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A new model of supersymmetry between bosons and fermions is proposed. Its representation space is spanned by states with PT symmetry and real energies but the inter-related partner Hamiltonians themselves remain complex and non-Hermitian.…
The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of ${\cal PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians…
We demonstrate that the recent paper by Abhinav and Panigrahi entitled `Supersymmetry, PT-symmetry and spectral bifurcation' [Ann.\ Phys.\ 325 (2010) 1198], which considers two different types of superpotentials for the PT-symmetric…
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…
We study the quantum-mechanical interpretation of models with non-Hermitian Hamiltonians and real spectra. We set up a general framework for the analysis of such systems in terms of Hermitian Hamiltonians defined in the usual Hilbert space…
We study certain linear and antilinear symmetry generators and involution operators associated with pseudo-Hermitian Hamiltonians and show that the theory of pseudo-Hermitian operators provides a simple explanation for the recent results of…
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of…
We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well as complex PT-invariant, double sinh-Gordon potential and show that even after adding perturbation terms, the resulting potentials, in both cases, are still QES…
In a remarkable development Bender and coworkers have shown that it is possible to formulate quantum mechanics consistently even if the Hamiltonian and other observables are not Hermitian. Their formulation, dubbed PT quantum mechanics,…
Quantum physics is generally concerned with real eigenvalues due to the unitarity of time evolution. With the introduction of $\mathcal{PT}$ symmetry, a widely accepted consensus is that, even if the Hamiltonian of the system is not…
Bender et al. have developed PT-symmetric quantum theory as an extension of quantum theory to non-Hermitian Hamiltonians. We show that when this model has a local PT symmetry acting on composite systems it violates the non-signaling…
We reply to Dukelsky, et al. regarding the article: L. A. Wu, M. S. Byrd and D. A. Lidar, Phys. Rev. Lett. 89, 057904 (2002).
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 introduce generalized versions of complex Scarf and Morse-type potentials that con- tain energy-dependent parameters. PT -symmetry and pseudo-hermiticity of the associated quantum systems are discussed, and a modified orthogonality…
Supersymmetry is one of the most important and indispensable ingredients of modern theoretical physics. However, the absence, at least at the time of publishing this review, of experimental verification of supersymmetry in elementary…
A transformation of the form x to iy; x,y in R, or an equivalent similarity transformation with a metric operator $\eta$ are shown to transform non-Hermitian PT-symmetric Hamiltonians into Hermitian partner Hamiltonians in Hilbert space.…
The {\eta} pseudo PT symmetry theory, denoted by the symbol {\eta}, explores the conditions under which non-Hermitian Hamiltonians can possess real spectra despite the violation of PT symmetry, that is the adjoint of H, denoted H^{{\dag}}…
We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues…
In this paper we present a general method to solve non hermetic potentials with PT symmetry using the introduction of two first-order operator against {\eta}-pseudo-hermetic({\eta}-weak-pseudo-hermiticity) with position dependent effective…
We analyze several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary…