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Quasilocalized modes appear in the vibrational spectrum of amorphous solids at low frequency. Though never formalized, these modes are believed to have a close relationship with other important local excitations, including shear transformations and two-level systems. We provide a theory for their frequency density, D-L (omega) similar to omega(alpha), that establishes this link for systems at zero temperature under quasistatic loading. It predicts two regimes depending on the density of shear transformations P(x) similar to x(theta) (with x the additional stress needed to trigger a shear transformation). If theta > 1/4, then alpha = 4 and a finite fraction of quasilocalized modes form shear transformations, whose amplitudes vanish at low frequencies. If theta < 1/4, then alpha = 3 + 4 theta and all quasilocalized modes form shear transformations with a finite amplitude at vanishing frequencies. We confirm our predictions numerically.
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glass transition'' problem; or by (c) exerting an external stress or strain associated with shear transformations, which control the plasticity. Hence, it is important to understand how temperature and system preparation determines the density and geometry of these excitations. The possible unification of these excitations into a common description is also a fundamental problem. These local excitations are thought to have a close relationship with
Quasi-localised modes (QLMs)'' which are present in the low-frequency vibrational spectrum in amorphous solids. Understanding the properties of QLMs and clarifying the relation between QLMs and these local excitations are important to the study of the latter.
In this thesis: (1) we provide a theory for the QLMs, D_L(omega) ~ omega^alpha, that establishes the link between QLMs and shear transformations for systems under quasi-static loading. It predicts two regimes depending on the density of shear transformations P(x)~ x^theta (with x the additional stress needed to trigger a shear transformation). If theta>1/4, alpha=4 and a finite fraction of quasi-localised modes form shear transformations, whose amplitudes vanish at low frequencies. If theta