Work

Irreducibility of the Bloch variety for periodic Schrödinger operators in arbitrary dimension

Year: 2026

Type: preprint

Abstract: Let $d\ge1$ and $V\in C(\mathbb{T}^d;\mathbb{C})$. We prove that the Bloch variety of $-Δ+V$ is irreducible modulo periodicity. The proof combines holomorphic continuation of spectral band functions with integer translations of quasimomentum. Using analytic geometry and perturbation estimates along imaginary rays, we show that, after suitable integer translations, all irreducible components contain the same holomorphic spectral branch.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.16763

Author: Liu, Wencai

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Institute for the Theory of Computing, University of California Berkeley

Award: (Semi)algebraic Geometry in Schrödinger Operators and Nonlinear Hamiltonian Partial Differential Equations

OpenAlex ID: W7213396732

Cites: 11

Cited by:

Related to: 10