The higher-dimensional continuous Fermi variety irreducibility conjecture

Let d3d\geq 3, let Vc:TdCdV_c:\mathbb{T}^d\to\mathbb{C}^d be a periodic function, and let Δc+Vc-\Delta_c+V_c be the corresponding continuous periodic Schrödinger operator, where Δc\Delta_c is the continuous Laplacian. Let its Fermi variety at energy λC\lambda\in\mathbb{C} be understood modulo periodicity. Higher-dimensional continuous Fermi variety conjecture. The Fermi variety of Δc+Vc-\Delta_c+V_c is irreducible modulo periodicity for every λC\lambda\in\mathbb{C}. The source presents this as motivated by results for discrete operators; no resolution status is given.

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Primary source

Wencai Liu, “Topics on Fermi varieties of discrete periodic Schrödinger operators”, arXiv:2111.01062 (2022).

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