Media

TL;DR

This paper investigates the nonequilibrium steady states of driven periodic media, revealing that disorder destroys long-range order and that the stable state is a transverse smectic with unique hydrodynamic properties, supported by renormalization group analysis.

Contribution

It derives microscopic hydrodynamic equations for driven media, identifies the transverse smectic as the stable state, and analyzes its finite temperature behavior using renormalization group methods.

Findings

Disorder destroys long-range order in driven media.

The stable state is a transverse smectic with flowing liquid channels.

Finite temperature behavior is less glassy and exhibits an analytic transverse response.

Abstract

We study a periodic medium driven over a random or periodic substrate. Our work is based on nonequilibrium continuum hydrodynamic equations of motion, which we derive microscopically. We argue that in the random case instabilities will always destroy the LRO of the lattice. In most, if not all, cases, the stable driven ordered state is a transverse smectic, with ordering wavevector perpendicular to the velocity. It consists of a periodic array of flowing liquid channels, with transverse displacements and density (``permeation mode'') as hydrodynamic variables. We present dynamic functional renormalization group calculations in two and three dimensions for an approximate model of the smectic. The finite temperature behavior is much less glassy than in equilibrium, owing to a disorder-driven effective ``heating'' (allowed by the absence of the fluctuation-dissipation theorem). This, in conjunction with the permeation mode, leads to a fundamentally analytic transverse response for $T>0$. Our results are compared to recent experiments and other theoretical work.