STRETCHING, MODE-COUPLING, AND THE GLASS-TRANSITION

The mode-coupling theory (MCT) of the glass transition can exhibit stretching (nonexponential) behavior observed in the primary relaxation of supercooled liquids near the glass transition. Gotze first showed that MCT can exhibit this stretching behavior in the alpha-relaxation regime by phenomenologically introducing a linear term into the mode-coupling integral for the dynamic viscosity. We show in this paper how this linear term can be generated using fundamental considerations. In particular, we extend fluctuating nonlinear hydrodynamics of compressible liquids, developed by Das and Mazenko [Phys., Rev. A 34, 2265 (1986)], to include another slow variable in addition to the conserved slow variables such as the mass and momentum densities and show that the extended theory naturally generates this linear term. The additional slow variable is defined as the distortion field of the local structure inherent in dense liquids. The suppression of the cutoff mechanism due to Das and Mazenko is also discussed.