Glass Anomaly in the Shear Modulus of Solid 4He

The shear modulus of solid H(4)e exhibits an anomalous increase at low temperatures that behaves qualitatively similar to the frequency change in torsional oscillator experiments. We propose that this stiffening of the shear modulus with decreasing temperature can be described with a glass susceptibility assuming a temperature-dependent relaxation time tau(T). Below a characteristic crossover temperature T-X, where omega tau(T-X) similar to 1, a significant slowing down of dynamics leads to an increase in the shear modulus. We predict that the maximum change of the amplitude of the shear modulus and the height of the dissipation peak are independent of the applied frequency omega. Our calculations also show a qualitative difference in behavior of the shear modulus depending on the temperature dependence of tau(T)