We present a method to estimate the number of irreducible components of the Fermi
varieties of periodic Schrödinger operators on graphs in terms of suitable asymptotics. Our …

We study flat bands of periodic graphs in a Euclidean space. These are infinitely degenerate
eigenvalues of the corresponding adjacency matrix, with eigenvectors of compact support …

Abstract Let Γ= q 1 Z⊕ q 2 Z⊕…⊕ qd Z Γ=q_1Z⊕q_2Z⊕...⊕q_dZ, where ql∈ Z+ q_l∈Z_+,
l= 1, 2,…, dl=1,2,...,d, are pairwise coprime. Let Δ+ V Δ+V be the discrete Schrödinger …

Let $\Delta+ V $ be the discrete Schr\" odinger operator, where $\Delta $ is the discrete
Laplacian on $\mathbb {Z}^ d $ and the potential $ V:\mathbb {Z}^ d\to\mathbb {C} $ is …

Abstract Let Γ= q 1 Z⊕ q 2 Z⊕⋯⊕ qd Z with arbitrary positive integers ql, l= 1, 2,⋯, d. Let Δ
discrete+ V be the discrete Schrödinger operator on Z d, where Δ discrete is the discrete …

For periodic graph operators, we establish criteria to determine the overlaps of spectral band
functions based on Bloch varieties. One criterion states that for a large family of periodic …

This paper is devoted to the investigation of the spectral theory and dynamical properties of
periodic graphs which are not locally finite but carry non-negative, symmetric and summable …

We give several quantum dynamical analogs of the classical Kronecker-Weyl theorem,
which says that the trajectory of free motion on the torus along almost every direction tends …

We give several quantum dynamical analogs of the classical Kronecker–Weyl theorem,
which says that the trajectory of free motion on the torus along almost every direction tends …

In this short note, we prove a sharp dispersive estimate ∥ e i t H f ∥ ∞ < t − d ∕ 3 ∥ f ∥ 1 \documentclass[12pt]{minimal}
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} …