We consider free Bosons hopping on a network(infinite graph). The condition for Bose-Einstein condensation is given in terms of the random walk on a graph. In case of periodic lattices, we also consider Boson moving in an external periodic potential and obatined the criterion for Bose-Einstein condensation.
On the effect of repulsive interactions on Bose-Einstein condensation in the Luttinger-Sy model
Instability of Bose-Einstein condensation on quantum graphs under repulsive perturbations
Bose-Einstein Condensation in the Luttinger-Sy Model
