Related papers: (1+1)-Dirac particle with position-dependent mass …
Spectroscopic labels for a few particles with spin that are harmonically trapped in one-dimension with effectively zero-range interactions are provided by quantum numbers that characterize the symmetries of the Hamiltonian: permutations of…
The paper deals with the semi-Dirac operator in a half-space arising in the description of quasiparticles in quantum mechanics as well as in semi-metals materials and related structures. It completely shows the self-adjointness, computes…
In the context of some deformed canonical commutation relations leading to isotropic nonzero minimal uncertainties in the position coordinates, a Dirac equation is exactly solved for the first time, namely that corresponding to the Dirac…
We study spectral and transport properties of one-dimensional tight-binding $\mathcal{PT}$-symmetric chains with alternating couplings. Based on the transfer matrix method, we have analytically developed the expressions for the transmission…
The spectral and localization properties of $\mathcal{PT}$-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are…
Light propagation in distributed feedback optical structures with gain/loss regions is shown to provide an accessible laboratory tool to visualize in optics the spectral properties of the one-dimensional Dirac equation with non-Hermitian…
By employing an exponential-type approximation scheme to replace the centrifugal term, we have approximately solved the Dirac equation for spin- particle subject to the complex -symmetric scalar and vector P\"oschl-Teller (PT) potentials…
In a previous work we have described the classical structure and analyzed the interaction of the classical Dirac particle with uniform and oscillating electric and magnetic fields. In the present paper we consider the interaction of the…
Quasi-one-dimensional chains of atoms can be effectively described by one-dimensional Dirac-type equation. Crystal structure of the chain is reflected by pseudo-spin of the quasi-particles. In the article, we present a simple framework…
We present a generalization of the perturbative construction of the metric operator for non-Hermitian Hamiltonians with more than one perturbation parameter. We use this method to study the non-Hermitian scattering Hamiltonian:…
The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in 3+1 dimensions onto a…
An elementary treatment of the Dirac Equation in the presence of a three-dimensional spherically symmetric $\delta (r-r_0)$-potential is presented. We show how to handle the matching conditions in the configuration space, and discuss the…
A new method for solving the time-dependent two-center Dirac equation is developed. The approach is based on the using of the finite basis of cubic Hermite splines on a three-dimensional lattice in the coordinate space. The relativistic…
We consider the N=1 supersymmetric kink on a circle, i.e., on a finite interval with boundary or transition conditions which are locally invisible. For Majorana fermions, the single-particle Dirac Hamiltonian as a differential operator…
Dirac particle represents a fundamental constituent of our nature. Simulation of Dirac particle dynamics by a controllable quantum system using quantum walks will allow us to investigate the non-classical nature of dynamics in its discrete…
Parity-time ($\mathcal{PT}$) symmetry plays an important role both in non-Hermitian and topological systems. In non-Hermitian systems $\mathcal{PT}$ symmetry can lead to an entirely real energy spectrum, while in topological systems…
The dynamical symmetry breaking in a quasi-(1+1)-dimensional relativistic model is investigated. The motions of particles in intrachain are described as a relativistic electron-hole gas, while the interchain hopping term is introduced as a…
We consider the nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction in the presence of external forces as well as damping of the form $\gamma^0 f(x,t) - i \mu \gamma^0 \Psi$, where both $f, \{f_j = r_i e^{i…
We show that the spectral theory of the Dirac operator $D = i\delsl-\sigma(x) -i\pi(x)\gam_5$ in a static background $(\sigma(x),\pi(x))$ in 1+1 space-time dimensions, is underlined by a certain generalization of supersymmetric quantum…
By analyzing the Dirac equation with static electric and magnetic fields it is shown that Dirac's theory is nothing but a generalized one-particle quantum theory compatible with the special theory of relativity. This equation describes a…