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

Marco Tarzia; Giulio Biroli; Jean-Philippe Bouchaud; Alexandre Lefèvre

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arXiv · 0812.3514

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

Marco Tarzia·Giulio Biroli·Jean-Philippe Bouchaud·Alexandre Lefèvre

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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 $α$ and $β$-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.

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Marco Tarzia, Giulio Biroli, Jean-Philippe Bouchaud, Alexandre Lefèvre. 2009-12-19. Anomalous non-linear response of glassy liquids: general arguments and a Mode-Coupling approach. https://arxiv.org/abs/0812.3514

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