Related papers: Complex periodic potentials with real band spectra
We discuss the band-gap structure and the integrated density of states for periodic elliptic operators in the Hilbert space $L_2(\R^m)$, for $m \ge 2$. We specifically consider situations where high contrast in the coefficients leads to…
We survey results concerning the spectral properties of limit-periodic operators. The main focus is on discrete one-dimensional Schr\"odinger operators, but other classes of operators, such as Jacobi and CMV matrices, continuum…
We show that non-reciprocal bands can be formed in a magnetized periodic chain of spherical plasmonic particles with two particles per unit cell. Simplified form of symmetry operators in dipole approximations are used to demonstrate…
We study the spectral linear elasticity problem in an unbounded periodic waveguide, which consists of a sequence of identical bounded cells connected by thin ligaments of diameter of order $ h >0$. The essential spectrum of the problem is…
The one-dimensional Schrodinger equation for the potential $x^6+\alpha x^2 +l(l+1)/x^2$ has many interesting properties. For certain values of the parameters l and alpha the equation is in turn supersymmetric (Witten), quasi-exactly…
We prove new monotonicity properties for joint and generalized spectral radius and their essential versions of weighted geometric symmetrizations of bounded sets of positive kernel operators on $L^2$. To our knowledge, several proved…
We suggest an inverse dispersion method for calculating photonic band diagram for materials with arbitrary frequency-dependent dielectric functions. The method is able to calculate the complex wave vector for a given frequency by solving…
Some general properties of the wave functions of complex-valued potentials with real spectrum are studied. The main results are presented in a series of lemmas, corollaries and theorems that are satisfied by the zeros of the real and…
We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $\cal PT$ symmetry may…
We calculate the photonic band gap of triply periodic bicontinuous cubic structures and of tubular structures constructed from the skeletal graphs of triply periodic minimal surfaces. The effect of the symmetry and topology of the periodic…
We introduce the periodic Airy-Schr\"odinger operator and we study its band spectrum. This is an example of an explicitly solvable model with a periodic potential which is not differentiable at its minima and maxima. We define a…
In this paper we constructively determine a family of the spectral invariants of the multidimensional Schrodinger operator with a periodic potential by the given band functions.
We present a detailed study of a generalised one-dimensional Kronig-Penney model using $\delta\text{-}\delta'$ potentials. We analyse the band structure and the density of states in two situations. In the first case we consider an infinite…
We present approximate methods for calculating the three-dimensional electric potentials of finite surface electrodes including gaps between electrodes, and estimate the effects of finite electrode thickness and an underlying dielectric…
Spatial gaps correspond to the projection in position space of the gaps of a periodic structure whose envelope varies spatially. They can be easily generated in cold atomic physics using finite-size optical lattice, and provide a new kind…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…
We consider $2p\ge 4$ order differential operator on the real line with a periodic coefficients. The spectrum of this operator is absolutely continuous and is a union of spectral bands separated by gaps. We define the Lyapunov function,…
We analyze the supersymmetric features of isolated double-well potentials, both symmetric ones and ones under an asymmetric perturbation. Our studies are in concert with results obtained elsewhere. Further on, a particular interest is paid…
Semiclassical approximations are implemented in the calculation of position and width of low energy resonances for radial barriers. The numerical integrations are delimited by t/T<<8, with t the period of a classical particle in the barrier…
Atomic effective pseudopotentials enable atomistic calculations at the level of accuracy of density functional theory for semiconductor nanostructures with up to fifty thousand atoms. Since they are directly derived from ab-initio…