Quanta of linear heat capacity and linear thermal inductance in nanoscale heat-conducting pipes

Background. The spatial localization of the phonon gas within a nanoribbon or nanotube, like the localization of a gas of free charge carriers, should cause quantization of the thermal characteristics of the nanothermoconductor, as well as the quantization of the electrical characteristics in electric current nanoconductors. There is a universal quantum of thermal conductivity and an inverse quantum of thermal resistance, similar to the von Klitzing resistance. The quanta of linear capacitance and linear inductance are also known. In this regard, there is an urgent task of searching for their thermal analogues, especially since the heat capacity is known, and the thermal inductance has recently been discovered. The purpose of this work is to solve this problem. Materials and methods. The objects of the study are heat conductors in the form of nanoribbons and nanotubes of ballistic length with transverse dimensions not exceeding 100 nm, made of hexagonal boron nitride, which is a dielectric. This makes it possible to exclude the contribution of electrons from thermal effects and limit the analysis to phonon effects only. The work used well-known methods of quantum physics, solid state physics, crystallophysics and quantum theory of transfer phenomena. Results. Explicit expressions are obtained for the quanta of linear thermal capacitance and linear thermal inductance, as well as the number of phonon channels of ballistic thermal conductivity in nanoscale two-dimensional heat conductors. It is shown that resonators of temperature waves of the terahertz frequency range can be created on the basis of such heat conductors. Conclusions. The possibility of the existence of quanta of linear thermal capacitance and linear thermal inductance in nanoribbons and nanotubes made of hexagonal boron nitride is shown and expressions describing them are obtained. It is shown that in the case of a small coefficient of thermoelastic interaction, both elastic and temperature traveling and standing waves can be excited independently in the above-mentioned nanoscale heat conductors.