Related papers: Spectral Singularities of a General Point Interact…
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In…
Spectra of the second derivative operators corresponding to the special PT-symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT-symmetric point interactions causing…
Random optical fields with two widely different correlation lengths generate far field speckle spots that are themselves highly speckled. We call such patterns speckled speckle, and study their critical points (singularities and stationary…
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 study Hamiltonian systems with point interactions and give a systematic description of the corresponding boundary conditions and the spectrum properties for self-adjoint, PT-symmetric systems and systems with real spectra. The…
The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum systems is investigated. We show that they emerge from a limit of band-edge states in a doubly periodic finite gap system when the imaginary period…
General point interactions for the second derivative operator in one dimension are studied. In particular, ${\mathcal P \mathcal T}$-self-adjoint point interactions with the support at the origin and at points $\pm l$ are considered. The…
First we study the spectral singularity at infinity and investigate the connections of the spectral singularities and the spectrality of the Hill operator. Then we consider the spectral expansion when there is not the spectral singularity…
Spectral singularities are among generic mathematical features of complex scattering potentials. Physically they correspond to scattering states that behave like zero-width resonances. For a simple optical system, we show that a spectral…
We study screening of optical singularities in random optical fields with two widely different length scales. We call the speckle patterns generated by such fields speckled speckle, because the major speckle spots in the pattern are…
A short resume is given about the nature of exceptional points (EPs) followed by discussions about their ubiquitous occurrence in a great variety of physical problems. EPs feature in classical as well as in quantum mechanical problems. They…
We study the Point/Tukey spectrum of a general directed set using PCF theoretic tools and uncover basic connections between the theories. In particular, we prove that if the supremum of the Tukey spectrum is singular, then its cofinality…
A curious feature of complex scattering potentials v(x) is the appearance of spectral singularities. We offer a quantitative description of spectral singularities that identifies them with an obstruction to the existence of a complete…
We study quantum mechanical systems with "spin"-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the…
Speckle patterns produced by random optical fields with two (or more) widely different correlation lengths exhibit speckle spots that are themselves highly speckled. Using computer simulations and analytic theory we present results for the…
Given two different self-adjoint extensions of the same symmetric operator, we analyse the intersection of their point spectra. Some simple examples are provided.
The spectral and localization properties of $\mathcal{PT}$-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are…
A PT-symmetric optically active medium that lases at the threshold gain also acts as a complete perfect absorber at the laser wavelength. This is because spectral singularities of PT-symmetric complex potentials are always accompanied by…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
The spectral singularity have been extensively studied over the last one and half decade for different non-Hermitian potentials in non-Hermitian quantum mechanics. The nature of spectral singularities have not been studied for the case of…