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Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us…
We observe returns of a simple random walk on a finite graph to a fixed node, and would like to infer properties of the graph, in particular properties of the spectrum of the transition matrix. This is not possible in general, but at least…
We consider $m$-th order linear recurrences that can be thought of as generalizations of the Lucas sequence. We exploit some interplay with matrices that again can be considered generalizations of the Fibonacci matrix. We introduce the…
Due to the recent interest in studying propagation of light through triangular air gaps, we calculate, by using the analogy between optics and quantum mechanics and the multiple step technique, the transmissivity through a triangular air…
We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We…
Starting from fundamental multiple scattering theory it is shown that negative refraction indices are feasible for matter waves passing a well-defined ensemble of scatterers. A simple approach to this topic is presented and explicit…
This article concerns the design of antireflection structures which, placed on a photonic crystal surface, significantly diminish the fraction of energy lost to reflected waves. After a review of the classes of these structures proposed to…
By solving Maxwell equations with the ideal-metal boundary conditions in the TM case, we have fully described the transmission and diffraction properties of a single slit regardless of its width. Efficiencies of the main transformation…
In a unified approach, we study the transport properties of periodic-on-average bi-layered photonic crystals, metamaterials and electron superlattices. Our consideration is based on the analytical expression for the localization length…
Carpet or ground-plane invisibility cloaks hide an object in reflection and inhibit transmission by construction. This concept has significantly reduced the otherwise demanding material requirements and has hence enabled various…
The transfer-matrix method is a standard approach to wave propagation in stratified media. With the advent of cold-atom-based quantum and photonic technologies, several experiments and many proposals consider light propagation in…
Transmission probabilities of Dirac fermions in graphene under linear barrier potential oscillating in time are investigated. Solving Dirac equation we end up with the solutions of the energy spectrum depending on several modes coming from…
The problem of electron scattering on the one-dimensional complexes is considered. We propose a novel theoretical approach to solution of the transport problem for a quantum graph. In the frame of the developed approach the solution of the…
We study relations between finite-dimensional representations of color Lie algebras and their cocycle twists. Main tools are the universal enveloping algebras and their FCR-properties (finite-dimensional representations are completely…
The optical rotation and selective transmission spectrum of ambichiral sculptured thin films using transfer matrix method have been calculated. The results of optical modeling showed that optical characteristics ambichiral sculptured thin…
A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…
Uncertainty propagation in a phaseless magnetic resonance-based electric properties tomography technique is investigated using the Monte Carlo method. The studied inverse method, which recovers the electric properties distribution at…
We describe a unified quantum approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. We also generalize the method to a chain of resonators with time delays, and reveal…
Light diffusion is usually associated with thick, opaque media. Indeed, multiple scattering is necessary for the onset of the diffusive regime and such condition is generally not met in almost transparent media. Nonetheless, at long enough…
We theoretically demonstrate direction-dependent polarization conversion efficiency, yielding unidirectional light transmission, through a two-layer nanostructure by using the angular spectrum representation of optical near-fields. The…