Anomalous nonlinear response of glassy liquids: general arguments and a mode-coupling approach

We study theoretically the nonlinear 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 nonlinear response and the derivative of the linear response with respect to temperature. Using results from mode-coupling theory and scaling arguments valid close to the glass transition, we obtain the frequency and temperature dependence of the nonlinear response in the alpha- and beta-regimes. Our results demonstrate that supercooled liquids are characterized by responses to external perturbations that become increasingly nonlinear as the glass transition is approached. These results are extended to the case of inhomogeneous perturbing fields.