Resonances in finitely perturbed quantum walks, resonance expansion and generic simplicity

2021/08/03 by Kenta Higuchi, Higuchi, Kenta, Hisashi Morioka +3
Computer Science · Mathematics · Physics and Astronomy · #47A70 #81U24 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Multiplicity (mathematics) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum computer #Quantum mechanics #Quantum walk #Resonance (particle physics) #S-matrix #Scattering #Simplicity #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:47A70 #msc:81U24 #quant-ph

paper · pdf · doi:10.48550/arxiv.2108.01345

16 pages, 2 figures

arxiv created 2021/08/03 · openalex publication_date 2021/08/03 · arxiv updated 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define resonances for finitely perturbed quantum walks as poles of the scattering matrix in the lower half plane. We show a resonance expansion which describes the time evolution in terms of resonances and corresponding Jordan chains. In particular, the decay rate of the survival probability is given by the imaginary part of resonances and the multiplicity. We prove generic simplicity of the resonances, although there are quantum walks with multiple resonances.

Citations

• Generalized eigenfunctions for quantum walks via path counting approach

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