Related papers: $\cal{PT}$ symmetric models with nonlinear pseudo …
We examine in detail the possibilty of applying Darboux transformation to non Hermitian hamiltonians. In particular we propose a simple method of constructing exactly solvable PT symmetric potentials by applying Darboux transformation to…
A series of exactly solvable non-trivial complex potentials (possessing real spectra) are generated by applying the Darboux transformation to the excited eigenstates of a non-Hermitian potential V(x). This method yields an infinite number…
A key feature of integrable systems is that they can be solved to obtain exact analytical solutions. We show how new models can be constructed through generalisations of some well known nonlinear partial differential equations with…
Non-hermitian, $\mathcal{PT}$-symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly…
We study a two-dimensional exactly solvable non-Hermitian $PT-$non-symmetric quantum model with real spectrum, which is not amenable to separation of variables, by supersymmetrical methods. Here we focus attention on the property of…
Searching for non-Hermitian (parity-time)$\mathcal{PT}$-symmetric Hamiltonians \cite{bender} with real spectra has been acquiring much interest for fourteen years. In this article, we have introduced a $\mathcal{PT}$ symmetric non-Hermitian…
We examine the properties and consequences of pseudo-supersymmetry for quantum systems admitting a pseudo-Hermitian Hamiltonian. We explore the Witten index of pseudo-supersymmetry and show that every pair of diagonalizable (not necessarily…
The energy spectra of two different quantum systems are paired through supersymmetric algorithms. One of the systems is Hermitian and the other is characterized by a complex-valued potential, both of them with only real eigenvalues in their…
The supersymmetric solutions of PT-symmetric and Hermitian/non-Hermitian forms of quantum systems are obtained by solving the Schrodinger equation for the Exponential-Cosine Screened Coulomb potential. The Hamiltonian hierarchy inspired…
Supersymmetric solution of PT-/non-PT-symmetric and non-Hermitian Morse potential is studied to get real and complex-valued energy eigenvalues and corresponding wave functions. Hamiltonian Hierarchy method is used in the calculations
We introduce a method for constructing Darboux (or supersymmetric) pairs of pseudoscalar and scalar Dirac potentials that are associated with exceptional orthogonal polynomials. Properties of the transformed potentials and regularity…
We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY…
A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation…
New types of irreducible second order Darboux transformations for the one dimensional Schroedinger equation are described. The main feature of such transformations is that the transformation functions have the eigenvalues grater then the…
We propose a new algebraic formalism for constructing complex non-Hermitian $\mathcal{PT}$-symmetric superpartners by extending a conventional shape-invariant superpotential into the complex domain. The resulting potential is an unbroken…
In this paper, we discuss the parametric symmetries in different exactly solvable systems characterized by real or complex P T symmetric potentials. We focus our at- tention on the conventional potentials such as the generalized Poschl…
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra sl(2, C). This…
We review recent work on the generalization of PT symmetry. We show that, in addition to PT-symmetric complex potentials, there are also large classes of non-PT-symmetric complex potentials which also feature all-real spectra. In addition,…
We study additional non-isospectral symmetries of constrained (reduced) N=2 supersymmetric KP hierarchies of integrable ``soliton''-like evolution equations. These symmetries are shown to form an infinite-dimensional non-Abelian superloop…
It is know that PT-symmetric models have real spectra provided the symmetry is not spontaneously broken. Even pseudo-hermitian models have real spectra, which enlarge the the class of non-hermitian models possessing real spectra. We however…