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PreprintarXiv licencearXiv

Band edges of periodic Schrödinger operators are generically isolated and nondegenerate

  • Zhongkai Tao
  • Mengxuan Yang
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Abstract

For periodic Schrödinger operators HV=−Δ+V with bounded real-valued potentials on ℝd with d≥2, we show that for generic potentials, each endpoint of every spectral gap is attained by a single Bloch band at only finitely many quasimomenta, and has a nondegenerate Hessian at every attaining point. This proves the Spectral Edge Conjecture for periodic Schrödinger operators.

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Cite

BibTeXRIS
BibTeX
@misc{tao2026band,
  title = {{Band edges of periodic Schrödinger operators are generically isolated and nondegenerate}},
  author = {Zhongkai Tao and Mengxuan Yang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30189},
  eprint = {2608.30189},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30189},
}
RIS
TY  - UNPB
TI  - Band edges of periodic Schrödinger operators are generically isolated and nondegenerate
AU  - Zhongkai Tao
AU  - Mengxuan Yang
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30189
UR  - https://arxiv.org/abs/2608.30189
AB  - For periodic Schrödinger operators H_V=−Δ+V with bounded real-valued potentials on ℝ^d with d≥2, we show that for generic potentials, each endpoint of every spectral gap is attained by a single Bloch band at only finitely many quasimomenta, and has a nondegenerate Hessian at every attaining point. This proves the Spectral Edge Conjecture for periodic Schrödinger operators.
ER  -