The article surveys the main topics, techniques, and results of the theory of periodic
operators arising in mathematical physics and other areas. Close attention is paid to …

7.1 Introduction A photonic crystal, or photonic band gap (PBG) optical material, is an
artificially created periodic low-loss dielectric medium in which electromagnetic waves of …

We report the first observation of the doubly magic nucleus 78 Ni 50 and the heavy isotopes
77 Ni, 73, 74, 75 Co, 80 Cu. The isotopes were produced by nuclear fission in collisions of …

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 the Bloch variety of discrete Schrödinger operators associated with a complex
periodic potential and a general finite-range interaction, showing that the Bloch variety is …

We study the spectral properties of Schrödinger operators on perturbed lattices. We shall
prove the non-existence or the discreteness of embedded eigenvalues, the limiting …

Let H 0 be a discrete periodic Schrödinger operator on ℓ 2 (Z d): H 0=-Δ+ V, where Δ is the
discrete Laplacian and V: Z d→ C is periodic. We prove that for any d≥ 3, the Fermi variety …

We consider a family of the discrete Schrödinger operators H λ μ, depending on two
parameters, in the d-dimensional lattice with a potential constructed via the delta function …

We construct two types of multi-layer quantum graphs (Schrödinger operators on metric
graphs) for which the dispersion function of wave vector and energy is proved to be a …

Dispersion relations and Fermi surfaces for periodic operators of mathematical physics are
some of the most common and important notions in condensed matter physics, in particular …