Related papers: Isoresonant complex-valued potentials and symmetri…
We calculate resonances which are formed by a particle in a potential which is either Coulombian or quadratic when the particle is strongly coupled to a massless boson, taking only two energy levels into consideration. From these…
Resonant metasurfaces are devices composed of nanostructured sub-wavelength scatterers that generate narrow optical resonances, enabling applications in filtering, nonlinear optics, and molecular fingerprinting. It is highly desirable for…
We obtain formulas for the spectral zeta function of the Laplacian on symmetric finitely ramified fractals, such as the Sierpinski gasket, and a fractal Laplacian on the interval. These formulas contain a new type of zeta function…
We define a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations, which we call causal symmetries, has the…
A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation…
We show that a global holomorphic section of $\mathscr{O}(d)$ restricted to a closed complex subspace $X \subset \mathbb{P}^n$ has an interpolant if and only if it satisfies a set of moment conditions that involves a residue current…
We investigate the longevity of oscillons numerically, paying particular attention to radially-symmetric oscillons that have been conjectured to have an infinitely-long lifetime. In two spatial dimensions, oscillons have not been seen to…
New exact solvable elliptic potentials with free constants for the spectral problems of the third order are found. A time dependence of such potentials gives their isospectral deformations and solutions of nonlinear integrable equations.
A new class of giant resonances in nuclei is discussed, i.e., giant resonances built on other giant resonances. These resonances are observed with very large cross sections in relativistic heavy ion collisions. A great experimental and…
We show that the complex PT-Symmetric potential, $V(x)=-V_1 {sech}^2x + iV_2 {sech}x ~\tanh x, $, entails a single zero-width resonance (spectral singularity) when $V_1+|V_2|=4n^2+4n+{3\over 4}(n=1,2,3.., |V_2|>|V_1|+ {{sgn}(V_1) \over 4})$…
In previous work, we have considered Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. Previously our Hamiltonians have represented free motion, but here we consider the…
We develop a new approach to build the eigenfunctions of a translationally shape-invariant potential. For this we show that their logarithmic derivatives can be expressed as terminating continued fractions in an appropriate variable. We…
The Eisenhart problem of finding parallel tensors treated already in the framework of quasi-constant curvature manifolds in \cite{x:j} is reconsidered for the symmetric case and the result is interpreted in terms of Ricci solitons. If the…
Let $\Gamma$ be a convex co-compact discrete group of isometries of the hyperbolic plane $\mathbb{H}^2$, and $X=\Gamma\backslash \mathbb{H}^2$ the associated surface. In this paper we investigate the behaviour of resonances of the Laplacian…
The classification of Riemannian manifolds by the holonomy group of their Levi-Civita connection picks out many interesting classes of structures, several of which are solutions to the Einstein equations. The classification has two parts.…
We extend Vasy's results on semiclassical high energy estimates for the meromorphic continuation of the resolvent for asymptotically hyperbolic manifolds to metrics that are not necessarily even. Vasy's method gives the meromorphic…
We give a new fractal Weyl upper bound for resonances of convex co-compact hyperbolic manifolds in terms of the dimension $n$ of the manifold and the dimension $\delta$ of its limit set. More precisely, we show that as $R\to\infty$, the…
To every Hermitian vector bundle with connection over a compact Riemannian manifold $M$ one can associate a corresponding connection Laplacian acting on the sections of the bundle. We define analogous combinatorial metric dependent…
We construct continuous families of Riemannian metrics on certain simply connected manifolds with the property that the resulting Riemannian manifolds are pairwise isospectral for the Laplace operator acting on functions. These are the…
We study continuous selections of the set-valued map that takes every skew-symmetric bilinear form on a vector space to its corresponding set of maximal isotropic subspaces. Applications are made to establishing continuity properties of the…