Brownian systems perturbed by mild shear: Comparing response relations

Abstract

We present a comprehensive study of the linear response of interacting underdamped Brownian particles to simple shear ow. We collect six di erent 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 di erent observables, where interesting e ects due to interactions and a nite particle mass are observed. Moreover, we compare the di erent response relations in terms of their statistical e ciency, 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.