Year: 2026
Type: preprint
Abstract: For periodic Schrödinger operators $H_V=-Δ+V$ with bounded real-valued potentials on $\mathbb R^d$ with $d\ge2$, 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.
Source: arXiv (Cornell University)
Authors: Tao, Zhongkai, Yang, Mengxuan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204870639