Related papers: Exactly solvable complex PT symmetry potential $A[…
A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral…
Dynamical systems exhibiting both PT and Supersymmetry are analyzed in a general scenario. It is found that, in an appropriate parameter domain, the ground state may or may not respect PT-symmetry. Interestingly, in the domain where…
We provide the first experimental demonstration of defect states in parity-time (PT) symmetric mesh-periodic potentials. Our results indicate that these localized modes can undergo an abrupt phase transition in spite of the fact that they…
Parity-time ($\mathcal{PT}$) symmetric systems are classical, gain-loss systems whose dynamics are governed by non-Hermitian Hamiltonians with exceptional-point (EP) degeneracies. The eigenvalues of a $\mathcal{PT}$-symmetric Hamiltonian…
It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when…
In "Comment on Supersymmetry, PT-symmetry and spectral bifurcation" \cite{BQ1}, Bagchi and Quesne correctly show the presence of a class of states for the complex Scarf-II potential in the unbroken PT-symmetry regime, which were absent in…
Closed expressions are derived for the pseudo-norm, norm and orthogonality relations for arbitrary bound states of the PT symmetric and the Hermitian Scarf II potential for the first time. The pseudo-norm is found to have indefinite sign in…
The one-dimensional Coulomb-like potential with a real coupling constant beta, and a centrifugal-like core of strength G = alpha^2 - {1/4}, viz. V(x) = {alpha^2 - (1/4)}/{(x-ic)^2} + beta/|x-ic|, is discussed in the framework of…
We study a three-parameter family of PT-symmetric Hamiltonians, related via the ODE/IM correspondence to the Perk-Schultz models. We show that real eigenvalues merge and become complex at quadratic and cubic exceptional points, and explore…
$PT$ symmetric quantum mechanics for a particle trapped by the generalized non-Hermitian harmonic oscillator potential is studied. It is shown that energy and the expectation value of the position operator $x$ can not be real…
The real spectrum of bound states produced by PT-symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. On the other hand, it is known that the…
The versatile and exactly solvable Scarf II has been predicting, confirming and demonstrating interesting phenomena in complex PT-symmetric sector, most impressively. However, for the non-PT-symmetric sector it has gone underutilized. Here,…
The effect of derivative nonlinearity and parity-time- (PT-) symmetric potentials on the wave propagation dynamics is investigated in the derivative nonlinear Schrodinger equation, where the physically interesting Scarff-II and…
We introduce the third independent exactly solvable hypergeometric potential, after the Eckart and the P\"oschl-Teller potentials, which is proportional to an energy-independent parameter and has a shape that is independent of this…
The exact bound state spectrum of rationally extended shape invariant real as well as $PT$ symmetric complex potentials are obtained by using potential group approach. The generators of the potential groups are modified by introducing a new…
We study the phase-diagram of a parity and time-reversal (PT) symmetric tight-binding chain with $N$ sites and hopping energy $J$, in the presence of two impurities with imaginary potentials $\pm i\gamma$ located at arbitrary (P-symmetric)…
Within the framework of the recently proposed formalism using non-hermitean Hamiltonians constrained merely by their PT invariance we describe a new exactly solvable family of the harmonic-oscillator-like potentials with non-equidistant…
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 study the behavior of steady state voltage potentials in two kinds of bidimensional media composed of material of complex permittivity equal to 1 (respectively $\alpha$) surrounded by a thin membrane of thickness $h$ and of complex…
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…