Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations

DOI10.1063/1.5035300zbMath1395.81143arXiv1804.05127OpenAlexW2796930482WikidataQ129406915 ScholiaQ129406915MaRDI QIDQ4586495

Toru Fuda, Akito Suzuki, Daiju Funakawa

Publication date: 13 September 2018

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

Full work available at URL: https://arxiv.org/abs/1804.05127

zbMATH Keywords

spectral mapping theorem

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Quantum stochastic calculus (81S25) Directed graphs (digraphs), tournaments (05C20) Singular perturbations for ordinary differential equations (34E15)

Related Items (15)

A constructive approach to topological invariants for one-dimensional strictly local operators ⋮ Absence of singular continuous spectra and embedded eigenvalues for one-dimensional quantum walks with general long-range coins ⋮ Supersymmetry for chiral symmetric quantum walks ⋮ The Witten index for 1D supersymmetric quantum walks with anisotropic coins ⋮ A weak limit theorem for a class of long-range-type quantum walks in 1d ⋮ An index theorem for split-step quantum walks ⋮ An index theorem for one-dimensional gapless non-unitary quantum walks ⋮ The Witten index for one-dimensional split-step quantum walks under the non-Fredholm condition ⋮ Spectral mapping theorem of an abstract non-unitary quantum walk ⋮ Weak limit theorem for a nonlinear quantum walk ⋮ Absence of wave operators for one-dimensional quantum walks ⋮ Generalized eigenfunctions and scattering matrices for position-dependent quantum walks ⋮ Dispersive estimates for quantum walks on 1D lattice ⋮ Unitary equivalence classes of split-step quantum walks ⋮ A new type of spectral mapping theorem for quantum walks with a moving shift on graphs

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