Marginally stable phases in structural glasses

A novel form of amorphous matter characterized by marginal stability was recently discovered in the mean-field theory of structural glasses. In the marginally stable phase, structural glasses inherit the richness of spin-glass physics characterized by ergodicity breaking transitions, complex free energy landscapes, rejuvenation and memory effects. We study analytically and numerically Weeks-Chandler-Andersen glasses. By changing external parameters, we continuously explore physical regimes relevant to granular matter, foams, emulsions, hard and soft colloids, and molecular glasses. Our results suggest that marginal phases should be observable for colloidal and non-Brownian particles near jamming. In this regime, we numerically observe rejuvenation and memory effects. By contrast, we find that molecular glasses do not present marginally stable phases, but our study reveals instead the presence of localised excitations presumably relevant for mechanical and vibrational properties of structural glasses.