Soft Modes in Glass-Forming Liquids: The Role of Local Stress

Liquids and glasses have localized low-frequency vibrational modes associated with disorder. These modes represent relaxational motion in double wells, and quasi-harmonic motions in single wells. Single- and double-well potentials are described by the soft-potential model, which is an extension of the two-level-system model for glasses. We use soft modes to derive the unstable frequency spectrum of instantaneous normal modes in liquids. In agreement with recent molecular-dynamics simulations, we find different frequency and temperature dependence of the spectrum for liquids in the normal and supercooled phase. We relate this crossover behavior to the presence of shear stress in the liquid. Assuming that the diffusion of particles requires hopping over potential barriers, we find exponential temperature dependence of the shear viscosity. Arrhenius and Zwanzig-Bässler behavior follows for liquids in the normal and supercooled phase, respectively. We discuss properties of the energy landscape in glass-forming liquids. Possible applications to protein dynamics are mentioned