Skip to content
DraconiticResearch
Search Sources API
197,785 studies31 sourcesUpdated 7 min ago
PreprintarXiv licencearXiv

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

  • Wencai Liu
Open at sourcePDFDOICite

Abstract

Let d≥1 and V∈ C(𝕋d;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.

Related

  1. Band edges of periodic Schrödinger operators are generically isolated and nondegenerate
    Zhongkai Tao, Mengxuan Yang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  2. Polynomial Spectral Gap Estimates for Finitely Differentiable Quasi-Periodic Schrödinger Operators
    Ao Cai, Yang Gao, Jiawei He
    arXivPreprintarXiv licenceFull textAnalysis & PDEsDynamical systemsarXiv
  3. Stability of Solitons in the Parametrically Driven and Damped Nonlinear Schrödinger Equation in Arbitrary Dimension
    Fernando Carreño-Navas
    arXivPreprintarXiv licenceFull textMathematical physicsStatistical & nonlinear physicsarXiv
  4. Periodic Tilings of Cardinality Twice a Prime or Nine in Arbitrary Dimension
    Hu Tan, Ying Zhang
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  5. Periodic structure and Schrodinger operators for codings of circle rotations
    Luke Hetzel, Ronnie Pavlov
    arXivPreprintCC BY 4.0Full textDynamical systemsarXiv

Cite

BibTeXRIS
BibTeX
@misc{liu2026irreducibility,
  title = {{Irreducibility of the Bloch variety for periodic Schrödinger operators in arbitrary dimension}},
  author = {Wencai Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16763},
  eprint = {2609.16763},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16763},
}
RIS
TY  - UNPB
TI  - Irreducibility of the Bloch variety for periodic Schrödinger operators in arbitrary dimension
AU  - Wencai Liu
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.16763
UR  - https://arxiv.org/abs/2609.16763
AB  - Let d≥1 and V∈ C(𝕋^d;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.
ER  -