Debye model for the surface phonons

TL;DR

This paper develops a quantum Debye model for surface phonons in isotropic elastic bodies, emphasizing their significant thermodynamic role in low-dimensional and porous materials, especially at low temperatures.

Contribution

It introduces a quantum description of surface waves without semiclassical quantization, formulating the problem in Lagrangian and Hamiltonian frameworks within a generalized Debye model.

Findings

Surface phonons significantly influence thermodynamic functions.

Their contribution to heat capacity increases as temperature decreases.

The model highlights the importance of surface phonons in low-dimensional systems.

Abstract

A quantum description of the surface waves in an isotropic elastic body without the use of the semiclassical quantization is proposed. The problem about the surface waves is formulated in the Lagrangian and Hamiltonian representations. Within the framework of the generalized Debye model, the contribution of the surface phonons (rayleighons) to thermodynamic functions is calculated. It is emphasized that the role of the surface phonons can be significant and even decisive in low-dimensional systems, granular and porous media, and that their contribution to the total heat capacity increases with decreasing temperature.