Anomalous non-linear response of glassy liquids: general arguments and a Mode-Coupling approach

TL;DR

This paper develops a theoretical framework linking the non-linear response of glassy liquids to their linear response derivatives, using Mode-Coupling Theory and scaling arguments to analyze behavior near the glass transition.

Contribution

It introduces a relation between non-linear and linear responses in glass formers based on general principles and Mode-Coupling Theory, extending to inhomogeneous fields.

Findings

Non-linear response increases as the glass transition is approached.

Derived frequency and temperature dependence of non-linear response in different regimes.

Extended analysis to inhomogeneous perturbations.

Abstract

We study theoretically the non-linear response properties of glass formers. We establish several general results which, together with the assumption of Time-Temperature Superposition, lead to a relation between the non-linear response and the derivative of the linear response with respect to temperature. Using results from Mode-Coupling Theory (MCT) and scaling arguments valid close to the glass transition, we obtain the frequency and temperature dependence of the non-linear response in the $\alpha$ and $\beta$-regimes. Our results demonstrate that supercooled liquids are characterized by responses to external perturbations that become increasingly non-linear as the glass transition is approached. These results are extended to the case of inhomogeneous perturbing fields.