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Lattice Equations and Semiclassical Asymptotics
Russian Journal of Mathematical Physics. 2023. Vol. 30. No. 2. P. 152–164.
V. L. Chernyshev, Nazaikinskii V. E., Tsvetkova A. V.
We consider linear equations with shifts of the arguments on the rectangular lattice with small step h in R^n and construct a version of the canonical operator providing semiclassical asymptotics for such equations. Examples include the Feynman checkers model arising in quantum theory and a problem on the wave packet propagation on a homogeneous tree.
Publication based on the results of:
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Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
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Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
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Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
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Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
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Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
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In his famous lectures, Richard Feynman gave an elementary introduction to quantum theory by discussing
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We give a new elementary proof of the theorem by Ambainis
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