Energy landscape statistics and coarsening in liquids: a relaxation mode analysis

Energy landscape, the high dimensional energy surface in the configuration space, has been widely applied to interpret slow processes that occur over a long time scale, such as slow relaxations of supercooled liquids approaching the glass transition. Despite extensive simulation studies, experimental characterization of the energy landscape still remains a challenge. To address this challenge, in this work, we developed a relaxation mode analysis (RMA) for liquids under a framework analogous to the normal mode analysis for solids. Using RMA, complicated relaxations of liquids are decoupled into a distribution of relaxation modes, from which important statistics of relaxation times and activation barriers on the energy landscape become accessible from experimentally measurable two-point density-density correlation functions, e.g. using quasi-elastic and inelastic scattering experiments. As demonstrations, this RMA approach was used to analyze three empirical models, i.e. exponential relaxation, stretched exponential relaxation, and relaxation arising from normally distributed activation energies. Furthermore, we applied RMA to study the relaxations of a Kob-Andersen liquid when dynamical cooperativity emerges in the landscape-influenced regime using molecular dynamics simulations. The results revealed a prominent dynamic decoupling and a coarsening effect of the energy landscape at different length scales. These demonstrations suggest that RMA is a promising tool to extract energy landscape statistics from experimental data. In the end, we discuss the future extensions of RMA from both application and theoretical perspectives