Related papers: $\cal{PT}$ symmetric models with nonlinear pseudo …
We investigate the properties of multidimensional parity-time symmetric periodic systems whose non-Hermitian periodicity is an integer multiple of the underlying Hermitian system's periodicity. This creates a natural set of degeneracies…
I will provide a pedagogical introduction to non-Hermitian quantum systems that are PT-symmetric, that is they are left invariant under a simultaneous parity transformation (P) and time-reversal (T). I will explain how generalised versions…
A generic PT-symmetric Hamiltonian is assumed tridiagonalized and truncated to N dimensions, and its up-down symmetrized special cases with J=[N/2] real couplings are considered. In the strongly non-Hermitian regime the secular equation…
We construct a two-parametric family of exactly solvable Dirac Hamiltonians by the Darboux transformation method. We obtain intertwining relations between different members of the Hamiltonian family. We investigate the spectral properties…
The pseudo-perturbation shifted-l expansion technique PSLET is shown applicable in the non-Hermitian PT-symmetric context. The construction of bound states for several PT-symmetric potentials is presented, with special attention paid to…
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the…
We construct Darboux transformations for the super-symmetric KP hierarchies of Manin--Radul and Jacobian types. We also consider the binary Darboux transformation for the hierarchies. The iterations of both type of Darboux transformations…
In this article, we consider an interesting class of optical and other systems in which the interaction or coupling makes the systems to be $\cal{PT}$-symmetric. We aim to compare their dynamical behaviors with that of the usual $\cal{PT}$…
In this paper, we present a general method to solve non-hermetic potentials with PT symmetry using the definition of two $\eta$-pseudo-hermetic and first-order operators. This generator applies to the Dirac equation which consists of two…
We introduce the simplest one-dimensional nonlinear model with the parity-time (PT) symmetry, which makes it possible to find exact analytical solutions for localized modes ("solitons"). The PT-symmetric element is represented by a…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
The exact solutions of the (2+1) dimensional Dirac equation on the torus and the new extension and generalization of the trigonometric Poschl-Teller potential families in terms of the torus parameters are obtained. Supersymmetric quantum…
A class of non-Hermitian quadratic su(2) Hamiltonians having an anti-linear symmetry is constructed. This is achieved by analysing the possible symmetries of such systems in terms of automorphisms of the algebra. In fact, different…
In (Nucci M.C. 1994, Physica D 78 p.124), we have found that iterations of the nonclassical symmetries method give rise to new nonlinear equations, which inherit the Lie point symmetry algebra of the given equation. In the present paper, we…
We investigate properties of the most general PT-symmetric non-Hermitian Hamiltonian of cubic order in the annihilation and creation operators as a ten parameter family. For various choices of the parameters we systematically construct an…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
Supersymmetry transformations of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. It is studied also the way in which the eigenfunctions…
Existence of a spectral singularity (SS) in the spectrum of {a Schr\"{o}dinger operator with} a non-Hermitian potential requires exact matching of parameters of the potential. We provide a necessary and sufficient condition for a potential…
A class of "elliptic soliton" solutions of the Kadomtsev-Petviashvili hierarchy, which includes a determinantal solution of Li and Zhang, is described in terms of pseudo-differential operator formulation. In our approach, the Li-Zhang…
PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous…