Bose Einstein condensation on inhomogeneous amenable graphs

TL;DR

This paper studies Bose-Einstein condensation on nonhomogeneous amenable graphs, revealing how network properties like volume growth and transience influence the condensation phenomena in Josephson junction arrays.

Contribution

It demonstrates that in nonhomogeneous networks, multiple topological and probabilistic factors affect Bose-Einstein condensation, unlike homogeneous networks where a single parameter suffices.

Findings

Particles condense in both momentum and configuration space on comb graphs.

Network properties such as volume growth and transience influence condensation behavior.

Condensation patterns differ significantly between homogeneous and nonhomogeneous networks.

Abstract

We investigate the Bose-Einstein Condensation on nonhomogeneous amenable networks for the model describing arrays of Josephson junctions. The resulting topological model, whose Hamiltonian is the pure hopping one given by the opposite of the adjacency operator, has also a mathematical interest in itself. We show that for the nonhomogeneous networks like the comb graphs, particles condensate in momentum and configuration space as well. In this case different properties of the network, of geometric and probabilistic nature, such as the volume growth, the shape of the ground state, and the transience, all play a role in the condensation phenomena. The situation is quite different for homogeneous networks where just one of these parameters, e.g. the volume growth, is enough to determine the appearance of the condensation.