Related papers: Eigenvalue and Eigenfunction for the $PT$-symmetri…
We describe a method that allows for a practical application of the theory of pseudo-Hermitian operators to PT-symmetric systems defined on a complex contour. We apply this method to study the Hamiltonians $H=p^2+x^2(ix)^\nu$ with…
Many non-Hermitian but PT-symmetric theories are known to have a real positive spectrum. Since the action is complex for there theories, Monte Carlo methods do not apply. In this paper the first field-theoretic method for numerical…
The energy spectrum of eigenvalues of the equal spin-spin interactions (ESSI) Hamiltonian has been found. The obtained spectrum is free from limitations imposed on number of spins and parameters of the ESSI Hamiltonian. This model can be…
A non-standard generalisation of the Bender potentials $x^2(\ii x^\ve)$ is suggested. The spectra are obtained numerically and some of their particular properties are discussed.
In this paper, we solve the eigenvalues and eigenvectors problem with Bohr collective Hamil- tonian for triaxial nuclei. The ? beta part of the collective potential is taken to be equal to Hulth?en potential while the gamma part is defined…
Path integral solutions are obtained for the the PT-/non-PT-Symmetric and non-Hermitian Morse Potential. Energy eigenvalues and the corresponding wave functions are obtained.
The spectral and localization properties of $\mathcal{PT}$-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are…
We prove the reality of the perturbed eigenvalues of some PT symmetric Hamiltonians of physical interest by means of stability methods. In particular we study 2-dimensional generalized harmonic oscillators with polynomial perturbation and…
In this note we consider a pair of particles moving on the positive half-line with the pairing generated by a hard-wall potential. This model was first introduced in [arXiv:1604.06693] and later applied to investigate condensation of pairs…
We investigate complex versions of the Korteweg-deVries equations and an Ito type nonlinear system with two coupled nonlinear fields. We systematically construct rational, trigonometric/hyperbolic, elliptic and soliton solutions for these…
This paper presents an underlying analytical relationship between the $\mathcal{PT}$-pseudo-norm associated with the $\mathcal{PT}$-symmetric Hamiltonian $H = p^2+ V(q)$ and the Stokes multiplier of the differential equation corresponding…
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 construct an isospectrum systems in terms of a real and complex potential to show that the underlying PT symmetric Hamiltonian possesses a real spectrum which is shared by its real partner.
In 1992 Bender, Boettcher, and Lipatov proposed in two papers a new and unusual nonperturbative calculational tool in quantum field theory. The objective was to expand the Green's functions of the quantum field theory as Taylor series in…
Recent investigations by Bender and Boettcher (Phys. Rev. Lett 80, 5243 (1998)) and Mezincescu (J. Phys. A. 33, 4911 (2000)) have argued that the discrete spectrum of the non-hermitian potential $V(x) = -ix^3$ should be real. We give…
Stability of soliton families in one-dimensional nonlinear Schroedinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of…
The problem of the electromagnetic self-force can be studied in terms of a quadratic PT-symmetric Hamiltonian. Here, we apply a straightforward algebraic method to determine the regions of model-parameter space where the quantum-mechanical…
The spectrum of the Hermitian Hamiltonian $H=p^2+V(x)$ is real and discrete if the potential $V(x)\to\infty$ as $x\to\pm\infty$. However, if $V(x)$ is complex and PT-symmetric, it is conjectured that, except in rare special cases, $V(x)$…
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…
We consider eigenvalue problems in quantum mechanics in one dimension. Hamiltonians contain a class of double well potential terms, x^6 + \alpha x^2, for example . The space coordinate is continued to a complex plane and the connection…