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arXiv · 2210.07306

Feynman checkers: number-theoretic properties

Fedor Kuyanov·Alexey Slizkov
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Abstract

We study Feynman checkers, an elementary model of electron motion introduced by R. Feynman. In this model, a checker moves on a checkerboard, and we count the turns. Feynman checkers are also known as a one-dimensional quantum walk. We prove some new number-theoretic results in this model, for example, sign alternation of the real and imaginary parts of the electron wave function in a specific area. All our results can be stated in terms of Young diagrams, namely, we compare the number of Young diagrams with an odd and an even number of steps.

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Fedor Kuyanov, Alexey Slizkov. 2022-10-13. Feynman checkers: number-theoretic properties. https://doi.org/10.1142/s0129055x23500228

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