Completeness of the Bethe ansatz on Weyl alcoves
E. Emsiz
TL;DR
This paper proves the completeness of Bethe ansatz eigenfunctions for the Laplacian on Weyl alcoves with boundary conditions, extending known results for quantum Bose gases to a broader mathematical setting.
Contribution
It establishes the completeness of Bethe ansatz eigenfunctions on Weyl alcoves, generalizing previous results for type A root systems and quantum gases.
Findings
Completeness proven for Weyl alcoves with boundary conditions
Extension of Bethe ansatz completeness to broader root systems
Connection to quantum Bose gas eigenfunctions
Abstract
We prove the completeness of the Bethe ansatz eigenfunctions of the Laplacian on a Weyl alcove with repulsive boundary condition at the walls. For the root system of type A this amounts to the result of Dorlas of the completeness of the Bethe ansatz eigenfunctions of the quantum Bose gas on the circle with repulsive delta-function interaction.
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Taxonomy
TopicsCold Atom Physics and Bose-Einstein Condensates · Quantum many-body systems · Quantum chaos and dynamical systems