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Memorial Conference on Analytic Number Theory and Applications Dedicated to the 130th Anniversary of I. M. Vinogradov
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Feynman Checkers: Number Theory in Quantum Electrodynamics A. V. Ustinova, M. B. Skopenkovb a Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics |
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Abstract: In the 40s, R. Feynman developed the simplest model of electron motion, now known asFeynman checkers. In this game, the checker moves around the chessboard according to simple rules and as a result describes the quantum-mechanical behavior of the electron. This model is also known as one-dimensional quantum walk or Ising model with imaginary temperature. We solve mathematically a problem by R. Feynman from 1965, which was to prove that the model reproduces the usual quantum-mechanical free-particle kernel for large time, small average velocity, and small lattice step. The main tools are the Fourier transform and the stationary phase method. A more detailed description of the model and known results can be found in [1]. [1] M. Skopenkov, A. Ustinov, Feynman checkers: towards algorithmic quantum theory // arXiv:2007.12879 [math-ph] (2020). |
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