Resonant tunneling effect for quantum walks on directed graphs

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1. Verfasser: Higuchi, Kenta
Format: Preprint
Veröffentlicht: 2025
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author Higuchi, Kenta
author_facet Higuchi, Kenta
contents Quantum walks that depend smoothly on a small parameter $\varepsilon\ge0$ are considered on directed graphs. The asymptotic behavior of the scattering matrix of the quantum walk as $\varepsilon\to+0$ is investigated. It is shown that, in this limit, the scattering matrix does not converge to that for $\varepsilon=0$ at points in the essential spectrum (the unit circle) that are asymptotically approached by a quantum resonance. Furthermore, a phenomenon resembling and extending the resonant tunneling effect is observed by analyzing this discrepancy through resonant states.
format Preprint
id arxiv_https___arxiv_org_abs_2504_15584
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Resonant tunneling effect for quantum walks on directed graphs
Higuchi, Kenta
Mathematical Physics
Spectral Theory
Quantum Physics
81U24 (Primary) 47A70, 47D06, 81U26 (Secondary)
Quantum walks that depend smoothly on a small parameter $\varepsilon\ge0$ are considered on directed graphs. The asymptotic behavior of the scattering matrix of the quantum walk as $\varepsilon\to+0$ is investigated. It is shown that, in this limit, the scattering matrix does not converge to that for $\varepsilon=0$ at points in the essential spectrum (the unit circle) that are asymptotically approached by a quantum resonance. Furthermore, a phenomenon resembling and extending the resonant tunneling effect is observed by analyzing this discrepancy through resonant states.
title Resonant tunneling effect for quantum walks on directed graphs
topic Mathematical Physics
Spectral Theory
Quantum Physics
81U24 (Primary) 47A70, 47D06, 81U26 (Secondary)
url https://arxiv.org/abs/2504.15584