Density of states of a scalar macroscopic field in an anisotropic medium with piecewise-constant parameters

Abstract

We calculate the effect of interfaces of any kind on the density of states of a scalar macroscopic field in an anisotropic medium with piecewise-constant parameters. An arbitrary anisotropic stratified medium (including as particular cases a half space, two half spaces in contact, a flat slab, and a three-layer system) is considered in detail as an important example of media with piecewise-constant parameters and as a starting point for obtaining general results. Any field of the class under consideration satisfies a generalized equation of the Helmholtz type and is therefore equivalent to the wave field of quasiparticles in the effective-mass tensor approximation. In this connection we discuss the surface and interface contribution, due to electrons, to the thermodynamic characteristics (in particular, the specific heat) of an assembly of small conducting particles (like a powder or a fine-grained polycrystal).