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Don't mind the gap: Absolutely Continuous Edge Spectrum in a Mobility Gap — arXiv:2609.25000

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.25000
License (as archived): CC0-1.0
Archived: 2026-10-09T23:40:31.243Z
SHA-256 of the archived text: 2052209266edbf6171651d0addbc56d7414e6488052e7d76b253b43bac8e0471
Stable URL of this page: https://metraipolis.com/documento/dc_ec5fcecd97cc

How to cite

Don't mind the gap: Absolutely Continuous Edge Spectrum in a Mobility Gap — arXiv:2609.25000 — arXiv (en), https://arxiv.org/abs/2609.25000 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ec5fcecd97cc (Metraipolis archive dc_ec5fcecd97cc, sha256 2052209266edbf6171651d0addbc56d7414e6488052e7d76b253b43bac8e0471)

BibTeX

@misc{dcec5fcecd97cc,
  title = {Don't mind the gap: Absolutely Continuous Edge Spectrum in a Mobility Gap — arXiv:2609.25000},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.25000},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ec5fcecd97cc; sha256 2052209266edbf6171651d0addbc56d7414e6488052e7d76b253b43bac8e0471},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.25000. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the edge spectrum of two-dimensional lattice Hamiltonians and magnetic Schrödinger operators in a mobility gap, an energy interval in which the bulk spectrum is potentially localized rather than necessarily absent. Under suitable localization and boundary assumptions, we prove that a constant nonzero bulk topological index implies that the entire interval belongs to the absolutely continuous spectrum of the corresponding half-space operator. The absolutely continuous spectral multiplicity is bounded below by the absolute value of the index at almost every energy in the interval. The first version of the auxiliary-space cut construction in Section 2.3 was generated using ChatGPT 6.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-22 in cond-mat.dis-nn).
Categorie arXiv: Mathematical Physics (math-ph) ; Disordered Systems and Neural Networks (cond-mat.dis-nn); Materials Science (cond-mat.mtrl-sci); Spectral Theory (math.SP).
Pagina del lavoro: https://arxiv.org/abs/2609.25000 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T22:46:33.854Z dalla pagina https://arxiv.org/catchup/cond-mat.dis-nn/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).