Average scattering entropy for periodic, aperiodic and random distribution of vertices in simple quantum graphs

TL;DR

This paper investigates the average scattering entropy in quantum graphs with various vertex distributions, revealing its dependence on topology, geometry, and number of vertices, thus providing a new tool for analyzing quantum system structures.

Contribution

It introduces the concept of average scattering entropy for quantum graphs with periodic, aperiodic, and random vertex distributions, highlighting its dependence on structural properties.

Findings

Scattering entropy varies with the number of vertices.

Topology and geometry influence scattering entropy.

Entropy can serve as a tool to explore quantum graph properties.

Abstract

This work deals with the average scattering entropy of quantum graphs. We explore this concept in several distinct scenarios that involve periodic, aperiodic and random distribution of vertices of distinct degrees. In particular, we compare distinct situations to see how they behave as we change the arrangements of vertices and the topology and geometry of the proposed structures. The results show that the average scattering entropy may depend on the number of vertices, and on the topological and geometrical disposition of vertices and edges of the quantum graph. In this sense, it can be seen as another tool to be used to explore geometric and topological effects of current interest for quantum systems.