Universal non-Debye low-frequency vibrations in sheared amorphous solids.

Abstract

We study energy minimised configurations of amorphous solids with a simple shear degree of freedom. We show that the low-frequency regime of the vibrational density of states of structural glass formers is crucially sensitive to the macroscopic stress of the sampled configurations. In both two and three dimensions, shear-stabilised configurations display a <i>D</i>(<i>ω</i>_min) ∼ <i>ω</i>5min regime, as opposed to the <i>ω</i>4min regime observed under unstrained conditions. In order to isolate the source of these deviations from crystalline behaviour, we also study configurations of two dimensional, strained amorphous solids close to a plastic event. We show that the minimum eigenvalue distribution at a strain '<i>γ</i>' near the plastic event occurring at '<i>γ</i>_P' assumes a universal form that displays a collapse when scaled by , and with the number of particles as <i>N</i>^-0.22. Notably, at low frequencies, this scaled distribution displays a robust <i>D</i>(<i>ω</i>_min) ∼ <i>ω</i>6min power-law regime, which survives in the large <i>N</i> limit. Finally, we probe the properties of these configurations through a characterisation of the second and third eigenvalues of the Hessian matrix near a plastic event.