namics of supercooled liquids ?

Europhysics Letters PREPRINT Are there localized saddles behind the heterogeneous dynamics of supercooled liquids? Abstract. – We numerically study the interplay between heterogeneous dynamics and properties of negatively curved regions of the potential energy surface in a model glassy system. We find that the unstable modes of saddles and quasi-saddles undergo a localization transition close to the Mode-Coupling critical temperature. We also find evidence of a positive spatial correlation between clusters of particles having large displacements in the unstable modes and dynamical heterogeneities. The dynamics of supercooled liquids is often described as a complex trajectory across their Potential Energy Surface (PES) [1]. This approach traces its origin back to the pioneering work of Goldstein [2], who argued that at low temperature these systems get trapped in the basins of attraction of local minima of the PES and hence the atomic dynamics is slowed down. In the last decade, several authors have addressed a quantitative study of the PES through numerical simulations of model systems. The original picture has evolved into a refined description of the dynamics in terms of collections of local minima (metabasins [3]) and transitions between them [4–6]. Other works have focused on the properties of the Hessian matrix of the potential energy, revealing even a more complex scenario, where not only local minima but also higher order stationary points (saddles) and more general points characterizing regions of negative curvature of PES (quasi-saddles) play an important role in the structural slowing down of the liquid [4–15]. Indeed, it has been shown [12, 13] that some information about the liquid-like diffusive dynamics is encoded in the imaginary spectrum of the Hessian matrix: the number of unstable modes n im of saddles is correlated with the diffusivity of supercooled model systems and decreases as the liquid is cooled. Attempts have been made [10–13] to identify the temperature at which the thermal average of n im extrapolates to zero with the critical temperature T c where the purely dynamical Mode-Coupling Theory (MCT) [16, 17] predicts