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Spectral localizer for unbounded topological Hamiltonians
Abstract
In a series of joint papers with Loring, it was shown how index parings of K-theory classes with Fredholm modules can be computed as the half-signature of a suitably constructed finite-dimensional matrix, called the spectral localizer. After offering a novel perspective on earlier results, it is shown how the framework can be extended to unbounded gapped Hamiltonians given as second-order linear differential operators (in particular, matrix-valued Schrödinger and regularized Dirac operators). Important insights are the coercive phase space localization and discretizations by means of wavelets.
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BibTeX
@misc{schulzbaldes2026spectral,
title = {{Spectral localizer for unbounded topological Hamiltonians}},
author = {Hermann Schulz-Baldes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34138},
eprint = {2610.34138},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34138},
}
RIS
TY - UNPB
TI - Spectral localizer for unbounded topological Hamiltonians
AU - Hermann Schulz-Baldes
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34138
UR - https://arxiv.org/abs/2610.34138
AB - In a series of joint papers with Loring, it was shown how index parings of K-theory classes with Fredholm modules can be computed as the half-signature of a suitably constructed finite-dimensional matrix, called the spectral localizer. After offering a novel perspective on earlier results, it is shown how the framework can be extended to unbounded gapped Hamiltonians given as second-order linear differential operators (in particular, matrix-valued Schrödinger and regularized Dirac operators). Important insights are the coercive phase space localization and discretizations by means of wavelets.
ER -