Relaxation Dynamics in the Energy Landscape of Glass-Forming Liquids

We numerically study the zero-temperature relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range initial temperatures. In mean-field Mari-Kurchan model, we find that changes power-law an exponential decay below well-defined temperature, consistent with recent findings in $p$-spin models. By contrast, for finite-dimensional systems, is always algebraic, non-trivial universal exponent at high temperatures crossing over harmonic value low demonstrate this apparent evolution controlled by temperature-dependent population localised glassy excitations. Our work unifies lines studies aiming detailed characterisation complex potential energy landscape glass-formers, and challenges both real space descriptions glasses.