The role of glass dynamics in the anomaly of the dielectric function of solid helium

We propose that acousto-optical coupling of the electric field to strain fields around defects in disordered $^4$He is causing an increase of the dielectric function with decreasing temperature due to the arrested dynamics of defect excitations. A distribution of such low-energy excitations can be described within the framework of a glass susceptibility of a small volume fraction inside solid $^4$He. Upon lowering the temperature the relaxation time $\tau(T)$ of defects diverges and an anomaly occurs in the dielectric function $\epsilon (\omega, T)$ when $\omega \tau(T) \sim 1$. Since $\epsilon (\omega, T)$ satisfies the Kramers-Kronig relation, we predict an accompanying peak in the imaginary part of $\epsilon (\omega, T)$ at the same temperature, where the largest change in the amplitude has been seen at fixed frequency. We also discuss recent measurements of the amplitude of the dynamic dielectric function that indicate a low-temperature anomaly similar to the one seen in the resonance frequency of the torsional oscillator and shear modulus experiments.