Related papers: Satellite potentials for hypergeometric Natanzon p…
We construct a scalar potential of supersymmetric left-right model in the limit when supersymmetry is valid.
One-dimensional potentials defined by $V^{(S)}(x) =S(S+1) \hbar^2 \pi^2 /[2ma^2\sin^2(\pi x/a)]$ (for integer $S$) arise in the repeated supersymmetrization of the infinite square well, here defined over the region $(0,a)$. We review the…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
We introduce a notion of maximal potentials and we prove that they form bounded operators from $L^p$ to the homogeneous Sobolev space $\dot{W}^{1,p}$ for all $n/(n-1)<p<n$. We apply this result to the problem of boundedness of the spherical…
We report the first angle-resolved photoemission measurement of the wave-vector dependent plasmon satellite structure of a three-dimensional solid, crystalline silicon. In sharp contrast to nanomaterials, which typically exhibit strongly…
We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The…
The interaction of a fast moving sine-Gordon soliton with an external periodic potential is examined. The resulting equation of motion for the collective coordinate representing the position of the soliton is given in relativistic form. We…
The static potential in the 3d SU(2) Higgs model is computed by a variational calculation employing Wilson loops and two-meson operators. String breaking is demonstrated numerically, the breaking scale is determined and the results are…
A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable…
We give a description of finite-zone PT-potentials in terms of explicit theta functional formulas.
The exactly solvable Schr\"{o}dinger equations with the conventional shape-invariant potentials are known to be related with each other through point cannonical transformations. In this paper, we extend the idea to integral formulae called…
Let $T$ be a positive closed current of unit mass on the complex projective space $\mathbb P^n$. For certain values $\alpha<1$, we prove geometric properties of the set of points in $\mathbb P^n$ where the Lelong number of $T$ exceeds…
The notion of potential output purity of a completely positive map is introduced as a generalization of the regularized output purity. An upper bound is derived for this quantity, and for several classes of maps (including CQ, QC and…
We obtain an infinite family of orthogonal hypergeometric groups, which are higher rank arithmetic groups. We also list cases of arithmetic hypergeometric groups whose real Zariski closure is O(2,3).
The self-similar potentials are formulated in terms of the shape-invariance. Based on it, a coherent state associated with the shape-invariant potentials is calculated in case of the self-similar potentials. It is shown that it reduces to…
Semiclassical quantization rules and numerical calculations are applied to study polariton modes of materials whose permittivity tensor has principal values of opposite sign (so-called hyperbolic materials). The spectra of volume- and…
The polarizability of a nanostructure is an important parameter that determines the optical properties. An exact semi-analytical solution of the electrostatic polarizability of a general geometry consisting of two segments forming a…
We obtain a series of lower bounds for the product set of combinatorial cubes, as well as some non--trivial upper estimates for the multiplicative energy of such sets.
We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…
We solve the Klein-Gordon equation in the presence of the hyperbolic tangent potential. The scattering solutions are derived in terms of hypergeometric functions. The reflection $R$ and transmission $T$ coefficients are calculated in terms…