Related papers: Comment on "Position-dependent effective mass Dira…
The quantum-field model described by non-Hermitian, but a ${\cal PT}$-symmetric Hamiltonian is considered. It is shown by the algebraic way that the limiting of the physical mass value $m \leq m_{max}= {m_1}^2/2m_2$ takes place for the case…
We study the spectrum of the 1D Dirac Hamiltonian encompassing the bound and scattering states of a fermion distorted by a static background built from $\delta$-function potentials. We distinguish between "mass-spike" and "electrostatic"…
The properties of asymmetric nuclear matter have been investigated in a relativistic Dirac-Brueckner-Hartree-Fock framework using the Bonn A potential. The components of the self-energies are extracted by projecting on Lorentz invariant…
We consider electronic transport accross one-dimensional heterostructures described by the Dirac equation. We discuss the cases where both the velocity and the mass are position dependent. We show how to generalize the Dirac Hamiltonian in…
We solved the one-dimensional position-dependent mass Dirac equation in the presence of the cusp potential and reported the solutions in terms of the Whittaker functions. We have derived the reflection and transmission coefficients by…
In 1992 Bender, Boettcher, and Lipatov proposed in two papers a new and unusual nonperturbative calculational tool in quantum field theory. The objective was to expand the Green's functions of the quantum field theory as Taylor series in…
We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
A 1D Dirac tight-binding model is considered and it is shown that its nonrelativistic limit is the 1D discrete Schr?odinger model. For random Bernoulli potentials taking two values (without correlations), for typical realizations and for…
We derive bounds on the location of non-embedded eigenvalues of Dirac operators on the half-line with non-Hermitian $L^1$-potentials. The results are sharp in the non-relativistic or weak-coupling limit. In the massless case, the absence of…
Relativistic PT-symmetric fermionic interacting systems are studied in 1+1 and 3+1 dimensions. The objective is to include non-Hermitian PT-symmetric interaction terms that give {\it real} spectra. Such interacting systems could describe…
We consider the one-dimensional Dirac equation for the harmonic oscillator and the associated second order separated operators giving the resonances of the problem by complex dilation. The same operators have unique extensions as closed…
The modified Dirac equations for the massive particles with the replacement of the physical mass $m$ with the help of the relation $m\rightarrow m_1+ \gamma_5 m_2$ are investigated. It is shown that for a fermion theory with a…
A fundamental problem regarding the Dirac quantization of a free particle on an $N-1$ curved hypersurface embedded in $N$($\geq 2$) flat space is the impossibility to give the same form of the curvature-induced quantum potential, the…
For the PT symmetric potential of Dorey, Dunning and Tateo we show that in the large angular momentum (i.e., strongly spiked) limit the low-lying eigenstates of this popular non-Hermitian problem coincide with the shifted Hermitian harmonic…
The one-dimensional effective-mass Klein-Gordon equation for the real, and non-\textrm{PT}-symmetric/non-Hermitian generalized Morse potential is solved by taking a series expansion for the wave function. The energy eigenvalues, and the…
The spherically symmetric potential $a \,\delta (r-r_0)+b\,\delta ' (r-r_0)$ is generalised for the $d$-dimensional space as a characterisation of a unique selfadjoint extension of the free Hamiltonian. For this extension of the Dirac…
We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in…
In this work, we provide a complete description of the scattering matrix elements and electron energy spectrum in one dimensional PT-symmetric hybrid finite systems, using the characteristic determinant approach. We present an analytical…
The general Dirac equation in 1+1 dimensions with a potential with a completely general Lorentz structure is studied. Considering mixed vector-scalar-pseudoscalar square potentials, the states of relativistic fermions are investigated. This…