Boson elementary excitations and the specific heat of non-crystalline solids: A short review

A simple theoretical approach to investigate the low-temperature behavior of the specific heat of a non-crystalline solid is proposed. We discuss the possibility that this behavior can be explained in analogy to what is done in the physics of superfluid helium. We assume that the low-temperature excitation spectrum of the system is formed by two ideal gases of boson quasiparticles. One of them is a phonon gas that is always present in the spectrum, leading to the Debye contribution; the other one, which is very important for very low temperature, is an ideal gas of another boson quasiparticles, whose dispersion relation is similar to the one proposed for the liquid helium. To explore in more details this analogy, we discuss the possibility to build a simple, but general framework to understand the temperature behavior of the specific heat at very low temperatures, by following a programme similar to the one developed by Bogoliubov for a system of interacting bosons.