1. Feynman checkers: external electromagnetic field and asymptotic properties
- Author
-
Ozhegov, Fedor
- Subjects
Mathematical Physics ,Mathematics - Combinatorics ,82B20, 33C45, 81T25 - 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., Comment: In English, 32 pages, 5 figures, 1 table (Changelog: many typos corrected)
- Published
- 2022
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