[QOART Seminar | 4 Aug 2026, 4:00 PM (MSK)] Isospectral Quantum Billiards as Generators of Distributive Logic Algebras
Dear colleagues,
We are pleased to announce the next online seminar on QOART (Quantum optics and related topics)!
Title of the talk: Isospectral quantum billiards as generators of the distributive logic algebras
Speaker: Sergey A. Titarenko
Abstract:
A quantum billiard is a compact domain with a free particle localized within the billiard by means of infinitely large outer potential (1D billiard = “a potential pit”). The billiard’s spectrum is the set of all energy levels of the particle which are computed from Schroedinger’s equation and are invariant under any isometries. But in 1990s-2000s there were found a whole gallery of non-isometric billiard pairs with the same spectra. This challenging effect is mainly induced by so-called cellular billiards as we recently proved [TMF, 224:2 (2025)] using a new method of 2-unitary operator. Such operator intertwines Sobolev’s spaces over the cells by means of reflection matrices (= symmetric orthogonal matrices). Two such isospectral m-cellular billiards are constructed by (m-1) mirror reflections of the same subdomain (= the cell) and are connected with a multi-valued cellular isometry. This mapping gives ordinary pairwise cell-to-cell isometries but globally it is an everywhere discontinuous non-homeomorphism inducing an extremely disconnected topology. Acc. to Lindenbaum-Tarski-Stone approach such mapping generates visual representations of logical theories by means of algebras of open-closed subsets. In particular we derive generalized double negation formula which corresponds to the logical foundations of quantum theory. Presentation of this talk is accompanied with numerous visual pictures.
Date and Time: 4 August 2026, 4:00 PM (Moscow Time)
Duration: 30–90 minutes
Language: The presentation will be delivered in Russian. The presentation slides will be in English.
Link to join the seminar: https://mian.ktalk.ru/cyi5u831v1cs?pinCode=6468
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Best regards,
Ranjit
+7 909 680 67 87
https://www.mathnet.ru/eng/person86793
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Optical ‘Cat-like’ State: https://www.mathnet.ru/eng/present47506
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QOART Seminar: https://sites.google.com/view/qoart/seminar