Related papers: Non-Hermitian Hamiltonians of Lie algebraic type
We show that a diagonalizable (non-Hermitian) Hamiltonian H is pseudo-Hermitian if and only if it has an antilinear symmetry, i.e., a symmetry generated by an invertible antilinear operator. This implies that the eigenvalues of H are real…
We investigate the quantum-mechanical interpretation of models with non-Hermitian Hamiltonians and real spectra. After describing a general framework to reformulate such models in terms of Hermitian Hamiltonians defined on the Hilbert space…
Non-alternating Hamiltonian Lie algebras in three variables over a perfect field of characteristic 2 are considered. A classification of non-alternating Hamiltonian forms over an algebra of divided powers in three variables and of the…
We calculate the eigenvalues of some two-dimensional non-Hermitian Hamiltonians by means of a pseudospectral method and straightforward diagonalization of the Hamiltonian matrix in a suitable basis set. Both sets of results agree remarkably…
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.…
We propose a noncommutative version of the Euclidean Lie algebra $E_2$. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of…
We in this paper study the hermiticity of Hamiltonian and energy spectrum for the SU(1; 1) systems. The Hermitian Hamiltonian can possess imaginary eigenvalues in contrast with the common belief that hermiticity is a suffcient condition for…
It is shown that for a given Hermitian Hamiltonian possessing supersymmetry, there is alwayas a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the…
A harmonic oscillator Hamiltonian augmented by a non-Hermitian \pt-symmetric part and its su(1,1) generalizations, for which a family of positive-definite metric operators was recently constructed, are re-examined in a supersymmetric…
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…
A set of r non-Hermitian oscillator Hamiltonians in r dimensions is shown to be simultaneously diagonalizable. Their spectra is real and the common eigenstates are expressed in terms of multiple Charlier polynomials. An algebraic…
A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form $ H=\omega J_{3}+\alpha J_{-}+\beta J_{+}$, $\alpha \neq \beta$, is analyzed. The metrics which…
A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator $\eta_+$ and defining the annihilation and creation operators to be $\eta_+$-pseudo-Hermitian adjoint to each other. The operator…
Hamiltonians of a wide-spread class of $G_{inv}$-invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as non-linear functions of $sl(2)$ generators. It enables us to use standard variational…
We give two characterization theorems for pseudo-Hermitian (possibly nondiagonalizable) Hamiltonians with a discrete spectrum that admit a block-diagonalization with finite-dimensional diagonal blocks. In particular, we prove that for such…
In this letter we will use higher-order supersymmetric quantum mechanics to obtain several families of complex solutions of the Painleve IV equation with real parameters. We shall also study the algebraic structure, the eigenfunctions and…
Over the past decade classical optical systems with gain or loss, modelled by non-Hermitian parity-time symmetric Hamiltonians, have been deeply investigated. Yet, their applicability to the quantum domain with number-resolved photonic…
The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian $\cal PT$-symmetric part, is re-examined in the light…
Quantum theory can be formulated with certain non-Hermitian Hamiltonians. An anti-linear involution, denoted by PT, is a symmetry of such Hamiltonians. In the PT-symmetric regime the non-Hermitian Hamiltonian is related to a Hermitian one…
We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire…