Exactly solvable interacting two-particle quantum graphs
Jens BolteDepartment of Mathematics, Royal Holloway, University of London, Egham, TW20 0EX, UKGeorge GarforthDepartment of Mathematics, Royal Holloway, University of London, Egham, TW20 0EX, UK
2017en
ABI
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.
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Cited by 30 references