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arXiv · 2504.15584

Resonant tunneling effect for quantum walks on directed graphs

Kenta Higuchi
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Abstract

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.

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Kenta Higuchi. 2025-04-22. Resonant tunneling effect for quantum walks on directed graphs. https://arxiv.org/abs/2504.15584

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