• Corpus ID: 235358526

Fermi isospectrality for discrete periodic Schrodinger operators

  title={Fermi isospectrality for discrete periodic Schrodinger operators},
  author={Wencai Liu},
. Let Γ = q 1 Z ⊕ q 2 Z ⊕· · ·⊕ q d Z , where q l ∈ Z + , l = 1 , 2 , · · · , d . Let ∆+ V be the discrete Schr¨odinger operator, where ∆ is the discrete Laplacian on Z d and the potential V : Z d → R is Γ-periodic. We prove three rigidity theorems for discrete periodic Schr¨odinger operators in any dimension d ≥ 3: In particular, all conclusions in (1), (2) and (3) hold if we replace the assumption “Fermi isospectrality” with a stronger assumption “Floquet isospectrality”. 

Algebraic Properties of the Fermi Variety for Periodic Graph Operators

It is shown how the abstract bound implies irreducibility in many lattices of interest, including examples with more than one vertex in the fundamental cell such as the Lieb lattice as well as certain models obtained by the process of graph decoration.

Bloch varieties and quantum ergodicity for periodic graph operators

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Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues

  • Wencai Liu
  • Mathematics
    Geometric and Functional Analysis
  • 2022
Let $$H_0$$ H 0 be a discrete periodic Schrödinger operator on $$\ell ^2(\mathbb {Z}^d)$$ ℓ 2 ( Z d ) : $$\begin{aligned} H_0=-\Delta +V, \end{aligned}$$ H 0 = - Δ + V , where $$\Delta $$ Δ is the

Fermi Isospectrality of Discrete Periodic Schrödinger Operators with Separable Potentials on $$\mathbb {Z}^2$$ Z 2

  • Wencai Liu
  • Mathematics
    Communications in Mathematical Physics
  • 2022
Given two coprime numbers $$q_1$$ q 1 and $$q_2$$ q 2 , let $$\Gamma =q_1\mathbb {Z}\oplus q_2 \mathbb {Z} $$ Γ = q 1 Z ⊕ q 2 Z . Let $$\Delta +X$$ Δ + X be the discrete periodic Schrödinger operator

Floquet isospectrality for periodic graph operators

Let $\Gamma=q_1\mathbb{Z}\oplus q_2 \mathbb{Z}\oplus\cdots\oplus q_d\mathbb{Z}$ with arbitrary positive integers $q_l$, $l=1,2,\cdots,d$. Let $\Delta_{\rm discrete}+V$ be the discrete Schr\"odinger

Topics on Fermi varieties of discrete periodic Schrödinger operators

  • Wencai Liu
  • Mathematics
    Journal of Mathematical Physics
  • 2022
This is a survey of recent progress on the irreducibility of Fermi varieties, rigidity results and embedded eigenvalue problems of discrete periodic Schrödinger operators.

Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues

  • Wencai Liu
  • Materials Science
    Geometric and Functional Analysis
  • 2022
Let H0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}


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