Synthesis of a quantum tree Weyl matrix

TL;DR

This paper introduces a step-by-step method for constructing the Weyl matrix of any quantum tree graph by iteratively adding edges and solving simple linear systems, facilitating analysis of quantum networks.

Contribution

It presents a novel iterative synthesis technique for the Weyl matrix of quantum trees, enabling systematic construction from boundary data.

Findings

Method allows efficient computation of Weyl matrices for complex quantum trees.

Provides a systematic approach for quantum graph analysis.

Simplifies the process of deriving Dirichlet-to-Neumann maps for quantum networks.

Abstract

A method for successive synthesis of a Weyl matrix (or Dirichlet-to-Neumann map) of an arbitrary quantum tree is proposed. It allows one, starting from one boundary edge, to compute the Weyl matrix of a whole quantum graph by adding on new edges and solving elementary systems of linear algebraic equations in each step.