Harmonic analysis on inhomogeneous amenable networks and the Bose--Einstein condensation

TL;DR

This paper explores the spectral properties of inhomogeneous amenable networks and their implications for Bose--Einstein condensation in quantum systems modeled by the Pure Hopping model.

Contribution

It provides a detailed spectral analysis of inhomogeneous networks and links these properties to Bose--Einstein condensation phenomena in quantum lattice models.

Findings

Spectral properties of adjacency matrices are characterized.

Connections established between network inhomogeneity and BEC.

Results applicable to arrays of Josephson junctions.

Abstract

We study in detail relevant spectral properties of the adjacency matrix of inhomogeneous amenable networks, and in particular those arising by negligible additive perturbations of periodic lattices. The obtained results are deeply connected to the systematic investigation of the Bose--Einstein condensation for the so called Pure Hopping model describing the thermodynamics of Bardeen--Cooper pairs of Bosons in arrays of Josephson junctions.