Related papers: Surprising spectra of PT-symmetric point interacti…
In this paper, we investigate the spectrum of the self adjoint differential operator with operator coefficitent in a separable Hilbert space. We also derive asymptotic formulas for the sum of eigenvalues of this operator.
The family of complex PT-symmetric sextic potentials is studied to show that for various cases the system is essentially quasi-solvable and possesses real, discrete energy eigenvalues. For a particular choice of parameters, we find that…
Relativistic PT-symmetric fermionic interacting systems are studied in 1+1 and 3+1 dimensions. The objective is to include non-Hermitian PT-symmetric interaction terms that give {\it real} spectra. Such interacting systems could describe…
A method of Parity-Time (PT)-symmetry analysis is introduced to study the high dimensional, complicated parameter space of drift wave instabilities. We show that spontaneous PT-symmetry breaking leads to the Ion Temperature Gradient (ITG)…
In this expository article some spectral properties of self-adjoint differential operators are investigated. The main objective is to illustrate and (partly) review how one can construct domains or potentials such that the essential or…
This is the third in a series of works devoted to spectral asymptotics for non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2. We assume that the unperturbed operator has a periodic Hamilton flow,…
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…
Within CPT-symmetric quantum mechanics the most elementary differential form of the charge operator C is assumed. A closed-form integrability of the related coupled differential self-consistency conditions and a natural embedding of the…
Recent progress on nonlinear properties of parity-time ($\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\cal PT$…
The symmetric Al-Salam--Chihara polynomials for $q>1$ are associated with an indeterminate moment problem. There is a self-adjoint second order difference operator on $\ell^2(\Z)$ to which these polynomials are eigenfunctions. We determine…
In this article we are interested for the numerical computation of spectra of non-self adjoint quadratic operators, in two and three spatial dimensions. Indeed, in the multidimensional case very few results are known on the location of the…
We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also…
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…
The physical aspects of partially coherent radiation interacting with deterministic non-Hermitian periodic materials remain largely unexplored in the statistical optics literature. Here, we consider the scattering of partially coherent…
We review some surprising links which have been discovered in the last few years between the theory of certain ordinary differential equations, and particular integrable lattice models and quantum field theories in two dimensions. An…
We describe one-dimensional stationary scattering of a two-component wave field by a non-Hermitian matrix potential which features odd-$PT$ symmetry, i.e., symmetry with $(PT)^2=-1$. The scattering is characterized by a $4\times 4$ transfer…
We discuss how introducing an equilibrium frame, in which a given Hamiltonian has balanced loss and gain terms, can reveal PT symmetry hidden in non-Hermitian Hamiltonians of dissipative systems. Passive PT-symmetric Hamiltonians, in which…
We consider the $\mathcal{PT}$-symmetric quantum field theory on the noncommutative spacetime with angular twist and construct its pseudo-Hermitian interpretation. We explore the differences between internal and spatial parities in the…
There are self-adjoint operators which determine both spectral and semispectral measures. These measures have very different commutativity and covariance properties. This fact poses a serious question on the physical meaning of such a…
There exists multiple branch points in the energy spectrum for some \emph{PT}-symmetric periodic potentials, where the real eigenvalues turn into complex ones. By studying the transmission amplitude for a localized complex potential, we…