Local excitations in re-heated ultrastable glasses

Quasilocalised modes are local excitations present at low frequency vibrational spectrum in glasses. We numerically study their frequency density D_loc(ω) evolution under thermal cycles at different temperatures T, starting from ultrastable glass configurations where these excitations are gapped. The latter are prepared by an algorithm where individual particles can "breathe", modelling the effect of the swap algorithm in a grand-canonical ensemble. We find that a quartic behavior D_loc(ω)=A₄ ω⁴ always appears at any finite T. The prefactor A₄, which characterizes the number of quasilocalised modes, can increase by a factor of thousands with growing T in our numerical observations. Moreover at small T, A₄ follows an Arrhenius behaviour: A₄ ~ exp(-E_a/T) where E_a is atypical energy that depends on the magnitude of the gap initially present. We provide arguments for this dependence. Overall, our result support that true gaps never exists at finite temperature in finite dimensions, and suggest that in some equilibrated super-cooled liquids A₄ may decrease exponentially at low T.