Generalized eigenfunctions for quantum walks via path counting approach

DOI10.1142/S0129055X21500197zbMath1483.81134arXiv2009.03498MaRDI QIDQ3385464

Norio Konno, Etsuo Segawa, Takashi Komatsu, Hisashi Morioka

Publication date: 18 December 2021

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.03498

zbMATH Keywords

scattering matrixquantum walktunneling effect

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) (S)-matrix theory, etc. in quantum theory (81U20) Scattering theory of linear operators (47A40) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70) Plurisubharmonic extremal functions, pluricomplex Green functions (32U35) Tunneling in quantum theory (81U26)

Related Items (7)

Asymptotic properties of generalized eigenfunctions for multi-dimensional quantum walks ⋮ Quantum walk and its application domains: a systematic review ⋮ Almost everything about the unitary almost Mathieu operator ⋮ Generalized eigenfunctions for quantum walks via path counting approach ⋮ Comfortable place for quantum Walker on finite path ⋮ Spectral and scattering theory of one-dimensional coupled photonic crystals ⋮ Stationary measure induced by the eigenvalue problem of the one-dimensional Hadamard walk

Cites Work

• Asymptotic velocity of a position-dependent quantum walk
• Stationary scattering theory for unitary operators with an application to quantum walks
• Asymptotic properties of solutions of differential equations with simple characteristics
• Scattering and inverse scattering for nonlinear quantum walks
• Quantum walks with an anisotropic coin. I: Spectral theory
• Stationary amplitudes of quantum walks on the higher-dimensional integer lattice
• Detection of edge defects by embedded eigenvalues of quantum walks
• Resonant-tunneling in discrete-time quantum walk
• Finite-dimensional perturbation and a representation of scattering operator
• Generalized eigenfunctions for quantum walks via path counting approach
• Spectral stability of unitary network models
• QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS
• Generalized eigenfunctions and scattering matrices for position-dependent quantum walks
• Quantum Walks
• Modifying quantum walks: a scattering theory approach
• Quantum walks and search algorithms
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Generalized eigenfunctions for quantum walks via path counting approach