Quantum statistics on graphs

摘要: Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks wires and states condensed matter. We consider statistics indistinguishable spinless particles on a graph, concentrating the simplest case Abelian two particles. In spite fact that locally one dimensional, anyon emerge in generalized form. A given graph may support family independent phases associated with topologically inequivalent exchange processes. addition, sufficiently graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs—equivalently, many-particle tight-binding model. The results demonstrate provide an arena which to study manifestations statistics. Possible applications include topological computing, insulators, fractional Hall effect, superconductivity molecular physics.