Transfer Matrices and Green Functions for the study of elementary excitations in multilayered heterostructures

TL;DR

This paper introduces the Associated Transfer Matrix T as a mathematical tool for analyzing elementary excitations in multilayered heterostructures, highlighting its properties and relation to Green functions.

Contribution

It establishes general properties of the transfer matrix T and its relation to Green functions for multilayer heterostructures, aiding in physical problem analysis.

Findings

Derived identities for the transfer matrix T

Properties of T related to Green functions

Practical monitoring of numerical computations

Abstract

This article is concerned with a mathematical tool, the Associated Transfer Matrix T, which proves useful in the study of a wide class of physical problems involving multilayer heterostructures. General properties of linear, second order differential matrix Sturm Liouville operators are discussed as a basis for establishing general properties of T, which is also generally related to the Green function G. Some identities satisfied by T are derived, which prove useful in practice to monitor the numerical quality of computational processes.