Related papers: Zero width resonance (spectral singularity) in a c…
We study resonant mode conversion in the PT-symmetric multimode waveguides, where symmetry breaking manifests itself in sequential destabilization (appearance of the complex eigenvalues) of the pairs of adjacent guided modes. We show that…
Investigation of scattering from rising potentials has just begun, these unorthodox potentials have earlier gone unexplored. Here, we obtain reflection amplitude ($r(E)$) for scattering from a two-piece rising exponential potential: $V(x\le…
For a general complex scattering potential defined on a real line, we show that the equations governing invisibility of the potential are invariant under the combined action of parity and time-reversal (PT) transformation. We determine the…
We calculate the spectrum of the linearized supergravity around the maximally supersymmetric pp-wave background in eleven dimensions. The resulting spectrum agrees with that of zero-mode Hamiltonian of a supermembrane theory on the pp-wave…
Complete energy spectrum is obtained for the quantum mechanical problem of N one dimensional equal mass particles interacting via potential $$V(x_1,x_2,...,x_N) = g\sum^N_{i < j}{1\over (x_i-x_j)^2} - {\alpha\over \sqrt{\sum_{i < j}…
The theory of a response of a two-energy-level system, irradiated by symmetrical light pulses, has been developed.(Suchlike electronic system approximates under the definite conditions a single ideal quantum well (QW) in a strong magnetic…
For an exact quantitative description of spectral properties of synchrotron radiation (SR), the concept of effective width of the spectrum is introduced. In the most interesting case, which corresponds to the ultrarelativistic limit of SR,…
For a very large class of potentials, $V(\vec{x})$, $\vec{x}\in R^2$, we prove the universality of the low energy scattering amplitude, $f(\vec{k}', \vec{k})$. The result is $f=\sqrt{\frac{\pi}{2}}\{1/log k)+O(1/(log k)^2)$. The only…
Inequality width-amplitude relations for three-dimensional Bernstein-Greene-Kruskal solitary waves are derived for magnetized plasmas. Criteria for neglecting effects of nonzero cyclotron radius are obtained. We emphasize that the form of…
We study both analytically and numerically the spectrum of inhomogeneous strings with $\mathcal{PT}$-symmetric density. We discuss an exactly solvable model of $\mathcal{PT}$-symmetric string which is isospectral to the uniform string; for…
The zero range potential is constructed for a system of two particles interacting via the Coulomb potential. The singular part of the asymptote of the wave function at the origin which is caused by the common effect of the zero range…
We describe a solitonic solution-generating technique for the five-dimensional General Relativity. Reducing the five-dimensional problem to the four-dimensional one, we can systematically obtain single-rotational axially symmetric vacuum…
When a single resonator is coupled to a continuous spectrum one obtains a resonance of finite half-width. Such a resonance is known in many fields of physics. The Friedel resonance is an example where a d-impurity is dissolved in a simple…
We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schr\"odinger equation is written through irreducible linear combinations of the Gauss hypergeometric functions. The potential,…
All of the PT-symmetric potentials that have been studied so far have been local. In this paper nonlocal PT-symmetric separable potentials of the form $V(x,y)=i\epsilon[U(x)U(y)-U(-x)U(-y)]$, where $U(x)$ is real, are examined. Two specific…
We investigate the parity- and time-reversal ($\mathcal{PT}$)-symmetry breaking in lattice models in the presence of long-ranged, non-hermitian, $\mathcal{PT}$-symmetric potentials that remain finite or become divergent in the continuum…
We reflect real spectra of new logarithmic model PT-symmetry operators with singular and non-singular in nature. We also notice that iso-spectral nature between inverted and non-inverted logarithmic PT-symmetric potentials. Present…
The discrete energy spectra of composite inverse power-law binding potentials of the form $V(r;\alpha,\beta,n)=-\alpha/r^2+\beta/r^n$ with $n>2$ are studied {\it analytically}. In particular, using a functional matching procedure for the…
Motivated by the recent argument that in the TeV-scale gravity trans-Planckian domains of spacetime as effective naked singularities would be generated by high-energy particle (and black-hole) collisions, we investigate the quantum particle…
We examine the completeness of bi-orthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for delta like and smooth potentials. Their form and…