Exactly solvable interacting two-particle quantum graphs

TL;DR

This paper develops exactly solvable models of two-particle quantum graphs with non-local interactions, using boundary conditions and the Bethe ansatz to analyze spectra and chaotic properties.

Contribution

It introduces a novel construction of exactly solvable two-particle quantum graphs with non-local interactions, extending the Bethe ansatz method to these models.

Findings

Derived secular equations for spectra

Compared spectral statistics to random matrix theory

Analyzed classical chaos properties

Abstract

We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing compatibility with the Bethe ansatz method, we calculate quantisation conditions in the form of secular equations from which the spectra can be deduced. We compare spectral statistics of some examples to well known results in random matrix theory, analysing the chaotic properties of their classical counterparts.