Related papers: Optimizing the second hyperpolarizability with min…
Second-harmonic generation (SHG) is a direct measure of the strength of second-order nonlinear optical effects, which also include frequency mixing and parametric oscillations. Natural and artificial materials with broken…
Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specifically, the supersymmetric partners of the Lame…
In a previous paper we solved a countably infinite family of one-dimensional Schr\"odinger equations by showing that they were supersymmetric partner potentials of the standard quantum harmonic oscillator. In this work we extend these…
We make use of a recently developed method to, not only obtain the exactly known eigenstates and eigenvalues of a number of quasi-exactly solvable Hamiltonians, but also construct a convergent approximation scheme for locating those levels,…
We discuss the construction of optimized electronic filters using inverse scattering methods. We study a wide range of densities and temperatures, room temperature included. Discretization methods of the potential (including the…
A new, weakly damped, {\em transverse} electromagnetic mode is predicted in graphene. The mode frequency $\omega$ lies in the window $1.667<\hbar\omega/\mu<2$, where $\mu$ is the chemical potential, and can be tuned from radiowaves to the…
We analyze by a renormalization method, the dynamics of a particle in a infinite square-well potential driven by an external monochromatic field. This method set up for Hamiltonian systems with two degrees of freedom allows us to analyze…
Two-dimensional transition metal di-chalcogenide semiconductors provide unique possibilities to investigate strongly confined excitonic physics and a plasmonic platform integrable to such materials constitutes a hybrid system that can be of…
A graph $G$ is class II, if its chromatic index is at least $\Delta+1$. Let $H$ be a maximum $\Delta$-edge-colorable subgraph of $G$. The paper proves best possible lower bounds for $\frac{|E(H)|}{|E(G)|}$, and structural properties of…
The one-loop polarization function of graphene has been calculated at zero temperature for arbitrary wavevector, frequency, chemical potential (doping), and band gap. The result is expressed in terms of elementary functions and is used to…
Parametric oscillation is a fundamental concept that underlies nonlinear wave-matter interactions, leading to generation or amplification of new frequency components. Using a temporal modulation generated by the heterodyne interference of a…
A hypergraph is said to be $\chi$-colorable if its vertices can be colored with $\chi$ colors so that no hyperedge is monochromatic. $2$-colorability is a fundamental property (called Property B) of hypergraphs and is extensively studied in…
A graph $H$ is {\em $p$-edge colorable} if there is a coloring $\psi: E(H) \rightarrow \{1,2,\dots,p\}$, such that for distinct $uv, vw \in E(H)$, we have $\psi(uv) \neq \psi(vw)$. The {\sc Maximum Edge-Colorable Subgraph} problem takes as…
We have studied the structure and properties of potassium clusters containing even number of atoms ranging from 2 to 20 at the ab initio level. The geometry optimization calculations are performed using all-electron density functional…
Optimally-chiral electromagnetic fields with maximized helicity density, recently introduced in [1], enable chirality characterization of optically small nanoparticles. Here, we demonstrate a technique to obtain optimally-chiral nearfields…
We perform experiments in the Large Plasma Device (LAPD) at the University of California, Los Angeles, studying how different end-electrode biasing schemes modify the radial potential profile in the machine. We impose biasing profiles of…
The paper is devoted to optimization of resonances in a 1-D open optical cavity. The cavity's structure is represented by its dielectric permittivity function e(s). It is assumed that e(s) takes values in the range 1 <= e_1 <= e(s) <= e_2.…
Over the past decade, physicists have developed deep but non-rigorous techniques for studying phase transitions in discrete structures. Recently, their ideas have been harnessed to obtain improved rigorous results on the phase transitions…
High-order harmonic generation (HHG) in the relativistic regime is employed to obtain zeptosecond pulses of $\gamma$-rays. The harmonics are generated from atomic systems in counterpropagating strong attosecond laser pulse trains of linear…
This paper concerns the geometric structure of optimizers for frame potentials. We consider finite, real or complex frames and rotation or unitarily invariant potentials, and mostly specialize to Parseval frames, meaning the frame potential…