Related papers: Eigenvalue problems for the complex PT-symmetric p…
In many PT symmetric models with real spectra, apparently, energy levels "merge and disappear" at a point of the spontaneous PT-symmetry breaking. We argue that such an oversimplified and discontinuous physical interpretation of this…
Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary…
Most studies of PT-symmetric quantum-mechanical Hamiltonians have considered the Schroedinger eigenvalue problem on an infinite domain. This paper examines the consequences of imposing the boundary conditions on a finite domain. As is the…
The appearances of complex eigenvalues in the spectra of PT-symmetric quantum-mechanical systems are usually associated with a spontaneous breaking of PT. In this letter we discuss a family of models for which this phenomenon is also linked…
We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $\cal PT$ symmetry may…
The broken and unbroken phases of PT and supersymmetry in optical systems are explored for a complex refractive index profile in the form of a Scarf potential, under the framework of supersymmetric quantum mechanics. The transition from…
We give a complete description, provided with a mathematical proof, of the shape of the spectrum of the Hill operator with a PT-symmetric periodic optical potential. We prove that the second critical point, after which the real parts of the…
We provide an explanation to the behaviour of the spectra of two exactly-solvable one-dimensional Hamiltonians with PT symmetry proposed earlier. We calculate the branch points at which pairs of eigenvalues coalesce and discuss the…
We study the effect of PT-symmetric complex potentials on the transport properties of non-Hermitian systems, which consist of an infinite linear chain and two side-coupled defect points with PT-symmetric complex on-site potentials. By…
Comparison between the exact value of the spectral zeta function, $Z_{H}(1)=5^{-6/5}[3-2\cos(\pi/5)]\Gamma^2(1/5)/\Gamma(3/5)$, and the results of numeric and WKB calculations supports the conjecture by Bessis that all the eigenvalues of…
In this work, we show that the traditional effective field approach can be applied to the $\mathcal{PT}$-symmetric wrong sign ($-x^{4}$) quartic potential. The importance of this work lies in the possibility of its extension to the more…
We consider discrete one-dimensional Schroedinger operators whose potentials decay asymptotically like an inverse square. In the super-critical case, where there are infinitely many discrete eigenvalues, we compute precise asymptotics of…
Recently, a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian $H=p^2+x^2(ix)^\epsilon$ was studied. It was found that the energy levels for this theory are real for all $\epsilon\geq0$. Here, the…
We consider an eigenvalue problem for an inverted one dimensional harmonic oscillator. We find a complete description for the eigenproblem in $C^{\infty}(\mathbb R)$. The eigenfunctions are described in terms of the confluent hypergeometric…
We study the eigenvalue problem -u"(z)-[(iz)^m+P(iz)]u(z)=\lambda u(z) with the boundary conditions that u(z) decays to zero as z tends to infinity along the rays \arg z=-\frac{\pi}{2}\pm \frac{2\pi}{m+2}, where P(z)=a_1 z^{m-1}+a_2…
The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral…
We study small, PT-symmetric perturbations of self-adjoint double-well Schr\"odinger operators in dimension $n\geq 1$. We prove that the eigenvalues stay real for a very small perturbation, then bifurcate to the complex plane as the…
We find theoretical results on energy eigenvalues and corresponding supersymmetric Hamiltonians reflect contradictory behavior for negative values of A. furthermore the resulting supersymmetric partners potentials can be model scattering…
A hollow matrix described by a graph $G$ is a real symmetric matrix having all diagonal entries equal to zero and with the off-diagonal entries governed by the adjacencies in $G$. For a given graph $G$, the determination of all possible…
We propose that the real spectrum and the orthogonality of the states for several known complex potentials of both types, PT-symmetric and non-PT-symmetric can be understood in terms of currently proposed $\eta$-pseudo-Hermiticity…