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Mechanical spectroscopy, i.e. cyclic deformations at varying frequencies, isused theoretically and numerically to measure dissipation in model glasses.From a normal mode analysis, we show that in the high-frequency THz regimewhere dissipation is harmonic, the quality factor (or loss angle) can beexpressed analytically. This expression is validated through non-equilibriummolecular dynamics simulations applied to a model of amorphous silica(SiO$_2$). Dissipation is shown to arise from non-affine relaxations triggeredby the applied strain through the excitation of vibrational eigenmodes that actas damped harmonic oscillators. We discuss an asymmetry vector field, whichencodes the information about the structural origin of dissipation measured bymechanical spectroscopy. In the particular case of silica, we find that themotion of oxygen atoms, which induce a deformation of Si-O-Si bonds is the maincontributor to harmonic energy dissipation.

Theory of harmonic dissipation in disordered solids