# Solvable models of interacting n-particle systems on quantum graphs

## TL;DR

This paper introduces a class of n-particle quantum graphs with singular interactions, allowing eigenfunctions to be expressed via Bethe ansatz, and derives a finite-dimensional determinant condition for eigenvalues, extending two-particle results.

## Contribution

It generalizes two-particle quantum graph models to n-particle systems with singular interactions, providing a Bethe ansatz solution and a determinant-based eigenvalue characterization.

## Key findings

- Eigenfunctions can be expressed using Bethe ansatz.
- Eigenvalues are characterized by a finite-dimensional determinant.
- Results extend previous two-particle quantum graph models.

## Abstract

We introduce n-particle quantum graphs with singular two-particle interactions in such a way that eigenfunctions can be given in the form of a Bethe ansatz. We show that this leads to a secular equation characterising eigenvalues of the Hamiltonian that is based on a finite-dimensional determinant. These findings generalise previous results about two-particle quantum graphs.