2025/11/06 by Jifeng Chu, Chu, Jifeng, Kang Lyu +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2511.03940
openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28
In this paper, we consider the discrete periodic Schrödinger operators Δ+V on \Zd, where V is Γ-periodic with Γ=q1 ℤ⊕ q2ℤ⊕⋯⊕ qdℤ and positive integers qj, j=1,2,⋯,d, are pairwise coprime. We introduce the notions of generalized partial Fermi isospectrality and weak separability, and prove that two generalized partially Fermi isospectral potentials have the same weak separability. As a direct application, we can prove that two potentials have the same (d1,d2,⋯,dr)-separability by assuming that they are generalized partially Fermi isospectral, instead of the Fermi isospectrality or Floquet isospectrality. Besides, we prove that each couples of components of the generalized Fermi isospectral potentials are Floquet isospectral in some sense.