The difference of perturbing a particle by force or velocity in a viscoelastic system

What is it about?

The motion of a Brownian particle in a Newtonian solvent is characterized by the famous Einstein equation, which establishes an inverse relation between friction and mobility. In contrast, in non-Markovian viscoelastic systems, the two concepts are generalized to time-dependent kernels, however, with unclear relationships. Recent experimental studies on microrheology reported several distinct relaxation times in contrast to the well-known (single timescale) Maxwell model that fits other observables, e.g. mean squared displacements (MSD). These apparent contradictions raise the question of how these relaxation times and the MSD are related and what they infer about the relation between friction and mobility in viscoelastic systems. In this work, we study this relation, using linear response theory as well as a generic bath particle model and mode-coupling theory (MCT), in comparison to experiments.

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Photo by FLY:D on Unsplash

Photo by FLY:D on Unsplash

Why is it important?

We believe that our work not only advances the understanding of the response of viscoelastic materials to force and velocity perturbations but also constitutes an important advancement in microrheological protocols.