A model for the generic alpha relaxation of viscous liquids

Dielectric measurements on molecular liquids just above the glass transition indicate that alpha relaxation is characterized by a generic high-frequency loss varying as $\omega^{-1/2}$, whereas deviations from this come from one or more low-lying beta processes (Olsen et al. , Phys. Rev. Lett. 86 (2001) 1271). Assuming that long-wavelength fluctuations dominate the dynamics, a model for the dielectric alpha relaxation based on the simplest coupling between the density and dipole density fields is proposed here. The model, which is solved in second-order perturbation theory in the Gaussian approximation, reproduces the generic features of alpha relaxation.