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

We study energy minimized 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 stress-ensemble from which the configurations are sampled. In both two and three dimensions, a shear-stabilized ensemble displays a $D(ω_{\min}) \sim ω^{5}_{\min}$ regime, as opposed to the $ω^{4}_{\min}$ regime observed under unstrained conditions. We also study an ensemble of two dimensional, strained amorphous solids near a plastic event. We show that the minimum eigenvalue distribution at a strain $γ$ near the plastic event occurring at $γ_{P}$, displays a collapse when scaled by $\sqrt{γ_P - γ}$, and with the number of particles as $N^{-0.22}$. Notably, at low-frequencies, this scaled distribution displays a robust $D(ω_{\min}) \sim ω^{6}_{\min}$ power-law regime, which survives in the large $N$ limit. Finally, we probe the universal properties of this ensemble through a characterization of the second and third eigenvalues of the Hessian matrix near a plastic event.