Bose-Einstein Condensation on inhomogeneous networks: mesoscopic aspects versus thermodynamic limit

TL;DR

This paper investigates Bose-Einstein condensation on inhomogeneous comb lattices, revealing unique macroscopic occupation patterns and anomalous correlations due to geometrical inhomogeneity, contrasting with standard lattice behavior.

Contribution

It demonstrates that in comb lattices, BEC involves multiple states near the ground state, unlike the standard case where only the ground state is macroscopically occupied.

Findings

BEC involves a finite number of states near the ground state.

Anomalous behavior in large-distance two-point correlations.

Conditions for standard BEC behavior are established.

Abstract

We study the filling of states in a pure hopping boson model on the comb lattice, a low dimensional discrete structure where geometrical inhomogeneity induces Bose-Einstein condensation (BEC) at finite temperature. By a careful analysis of the thermodynamic limit on combs we show that, unlike the standard lattice case, BEC is characterized by a macroscopic occupation of a finite number of states with energy belonging to a small neighborhood of the ground state energy. Such remarkable feature gives rise to an anomalous behaviour in the large distance two-point correlation functions. Finally, we prove a general theorem providing the conditions for the pure hopping model to exhibit the standard behaviour, i.e. to present a macroscopic occupation of the ground state only.