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

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 D(omega(min)) similar to omega(5)(min) in regime, as opposed to the omega(min)4 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 'gamma' near the plastic event occurring at '(gamma p)' assumes a universal form that displays a collapse when scaled by root gamma(p) - gamma, and with the number of particles as N-0.22 Notably, at low frequencies, this scaled distribution displays a robust D(omega(min)) similar to omega(6)(min) power-law regime, which survives in the large N 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.