Instantaneous normal modes of a glass-forming liquid during the relaxation process

Understanding glass formation by quenching remains a challenge in soft condensed matter physics. Recent numerical studies on steepest descent dynamics, which is one of the simplest models of quenching, revealed that quenched liquids undergo slow relaxation with a power law towards mechanical equilibrium and that local rearrangements of particles govern the late stage of the process. These advances motivate the detailed study of instantaneous normal modes during the relaxation process because they are significant in the dynamics governed by stationary points of the potential energy landscape. Here, we performed a normal mode analysis of configurations during relaxation and found that unstable localized modes dominate the dynamics. We also observed power-law relations between several fundamental observables and a stretched exponential law in the most unstable mode of a configuration. These findings substantiate our naive expectation about the relaxation dynamics based on quantitative analysis.