Frequency-dependent specific heat of viscous silica - art. no. 104204

We apply the Mori-Zwanzig projection operator formalism to obtain an expres sion for the frequency dependent specific heat c(z) of a liquid. By using a n exact transformation formula due to Lebowitz et al., we derive a relation between c(z) and K(t), the autocorrelation function of temperature fluctua tions in the microcanonical ensemble. This connection thus allows to determ ine c(z) from computer simulations in equilibrium, i.e., without an externa l perturbation. By considering the generalization of K(t) to finite wavevec tors, we derive an expression to determine the thermal conductivity lambda from such simulations. We present the results of extensive computer simulat ions in which we use the derived relations to determine c(z) over eight dec ades in frequency, as well as lambda. The system investigated is a simple b ut realistic model for amorphous silica. We find that at high frequencies t he real part of c(z) has the value of an ideal gas. c'(w) increases quickly at those frequencies which correspond to the vibrational excitations of th e system. At low temperatures c'(w) shows a second step. The frequency at w hich this step is observed is comparable to the one at which the alpha -rel axation peak is observed in the intermediate scattering function. Also the temperature dependence of the location of this second step is the same as t he one of the alpha peak, thus showing that these quantities are intimately connected to each other. From c'(w) we estimate the temperature dependence of the vibrational and configurational part of the specific heat. We find that the static value of c(z) as well as lambda are in good agreement with experimental data.