Exactly solvable tight-binding models on two scale-free networks with identical degree distribution

TL;DR

This paper presents exactly solvable tight-binding models on two scale-free networks with identical degree distributions, revealing different spectral properties and Bose-Einstein condensation behaviors.

Contribution

It provides exact solutions for energy spectra on two scale-free networks and demonstrates their distinct thermodynamic properties despite identical degree distributions.

Findings

Bose-Einstein condensation occurs only on G_2

Spectral dimensions differ: d_{s_1} = 2, d_{s_2} = 2 ln 4 / ln 3

Topology influences thermodynamic behavior

Abstract

We study ideal Bose gas upon two scale-free structures with identical degree distribution. Energy spectra belonging to tight-binding Hamiltonian are exactly solved and the related spectral dimensions of $G_1$ and $ G_2$ are obtained as $d_{s_1} = 2$ and $d_{s_2} = 2 \ln 4/ \ln 3$. We show Bose-Einstein condensation will only take place upon $G_2$ instead of $G_1$. The topology and thermodynamical property of the two structures are proven to be totally different.