Related papers: Surprising spectra of PT-symmetric point interacti…
The observation that PT-symmetric Hamiltonians can have real-valued energy levels even if they are non-Hermitian has triggered intense activities, with experiments, in particular, focusing on optical systems, where Hermiticity can be broken…
The present study is the first such attempt to examine rigorously and comprehensively the spectral properties of a three-dimensional ultracold atom when both the spin-orbit interaction and the Zeeman field are taken into account. The model…
Symmetry underpins our understanding of physical law. Open systems, those in contact with their environment, can provide a platform to explore parity-time symmetry. While classical parity-time symmetric systems have received a lot of…
The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the…
In this paper we study the self-adjointness and spectral properties of two-dimensional Dirac operators with electrostatic, Lorentz scalar, and anomalous magnetic $\delta$-shell interactions with constant weights that are supported on a…
We prove that in finite dimensions, a Parity-Time (PT)-symmetric Hamiltonian is necessarily pseudo-Hermitian regardless of whether it is diagonalizable or not. This result is different from Mostafazadeh's, which requires the Hamiltonian to…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
In this paper, we study self-adjointness and spectrum of operators of the form $$H=\displaystyle -\frac{d^2}{dx^2}+Fx, F>0 \quad\text{on} \quad \mathcal{H}=L^{2}(-L,L).$$ $H$ is called Stark operator and describes a quantum particle in a…
We analyze several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary…
The concept of the PT-symmetry, originating from the quantum field theory, has been intensively investigated in optics, stimulated by the similarity between the Schr\"odinger equation and the paraxial wave equation that governs the…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
We investigate complex versions of the Korteweg-deVries equations and an Ito type nonlinear system with two coupled nonlinear fields. We systematically construct rational, trigonometric/hyperbolic, elliptic and soliton solutions for these…
In this letter, we study how the spectrum of pseudo-Hermitian systems is influenced by the ambiguity in the choice of the pseudo-metric operator. In particular, we analyze the case when different parameter-independent choices of…
We demonstrate that large class of PT-symmetric complex potentials, which can have isospectral real partner potentials, possess two different superpotentials. In the parameter domain, where the superpotential is unique, the spectrum is real…
The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain --- when the region within the heterojunctions is described by a non Hermitian ${\cal{PT}}$ symmetric…
Temporal interfaces introduced by abrupt switching of the constitutive parameters of unbounded media enable unusual wave phenomena. So far, their explorations have been mostly limited to lossless media. Yet, non-Hermitian phenomena…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…
We study how to understand the complex coordinates involved in the non-Hermitian but PT-symmetric systems. We explore a PT-symmetric oscillator model to show that the entire information on the complex position is attainable. Its real part…
Not necessarily self-adjoint quantum graphs -- differential operators on metric graphs -- are considered. Assume in addition that the underlying metric graph possesses an automorphism (symmetry) $ \mathcal P $. If the differential operator…
We investigate a two-parametric family of one-dimensional non-Hermitian complex potentials with parity-time ($\mathcal{PT}$) symmetry. We find that there exist two distinct types of phase transitions, from an unbroken phase (characterized…