Overdamped van Hove function of atomic liquids

Using the generalized Langevin equation formalism and the process of contraction of the description we derive a general memory function equation for the thermal fluctuations of the local density of a simple atomic liquid. From the analysis of the long-time limit of this equation, a striking equivalence is suggested between the long-time dynamics of the atomic liquid and the dynamics of the corresponding \emph{Brownian} liquid. This dynamic equivalence is confirmed here by comparing molecular and Brownian dynamics simulations of the self-intermediate scattering function and the long-time self-diffusion coefficient for the hard-sphere liquid.Comment: 4 Figures, 23 page

Density-Temperature-Softness Scaling of the Dynamics of Glass-forming Soft-sphere Liquids

The principle of dynamic equivalence between soft-sphere and hard-sphere fluids [Phys. Rev. E \textbf{68}, 011405 (2003)] is employed to describe the interplay of the effects of varying the density n, the temperature T, and the softness (characterized by a softness parameter {\nu}^{-1}) on the dynamics of glass-forming soft-sphere liquids in terms of simple scaling rules. The main prediction is that the dynamic parameters of these systems, such as the {\alpha}-relaxation time and the long-time self-diffusion coefficient, depend on n, T, and {\nu} only through the reduced density n^\ast \equiv n{\sigma}^{3}_{HS}(T, {\nu}),where the effective hard-sphere diameter {\sigma}_{HS}(T, {\nu}) is determined, for example, by the Andersen-Weeks-Chandler condition for soft-sphere-hard-sphere structural equivalence. A number of scaling properties observed in recent simulations involving glass-forming fluids with repulsive short range interactions are found to be a direct manifestation of this general dynamic equivalence principle. The self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics is shown to accurately capture these scaling rule

Inner clocks of glass-forming fluids

Providing a physically sound explanation of aging phenomena in non-equilibrium amorphous materials is a challenging problem in modern statistical thermodynamics. The slow evolution of physical properties after quenches of control parameters is empirically well interpreted via the concept of material time (or internal clock) based on the Tool–Narayanaswamy–Moynihan model. Yet, the fundamental reasons of its striking success remain unclear. We propose a microscopic rationale behind the material time on the basis of the linear laws of irreversible thermodynamics and its extension that treats the corresponding kinetic coefficients as state functions of a slowly evolving material state. Our interpretation is based on the recognition that the same mathematical structure governs both the Tool model and the recently developed non-equilibrium extension of the self-consistent generalized Langevin equation theory, guided by the universal principles of Onsager’s theory of irreversible processes. This identification opens the way for a generalization of the material-time concept to aging systems where several relaxation modes with very different equilibration processes must be considered, and partially frozen glasses manifest the appearance of partial ergodicity breaking and, hence, materials with multiple very distinct inner clocks

Arrested dynamics of the dipolar hard-sphere model

We report the combined results of molecular dynamics simulations and theoretical calculations concerning various dynamical arrest transitions in a model system representing a dipolar fluid, namely, N (softcore) rigid spheres interacting through a truncated dipole-dipole potential. By exploring different regimes of concentration and temperature, we find three distinct scenarios for the slowing down of the dynamics of the translational and orientational degrees of freedom: At low ({$\eta$} = 0.2) and intermediate (${\eta}$ = 0.4) volume fractions, both dynamics are strongly coupled and become simultaneously arrested upon cooling. At high concentrations ({$\eta$} $\lt$ 0.6), the translational dynamics shows the features of an ordinary glass transition, either by compressing or cooling down the system, but with the orientations remaining ergodic, thus indicating the existence of partially arrested states. In this density regime, but at lower temperatures, the relaxation of the orientational dynamics also freezes. The physical scenario provided by the simulations is discussed and compared against results obtained with the self-consistent generalized Langevin equation theory, and both provide a consistent description of the dynamical arrest transitions in the system. Our results are summarized in an arrested states diagram which qualitatively organizes the simulation data and provides a generic picture of the glass transitions of a dipolar fluid