Brownian systems perturbed by mild shear: Comparing response relations

TL;DR

This paper investigates the linear response of interacting underdamped Brownian particles under shear flow, comparing multiple computational methods, including an extended Green-Kubo relation, and analyzing their efficiency and limitations.

Contribution

It introduces six response computation routes, extends the Green-Kubo relation to underdamped systems, and compares their effectiveness and breakdown at higher shear rates.

Findings

Six response computation methods compared.

Extended Green-Kubo relation includes two new terms.

Response relaxation and breakdown analyzed under shear.

Abstract

We present a comprehensive study of the linear response of interacting underdamped Brownian particles to simple shear flow. We collect six different routes for computing the response, two of which are based on the symmetry of the considered system and observable with respect to the shear axes. We include the extension of the Green-Kubo relation to underdamped cases, which shows two unexpected additional terms. These six computational methods are applied to investigate the relaxation of the response towards the steady state for different observables, where interesting effects due to interactions and a finite particle mass are observed. Moreover, we compare the different response relations in terms of their statistical efficiency, identifying their relative demand on experimental measurement time or computational resources in computer simulations. Finally, several measures of breakdown of linear response theory for larger shear rates are discussed.