The spectrum of the Hermitian Hamiltonian 1 2p 2 + 12m 2x2 + gx4 (g > 0), which describes the quantum anharmonic oscillator, is real and positive. The non-Hermitian quantum-mechanical Hamiltonian H = 1 2p 2 + 12m 2x2 − gx4, where the coupling constant g is real and positive, is PT -symmetric. As a consequence, the spectrum ofH is known to be real and positive as well. Here, it is shown that the...

We present a generalized Floquet formulation of time-dependent current-density-functional theory for nonperturbative treatment of multiphoton processes of many-electron systems in intense monochromatic electric and magnetic fields. It is shown that the time-dependent Kohn-Sham-like equation can be transformed into an equivalent time-independent Floquet Hamiltonian matrix eigenvalue problem. A p...

A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator algebra. The different representations yield drastically different Hilbert spaces. In particular, all the spaces obtained in the antiholomorphic representation vi...

We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT -symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermit...

in this paper energy bands and berry curvature of graphene was studied. desired hamiltonian regarding the next-nearest neighbors obtained by tight binding model. by using the second quantization approach, the transformation matrix is calculated and the hamiltonian of system is diagonalized. with this hamiltonian, the band structure and wave function can be calculated. by using calculated wave f...

We develop relativistic wave equations in the framework of the new non-hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT -symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no cou...

The computation of eigenvalues and eigenvectors of matrix polynomials is an important, but di cult, problem. The standard approach to solve this problem is to use linearizations, which are matrix polynomials of degree 1 that share the eigenvalues of P ( ). Hermitian matrix polynomials and their real eigenvalues are of particular interest in applications. Attached to these eigenvalues is a set o...

A semiclassical approximation for an evolving density operator, driven by a 'closed' Hamiltonian and 'open' Markovian Lindblad operators, is reviewed. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian is a quadratic function and the Lindblad operators are linear functio...

Perturbation bounds for the generalized eigenvalue problem of a diagonalizable matrix pencil A-ÀB with real spectrum are developed. It is shown how the chordal distances between the generalized eigenvalues and the angular distances between the generalized eigenspaces can be bounded in terms of the angular distances between the matrices. The applications of these bounds to the spectral variation...

A family of non-Hermitian real and tridiagonal-matrix candidates H(N)(λ)=H0(N)+λW(N)(λ) for a hiddenly Hermitian (a.k.a. quasi-Hermitian) quantum Hamiltonian is proposed studied. Fairly weak assumptions are imposed upon the unperturbed matrix [the square-well-simulating spectrum H0(N) not assumed equidistant)] its maximally N-parametric antisymmetric-matrix perturbations [matrix W(N)(λ) even re...