Exactly solvable interacting two-particle quantum graphs

Jens Bolte, George Garforth

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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.
Original languageEnglish
Article number105101
Pages (from-to)1-27
Number of pages27
JournalJournal of Physics A: Mathematical and Theoretical
Volume50
Issue number10
Early online date10 Jan 2017
DOIs
Publication statusPublished - 2 Feb 2017

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