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arXiv · 2407.03258

Feynman checkers: through the looking-glass

Fedor Ozhegov·Mikhail Skopenkov·Alexey Ustinov
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Abstract

Feynman gave a famous elementary introduction to quantum theory by discussing the thin-film reflection of light. We make his discussion mathematically rigorous, keeping it elementary, using his other idea. The resulting model leads to accurate quantitative results and allows us to derive a well-known formula from optics. In the process, we get acquainted with mathematical tools such as Smirnov's fermionic observables, transfer matrices, and spectral radii. Quantum walks and the six-vertex model arise as the next step in this direction.

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Fedor Ozhegov, Mikhail Skopenkov, Alexey Ustinov. 2024-07-03. Feynman checkers: through the looking-glass. https://doi.org/10.1007/s00283-024-10401-x

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