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

Abstract

We propose that the acousto-optical (electro-elastic) coupling of the electric field to strain fields localized around defects in disordered 4He causes 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 4He. Upon lowering the temperature the relaxation time τ(T) of defects increases and an anomaly occurs in the dielectric function ϵ(ω,T) when ωτ(T) ∼ 1. Since ϵ(ω,T) satisfies the Kramers–Kronig relation, we predict an accompanying peak in the imaginary part of ϵ(ω,T) at the same temperature that the largest change in amplitude occurs at a fixed frequency. We also discuss recent measurements of the amplitude of the dynamic dielectric function that indicate a low-temperature anomaly similar to that seen in the resonance frequency of the torsional oscillator and shear modulus experiments.