A constructive approach to topological invariants for one-dimensional strictly local operators

DOI10.1016/j.jmaa.2021.125072zbMath1460.81029arXiv2010.14466OpenAlexW3094798731MaRDI QIDQ2661246

Yohei Tanaka

Publication date: 3 April 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.14466

zbMATH Keywords

Toeplitz operatoressential spectrumquantum walkFredholm indexstrictly local operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Symmetries, invariants of ordinary differential equations (34C14) General spectral theory of ordinary differential operators (34L05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) (Semi-) Fredholm operators; index theories (47A53) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (4)

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 ⋮ Unitary equivalence classes of split-step quantum walks

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