Exactly solvable interacting two-particle quantum graphs

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.

References in corpus (11)

• Universal quantum computation using the discrete time quantum walk
• Kirchhoff's Rule for Quantum Wires
• The trace formula for quantum graphs with general self adjoint boundary conditions
• The inverse scattering problem for metric graphs and the traveling salesman problem
• Green's function approach for quantum graphs: an overview
• Quantum graphs with singular two-particle interactions
• Universal scaling of spectral fluctuation transitions for interacting chaotic systems
• Quantum graphs with two-particle contact interactions
• Exact results for the one-dimensional many-body problem with contact interaction: Including a tunable impurity
• Quantum oscillations in mesoscopic rings and anomalous diffusion
• Many-particle quantum graphs and Bose-Einstein condensation

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• On pairs of interacting electrons in a quantum wire
• Semiclassics in a system without classical limit: The few-body spectrum of two interacting bosons in one dimension
• Many-particle quantum graphs: A review
• Dirac particles on periodic quantum graphs
• Solvable models of interacting n-particle systems on quantum graphs