Relaxation Dynamics in the Energy Landscape of Glass-Forming Liquids

Abstract

We numerically study the zero-temperature relaxation dynamics of several\nglass-forming models to their inherent structures, following quenches from\nequilibrium configurations sampled across a wide range of initial temperatures.\nIn a mean-field Mari-Kurchan model, we find that relaxation changes from a\npower-law to an exponential decay below a well-defined temperature, consistent\nwith recent findings in mean-field $p$-spin models. By contrast, for\nfinite-dimensional systems, the relaxation is always algebraic, with a\nnon-trivial universal exponent at high temperatures crossing over to a harmonic\nvalue at low temperatures. We demonstrate that this apparent evolution is\ncontrolled by a temperature-dependent population of localised glassy\nexcitations. Our work unifies several recent lines of studies aiming at a\ndetailed characterisation of the complex potential energy landscape of\nglass-formers, and challenges both mean-field and real space descriptions of\nglasses.\n