Abstract
We construct models of many-particle quantum graphs with singular two-particle contact interactions, which can be either hardcore- or delta-interactions. Self-adjoint realisations 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 identicle bosons. Furthermore, we
extend the models to N bosons with two-particle interactions, thus
implementing the Lieb-Liniger model on a graph.
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 identicle bosons. Furthermore, we
extend the models to N bosons with two-particle interactions, thus
implementing the Lieb-Liniger model on a graph.
| Original language | English |
|---|---|
| Article number | 045207 |
| Number of pages | 18 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 46 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2013 |