Thermal origin of quasi-localised excitations in glasses

Abstract: 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 quasi-localised modes of the Hessian that grows upon cooling, while others predict a pseudo-gap ${D_L(\omega)} \sim \omega^\alpha$. To unify these views and observations, we generate glassy configurations of controlled gap magnitude $\omega_c$ at temperature ${T=0}$, using so-called `breathing' particles, and study how such gapped states respond to thermal fluctuations. We find that \textit{(i)}~the gap always fills up at finite $T$ with ${D_L(\omega) \approx A_4(T) \, \omega^4}$ and ${A_4 \sim \exp(-E_a / T)}$ at low $T$, \textit{(ii)}~$E_a$ rapidly grows with $\omega_c$, in reasonable agreement with a simple scaling prediction ${E_a\sim \omega_c^4}$ and \textit{(iii)}~at larger $\omega_c$ excitations involve fewer particles, as we rationalise, and eventually become string-like. 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 pseudo-gap 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 string-like relaxation occurring near the glass transition.