Related papers: PT-Symmetric Cubic Anharmonic Oscillator as a Phys…
We provide a systematic procedure to relate a three dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables describing noncommutative spaces. The large number of possible free parameters in…
In study of pseudo(quasi)-hermitian operators, the key role is played by the positive-definite metric operator. It enables physical interpretation of the considered systems. In the article, we study the pseudo-hermitian systems with…
The potential -x^4, which is unbounded below on the real line, can give rise to a well-posed bound state problem when x is taken on a contour in the lower-half complex plane. It is then PT-symmetric rather than Hermitian. Nonetheless it has…
Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a $\gamma_5$ mass term the Hamiltonian is $\cal PT$-symmetric. Depending on the mass…
Using a PT symmetric regularization technique we reminad the reader that and how (a) the SUSY is re-established between the two shifted harmonic oscillator potentials $ V(q)=q^2+{G}/{q^2}+ const$ and (b) many non-equivalent Hermitian and…
We introduce a general framework for realizing $\mathcal{PT}$-like phase transitions in non-Hermitian systems without imposing explicit parity--time ($\mathcal{PT}$) symmetry. The approach is based on constructing a Hamiltonian as the…
While Hermiticity of a time-independent Hamiltonian leads to unitary time evolution, in and of itself, the requirement of Hermiticity is only sufficient for unitary time evolution. In this paper we provide conditions that are both necessary…
We introduce and develop a novel approach to extend the ordinary two-flavor neutrino oscillation formalism in matter using a non-Hermitian PT symmetric effective Hamiltonian. The condition of PT symmetry is weaker and less mathematical than…
The classical trajectories of the family of complex PT-symmetric Hamiltonians $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) form closed orbits. All such complex orbits that have been studied in the past are PT symmetric (left-right symmetric).…
In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…
For a subclass of a general $\mathcal{PT}-$symmetric Hamiltonian obeying anti-commutation relation with its conjugate, a Hermitian basis is found that spans the bi-orthonormal energy eigenvectors. Using the modified projectors constructed…
We employ the technique of perturbative analytic null bootstrap to obtain the energy eigenvalues and ladder operators of the sextic anharmonic oscillator up to second order in the coupling. We confirm our results by deriving the same from…
In this paper, we extend the result of [Andreas Fring et al J. Phys. A 43, 345401 (2010)] in noncommutative phase-space (NCPS). We compute the non-Hermitian Hamiltonian of a harmonic oscillator in NCPS. We construct a new P T-symmetry in…
One of the postulates of quantum mechanics is that the Hamiltonian is Hermitian, as this guarantees that the eigenvalues are real. Recently there has been an interest in asking if $H^\dagger = H$ is a necessary condition, and has lead to…
Non-Hermitian but P(phi)T(phi)-symmetrized spherically-separable Dirac and Schrodinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H(r), H(theta), and H(phi) play essential roles and offer some…
By embedding a $\cal PT$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $\cal{PT}$-symmetric Hamiltonians and weak measurement theory. We show that the amplification effect in weak…
We consider a two-level system such as a two-level atom, interacting with a cavity field mode in the rotating wave approximation, when the atomic transition frequency or the field mode frequency is periodically driven in time. We show that…
The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…
We study some quantum systems described by noncanonical commutation relations formally expressed as [q,p]=ihbar(I + chi H), where H is the associated (harmonic oscillator-like) Hamiltonian of the system, and chi is a Hermitian (constant)…
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…