Bounds and Phase Transitions for Phonons in Complex Network Structures

TL;DR

This paper investigates how the structure of complex networks influences phonon behavior, providing bounds on phonon numbers and heat capacity based on network resistance, revealing structural effects on physical properties.

Contribution

It introduces bounds for phonon count and specific heat in networked systems using Wiener capacity, linking network structure to physical behavior.

Findings

Bounds for total phonons and specific heat are derived.

Network resistance influences phonon and heat capacity behavior.

Structural differences lead to distinct phonon and thermal properties.

Abstract

We study a model of networked atoms or molecules oscillating around their equilibrium positions. The model assumes the harmonic approximation of the interactions. We provide bounds for the total number of phonons, and for the specific heat, in terms of the average Wiener capacity, or resistance, of the network. Thanks to such bounds, we can distinguish qualitatively different behaviours in terms of the network structure alone.