What is it about?
We utilize analytic number-theoretic methods to study boson systems, particularly through a specialized application of the generalized Fourier transform. This novel approach offers exact computational algorithms for simulating multiparticle dynamics in the Bose-Hubbard model, providing concrete evidence of quantum phase transitions. Moreover, our work establishes, via the Fourier duality, a theoretical link between the Bost-Connes and Kastrup frameworks. The duality also bridges the Bose-Hubbard model with a system of spin moments with an anisotropy.
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Why is it important?
The new mathematical approach demonstrates relations between different branches of physics. Also, one of the mathematical tidbits is viewing infinite matrices as collections of rays. A single creation or single annihilation operator is an example of a ray. This direction enables many more new insights to be disseminated soon.
Perspectives
The crucial driving force behind this work is the interplay between mathematical and physical insights, which is central to our approach.
Dr Artur P Sowa
University of Saskatchewan
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This page is a summary of: Solving the Bose-Hubbard model in new ways, Quantum, June 2022, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften,
DOI: 10.22331/q-2022-06-02-728.
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