Within the mode-coupling theory ͑MCT͒ for the dynamics of simple liquids, the leading corrections to the asymptotic solutions for the relaxation in the vicinity of an ideal glass transition are derived. The formulas are used to determine the range of validity of the scaling-law description of the MCT results for the ␣ and ␤ processes in glass-forming systems. Solutions of the MCT equations of motion are calculated for a hard-sphere colloidal suspension model and compared with the derived analytical results. The leading-order formulas are shown to describe the major qualitative features of the bifurcation scenario near the transition and the leadingplus-next-to-leading-order formulas are demonstrated to give a quantitative description of the evolution of structural relaxation for the model. ͓S1063-651X͑97͒06005-4͔

The mode-coupling theory for ideal liquid-glass transitions is extended so that the structural relaxation for the reorientational degrees of freedom of a linear molecule, which is immersed in a system of spherical particles, can be described. Closed equations of motion for the correlation functions formed with tensor density fluctuations are derived, which deal with the molecule's translational and reorientational motion. From these equations the nonergodicity parameters of a hard dumbbell molecule are calculated, which quantify its arrest in a hard-sphere glass. For top-down symmetric molecules it is shown that the odd-angular-momentum variables can exhibit an ergodic-to-nonergodic transition, characterized by a continuous increase of the EdwardsAnderson parameters near the critical points. ͓S1063-651X͑97͒03011-0͔

Tuning the energy levels of halide perovskite by controlling the deposition of dipolar self-assembled monolayers.

The structural relaxation spectra and the crossover from relaxation to oscillation dynamics, as measured by Wuttke et al. ͓Phys. Rev. Lett. 72, 3052 ͑1994͔͒ for glycerol within the GHz band by depolarized light scattering, are described by the solutions of a schematic mode coupling theory model. The applicability of scaling laws for the discussion of the model solutions is considered.

A discrete-dynamics model, which is specified solely in terms of the system's equilibrium structure, is defined for the density correlators of a simple fluid. This model yields results for the evolution of glassy dynamics which are identical with the ones obtained from the mode-coupling theory for ideal liquid-glass transitions. The decay of density fluctuations outside the transient regime is shown to be given by a superposition of Debye processes. The concept of structural relaxation is given a precise meaning. It is proven that the long-time part of the mode-coupling-theory solutions is structural relaxation, while the transient motion merely determines an overall time scale for the glassy dynamics.