Quantum graphs with two-particle contact interactions

摘要: 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 the Laplacian including such interactions are obtained via their associated quadratic forms. prove discreteness spectra as well Weyl laws for asymptotic eigenvalue counts. These constructions first performed two distinguishable particles and then identical bosons. Furthermore, we extend to N bosons thus implementing Lieb–Liniger model on a graph.