Related papers: Spectral singularity and deep multiple minima in t…
Non-Hermitian topological systems simultaneously posses two antagonistic features: ultra sensitivity due to exceptional points and robustness of topological zero energy modes, and it is unclear which one prevails under different…
Non-Hermitian physics has unveiled unconventional spectral, topological and critical phenomena, challenging traditional band theories. This thesis advances its understanding in three aspects. First, the non-Hermitian skin effect (NHSE) is…
Based on the recent work \cite{KKK} for compact potentials, we develop the spectral theory for the one-dimensional discrete Schr\"odinger operator $$ H \phi = (-\De + V)\phi=-(\phi_{n+1} + \phi_{n-1} - 2 \phi_n) + V_n \phi_n. $$ We show…
We propose that the real spectrum and the orthogonality of the states for several known complex potentials of both types, PT-symmetric and non-PT-symmetric can be understood in terms of currently proposed $\eta$-pseudo-Hermiticity…
We enumerate generalizations of the superintegrability property $<character>\ \sim {\rm character}$ and illuminate possible general structures behind them. We collect variations of original formulas available up to date and emphasize the…
We consider a class of (possibly nondiagonalizable) pseudo-Hermitian operators with discrete spectrum, showing that in no case (unless they are diagonalizable and have a real spectrum) they are Hermitian with respect to a semidefinite inner…
One of the primary goals of contemporary physics of neutrinos after discovery of their masses become the investigation of their electromagnetic properties. This is a necessary step for creation of new physics beyond the Standard Model (SM),…
In the General Next-to-Minimal Supersymmetric Standard Model (GNMSSM), singlet particles may form a secluded sector of dark matter (DM), in which Singlino-like DM could achieve the observed relic abundance through various channels such as…
Exceptional point and spectral singularity are two types of singularity that are unique to non-Hermitian systems. Here, we report the high-order spectral singularity as a high-order pole of the scattering matrix for a non-Hermitian…
We explore some fundamental differences in the phenomenology, cosmology and model building of Split Supersymmetry compared with traditional low-scale supersymmetry. We show how the mass spectrum of Split Supersymmetry naturally emerges from…
We study non-Hermitian quantum mechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in…
Following a generic approach that leads to Bogomolny-Prasad-Sommerfield (BPS) soliton solutions by imposing self-duality, we investigate three different types of non-Hermitian field theories. We consider a complex version of a logarithmic…
The paper formulates a principal positions of non-Hermitian models with $\gamma_5$-mass extensions, which often be ignored in some investigations for this subject. In fact in this case Hamiltonians contain not only Hermitian masses $m_1$,…
The DAMA annual modulation signature, interpreted as evidence for a spin-independent WIMP coupling, seems in conflict with null results from CDMS. However, in models of ``inelastic dark matter'', the experiments are compatible. Inelastic…
This paper provides a comprehensive discussion of neutralino dark matter within classes of extended supersymmetric models referred to as the USSM containing one additional SM singlet Higgs plus an extra $Z'$, together with their…
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…
Reflectionless defects in Hermitian tight-binding lattices, synthesized by the intertwining operator technique of supersymmetric quantum mechanics, are generally not invisible and time-of-flight measurements could reveal the existence of…
Physically, one tends to think of non-Hermitian systems in terms of gain and loss: the decay or amplification of a mode is given by the imaginary part of its energy. Here, we introduce an alternative avenue to the realm of non-Hermitian…
Protected zero modes in quantum physics traditionally arise in the context of ground states of many-body Hamiltonians. Here we study the case where zero modes exist in the center of a reflection-symmetric many-body spectrum, giving rise to…
Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between spectral singularities in complex crystals and…