Quantum graphs with two-particle contact interactions

Abstract

We construct models of many-particle quantum graphs with singular two-particle contact interactions, which can be either hardcore- or δ-interactions. Self-adjoint realizations of the two-particle Laplacian including such interactions are obtained via their associated quadratic forms. We prove discreteness of spectra as well as Weyl laws for the asymptotic eigenvalue counts. These constructions are first performed for two distinguishable particles and then for two identical bosons. Furthermore, we extend the models to N bosons with two-particle interactions, thus implementing the Lieb–Liniger model on a graph.