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Quantum Bianchi-VII problem, Mathieu functions and arithmetic
journal contribution
posted on 2024-02-22, 14:10 authored by Alexander VeselovAlexander Veselov, Y YeThe geodesic problem on the compact threefolds with the Riemannian metric of Bianchi-VII0 type is studied in both classical and quantum cases. We show that the problem is integrable and describe the eigenfunctions of the corresponding Laplace-Beltrami operators explicitly in terms of the Mathieu functions with parameter depending on the lattice values of some binary quadratic forms. We use the results from number theory to discuss the level spacing statistics in relation with the Berry-Tabor conjecture and compare the situation with Bianchi-VI0 case (Sol-case in Thurston's classification) and with Bianchi-IX case, corresponding to the classical Euler top.
Funding
XJTLU Research Development Funding (grant number: RDF-21-01-031)
History
School
- Science
Department
- Mathematical Sciences
Published in
Journal of Geometry and PhysicsVolume
189Publisher
ElsevierVersion
- VoR (Version of Record)
Rights holder
© The AuthorsPublisher statement
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Acceptance date
2023-03-29Publication date
2023-04-06Copyright date
2023ISSN
0393-0440eISSN
1879-1662Publisher version
Language
- en