Generalized hydrodynamics and specific heat spectroscopy of the glass transition

Recently Birge and Nagel have developed a new experimental technique for studying the frequency dependent thermal response of supercooled liquids approaching the glass transition. We use projection operator methods to analyze their experiments and to show the relation between the frequency and wave vector dependent thermal conductivity and their frequency dependent specific heat. We show that even in liquids with a single internal mode, two relaxation times appear and the spectrum is non-Lorentzian. We relate frequency and time domain thermal response measurements to one another using our formalism.