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Key aspects of glasses are controlled by the presence of excitations in which a group of particles can rearrange. Surprisingly, recent observations indicate that their density is dramatically reduced and their size decreases as the temperature of the supercooled liquid is lowered. Some theories predict these excitations to cause a gap in the spectrum of quasilocalized modes of the Hessian that grows upon cooling, while others predict a pseudogap D-L (omega) similar to omega(alpha). To unify these views and observations, we generate glassy configurations of controlled gap magnitude w e at temperature T = 0, using so-called breathing particles, and study how such gapped states respond to thermal fluctuations. We find that (i) the gap always fills up at finite T with D-L (omega) approximate to A(4)(T) omega(4) and A(4) similar to exp(-E-a/T) at low T, (ii) E-a rapidly grows with omega(c), in reasonable agreement with a simple scaling prediction E-a similar to omega(4)(c) and (iii) at larger omega(c) excitations involve fewer particles, as we rationalize, and eventually become stringlike. We propose an interpretation of mean-field theories of the glass transition, in which the modes beyond the gap act as an excitation reservoir, from which a pseudogap distribution is populated with its magnitude rapidly decreasing at lower T. We discuss how this picture unifies the rarefaction as well as the decreasing size of excitations upon cooling, together with a stringlike relaxation occurring near the glass transition.
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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 thetaLászló Forró, Richard Gaal, Sylvia Jeney, Flavio Maurizio Mor