Related papers: Spectral analysis of a quantum system with a doubl…
Optical nonlinearities typically require macroscopic media, thereby making their implementation at the quantum level an outstanding challenge. Here we demonstrate a nonlinearity for one atom enclosed by two highly reflecting mirrors. We…
We consider a straight three dimensional quantum layer with singular potential supported on a straight wire which is localized perpendicularly to the walls and connects them. We prove that the infinite number of embedded eigenvalues appears…
Static properties of an anharmonic potential model for planar two-electron quantum dots are investigated using a method which allows for the exact representation of the matrix elements, including the full Coulombic electron - electron…
We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of…
To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wave functions at the singularity. Generalizing the scheme used for point interactions in one dimension, we…
We introduce and explore two questions concerning spectra of operators that are of interest in the theory of entanglement in symmetric (i.e., bosonic) quantum systems. First, we investigate the inverse eigenvalue problem for symmetric…
The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…
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…
In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…
Two-photon interference underlies the functioning of many quantum photonics devices. It also serves as the prominent tool for testing the indistinguishability of distinct photons. However, as their time-spectral profile becomes more…
We quantise integrable point-particle systems with opposite-sign kinetic terms and nontrivial interactions. Using methods from separability theory, we show that previously determined classical stability conditions also imply discrete…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
Nonlinear spectroscopy with quantum entangled photons is an emerging field of research that holds the promise to achieve a superior signal-to-noise ratio and effectively isolate many-body interactions. Photon sources used for this purpose…
The existence of several exotic phenomena, such as duality and spectral anholonomy is pointed out in one-dimensional quantum wire with a single defect. The topological structure in the spectral space which is behind these phenomena is…
Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which…
We explore the energy spectrum of a non-relativistic particle bound in a linear finite range, attractive potential, envisaged as a quark-confining potential. The intricate transcendental eigenvalue equation is solved numerically to obtain…
The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of ${\cal PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with…
Until very recently, two-photon interaction processes have been considered only as arising from second- or higher-order effects in driven systems, and so limited to extremely small coupling strengths. However, a variety of novel physical…