Related papers: Super Periodic Potential
In this paper, we introduce and analyze the Smith-Volterra-Cantor potential of power \( n \), denoted as SVC\(\left(\rho, n\right)\). Bridging the gap between the general Cantor and SVC systems, this novel potential offers a fresh…
We study the tunneling problem from general Smith-Volterra-Cantor (SVC) potential of finite length $L$ characterized by the scaling parameter $\rho$ and stage $G$. We show that the SVC($\rho$) potential of stage $G$ is the special case of…
To bridge the fractal and non-fractal potentials we introduce the concept of generalized unified Cantor potential (GUCP) with the key parameter $N$ which represents the potential count at the stage $S=1$. This system is characterized by…
We introduce the one-dimensional PT-symmetric Schrodinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatory-like…
We recently formulated the canonical boundary-value problem of propagation of surface plasmon-polariton (SPP) waves along the direction of periodicity of a one-dimensional photonic crystal. Here we present the general formulation of that…
We introduce the unique class of propagation-invariant surface plasmon polaritons (SPPs) representing pulsed surface wave packets propagating along unpatterned metal-dielectric interfaces and are localized in all dimensions - with…
A rigorous formulation for the scattering of surface plasmon polaritons (SPP) from a one-dimensional surface defect of any shape that yields the electromagnetic field in the vacuum half-space above the vacuum-metal interface is developed by…
We demonstrate that a system of self-propelled particles (SPP) exhibits spontaneous symmetry breaking and self-organization in one dimension, in contrast with previous analytical predictions. To explain this surprising result we derive a…
Existence of a spectral singularity (SS) in the spectrum of {a Schr\"{o}dinger operator with} a non-Hermitian potential requires exact matching of parameters of the potential. We provide a necessary and sufficient condition for a potential…
The stationary phase point (SPP) method in one-dimensional case is introduced to treat the diffractive scintillation. From weak scattering, where the SPP number N=1, to strong scattering (N$\gg$1), via transitional scattering regime…
In 'supersingular' scattering the potential $g^2U_A(r)$ involves a variable nonlinear parameter $A$ upon the increase of which the potential also increases beyond all limits everywhere off the origin and develops a uniquely high level of…
We consider the electromagnetic field near an interface between two media with arbitrary real frequency-dependent permittivities and permeabilities, under conditions supporting the surface plasmon-polariton (SPP) propagation. The dispersion…
We study the scattering properties of $N$ identical one-dimensional localized $\mathcal{PT}$-symmetric potentials, connected in series as well as in parallel. We derive a general transfer matrix formalism for parallel coupled quantum…
Tunneling of electrons through a barrier with complex potential is investigated. We focus on two cases, symmetric double rectangular barrier and double delta potential barrier, and give expressions for resonant transmission probability for…
We introduce a new type of potential system that combines the families of general Cantor (fractal system) and general Smith-Volterra-Cantor (non-fractal system) potentials. We call this system as Unified Cantor Potential (UCP) system. The…
We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of…
The scattering amplitude for the recently discovered exactly solvable shape invariant potential, which is isospectral to the generalized P\"oschl-Taylor potential, is calculated explicitly by considering the asymptotic behavior of the…
In this work, we study the transmission properties of one dimensional finite periodic systems with $\mathcal{PT}$-symmetry. A simple closed form expression is obtained for the total transmittance from a lattice of N cells, that allows us to…
The exact analytical solutions of the Schr\"odinger equation for the generalized symmetrical Woods-Saxon potential are examined for the scattering, bound and quasi-bound states in one dimension. The reflection and transmission coefficients…
We consider propagation of surface plasmon polaritons (SPPs) in linear periodic chains (LPCs) of prolate and oblate metallic spheroids. We show that the SPP group velocity can be efficiently controlled by varying the aspect ratio of the…