The family of metric operators, constructed by Musumbu et al (2007 J. Phys. A: Math. Theor. 40 F75), for a harmonic oscillator Hamiltonian augmented by a nonHermitian PT -symmetric part, is re-examined in the light of an su(1,1) approach. An alternative derivation, only relying on properties of su(1,1) generators, is proposed. Being independent of the realization considered for the latter, it o...

The family of metric operators, constructed by Musumbu et al (2007 J. Phys. A: Math. Theor. 40 F75), for Swanson’s PT -symmetric Hamiltonian, is re-examined in the light of an su(1,1) approach. An alternative derivation, only relying on properties of su(1,1) generators, is proposed. Being independent of the realization considered for the latter, it opens the way towards the construction of gene...

It is well known that the unitary evolution of a closed $M-$level quantum system can be generated by non-Hermitian Hamiltonian $H$ with real spectrum. Its Hermiticity restored via an amended inner-product metric $\Theta$. In Hermitian cases evaluation spectrum (i.e., bound-state energies) usually achieved diagonalization Hamiltonian. (or, more precisely, in $\Theta-$quasi-Hermitian) mechanics w...

An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and veloci...

We exploit the hidden symmetry structure of a recently proposed non-Hermitian Hamiltonian and of its Hermitian equivalent one. This sheds new light on the pseudoHermitian character of the former and allows access to a generalized quantum condition. Special cases lead to hyperbolic and Morse-like potentials in the framework of a coordinate-dependent mass model.

A generalized non-Hermitian oscillator Hamiltonian is proposed that consists of additional linear terms which break PT -symmetry explicitly. The model is put into an equivalent Hermitian form by means of a similarity transformation and the criterion of N -fold supersymmetry with a position-dependent mass is shown to reside in it.

We study the question of diagonalizability of the Hamiltonian for the FaddeevReshetikhin (FR) model in the two particle sector. Although the two particle S-matrix element for the FR model, which may be relevant for the quantization of strings on AdS5×S, has been calculated recently using field theoretic methods, we find that the Hamiltonian for the system in this sector is not diagonalizable. W...

Attention has been brought to the possibility that statistical fluctuation properties of several complex spectra, or, well-known number sequences may display strong signatures that the Hamiltonian yielding them as eigenvalues is PT-symmetric (Pseudo-Hermitian). We find that the random matrix theory of pseudo-Hermitian Hamiltonians gives rise to new universalities of levelspacing distributions o...

in this paper we consider the solutions of linear systems of saddle point problems‎. ‎by using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the hermitian and skew hermitian splitting method‎.