Geodesic
Feynman checkers with absorption
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 626-637

Voir la notice de l'article provenant de la source Math-Net.Ru

We give a new elementary proof of the theorem by Ambainis et al. that for a quantum walk, the probability amplitudes of absorption at the initial point after 4n steps are proportional to the Catalan numbers. We also calculate the absorption probabilities at points close to the initial one and prove a relation that connects the probability amplitudes along the diagonal.
Keywords: Feynman checkers, quantum walks, Catalan numbers, reflection method. 
@article{SEMR_2023_20_2_a32,
     author = {M. D. Dmitriev},
     title = {Feynman checkers with absorption},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {626--637},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a32/}
}
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M. D. Dmitriev. Feynman checkers with absorption. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 626-637. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a32/