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arXiv · 2209.00938

Feynman checkers: external electromagnetic field and asymptotic properties

Fedor Ozhegov
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Abstract

We study Feynman chekers - one of the most elementary models of electron motion. It is also known as one-dimensional quantum walk or an Ising model at imaginary temperature. We add the simpliest nontrivial electromagnetic field to the model and find the limits of the resulting model for a small lattice step and a large time, similar to the results by J. Narlikar 1972 and G. Grimmet - S. Jason - P. Scudo from the 2000s. It turns out that the limits in the model with the field are obtained from the known ones without a field by a mass renormalization. We also find an exact solution for the resulting model.

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Fedor Ozhegov. 2024-02-06. Feynman checkers: external electromagnetic field and asymptotic properties. https://doi.org/10.1142/s0129055x2450017x

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