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This is a Experimental Study study.

October 1, 2025Open Access

Resonant tunneling effect for quantum walks on directed graphs

Key Points

The asymptotic behavior of the scattering matrix is not straightforward as $-\varepsilon$ approaches zero.
Points in the essential spectrum are shown to diverge in terms of the quantum resonance effect.
An extended phenomenon similar to the resonant tunneling effect is observed during analysis.
The study focuses on quantum walks along directed graphs under specific parameter conditions.

Abstract

Quantum walks that depend smoothly on a small parameter 0 are considered on directed graphs. The asymptotic behavior of the scattering matrix of the quantum walk as +0 is investigated. It is shown that, in this limit, the scattering matrix does not converge to that for =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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Cite This Study

Kenta Higuchi (Tue,) studied this question.

synapsesocial.com/papers/68dd91c7fe798ba2fc49858d https://doi.org/https://doi.org/10.48550/arxiv.2504.15584

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