Statistics on networks

One-dimensional networks are excellent examples of topological spaces which are not manifolds and which admit interesting quantum physics. They are of importance in the free electron model for molecules and crystals. They also occur as fabricated mesoscopic networks. In this paper, the authors review single-particle quantum physics on networks from topological and operator theoretic points of view and then initiate study of identical particles on networks. It is established that the available statistics on networks in its range and complexity rival the richness of statistical options in two dimensions. The authors treat two-particle statistics on simple networks with detail, taking care to cover operator theoretic issues pertaining to multiple connectivity and also those due to basic topological differences between a generic network and a manifold