Stefano Mossa — CEA Grenoble - IRIG #
Theory and simulation of instantaneous normal modes in liquids #
In liquids, the vibrational density of states of glasses is replaced with the Instantaneous Normal Modes (INM) spectrum. While in glasses instantaneous system configurations correspond to minima of the potential energy landscape with the eigenvalues of the associated Hessian matrix all positive (stable modes), in liquids this is no longer the case, and negative eigenvalues (unstable modes) appear. The latter provide important information on liquid dynamics and transport properties, and have been characterized numerically in the past. A systematic deeper theoretical understanding of the matter is provided by the Heterogeneous Elasticity Theory (HET). Here, space-dependent fluctuating moduli are included in the elasticity equations, naturally reproducing many aspects of the low-frequency vibrational excitations in glasses.   In this talk I will present our extension of the HET to the liquid state [1], where the instantaneous-normal-mode spectrum of the liquid is described as that of an elastic medium with local shear moduli exhibiting strong spatial fluctuations, including a large number of negative values. This view provides quantitative predictions which consistently reproduce the outcome of extensive Molecular Dynamics simulations of a model soft-spheres liquid.    We have characterized in depth the spectrum of the Hessian matrix, which displays a sharp maximum close to zero energy and has a strongly temperature-dependent shape, symmetric at high temperatures and becoming rather asymmetric at low temperatures, close to the dynamical critical temperature. Most importantly, we have demonstrated that the theory naturally reproduces a surprising phenomenon, a zero-energy spectral singularity with a cusp-like character developing in the vibrational spectra upon cooling. This feature, although noticed in a few previous numerical studies, was generally overlooked due to a misleading representation of the data. I will provide a thorough analysis of these issues, based on both accurate predictions of the theory and simulation data for systems of large size.  [1] S. Mossa, T. Bryk, G. Ruocco, W. Schirmacher, "Heterogeneous-elasticity theory of instantaneous normal modes in liquids", ​Sci. Rep. 13, 21442 (2023)​