Related papers: Confining massless Dirac particles in two-dimensio…
A basic theoretical framework is developed in which elementary particles have a component of their wave function extending into higher spatial dimensions. This model postulates an extension of the Schrodinger equation to include a 4th and…
Presented is a quantum lattice gas algorithm to efficiently model a system of Dirac particles interacting through an intermediary gauge field. The algorithm uses a fixed qubit array to represent both the spacetime and the particles…
One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for…
We adapt a finite difference method of solution of the two-dimensional massless Dirac equation, developed in the context of lattice gauge theory, to the calculation of electrical conduction in a graphene sheet or on the surface of a…
The Schr\"odinger equation in a square or rectangle with hard walls is solved in every introductory quantum mechanics course. Solutions for other polygonal enclosures only exist in a very restricted class of polygons, and are all based on a…
We consider fermion systems on a square lattice with a mass term having a curved domain-wall. Similarly to the conventional flat domain-wall fermions, massless and chiral edge states appear on the wall. In the cases of $S^1$ and $S^2$…
In a 6D model, where the extra dimensions form a discretised curved disk, we investigate the mass spectra and profiles of gravitons and Dirac fermions. The discretisation is performed in detail leading to a star-like geometry. In addition,…
Quantum confinement of graphene Dirac-like electrons in artificially crafted nanometer structures is a long sought goal that would provide a strategy to selectively tune the electronic properties of graphene, including bandgap opening or…
The symmetries that protect massless Dirac fermions from a gap opening may become ineffective if the Dirac equation is discretized in space and time, either because of scattering between multiple Dirac cones in the Brillouin zone (fermion…
In Foldy-Wouthuysen representation, we deduce the effective quantum mechanics for a particle confined to a curved surface by using the thin-layer quantization scheme. We find that the spin effect caused by confined potential as the results…
In this paper, we determine the relativistic bound-state solutions for the Dirac oscillator (DO) in the curved spacetime of a cloud of strings in $(3+1)$-dimensions, where such solutions are given by the four-component normalized Dirac…
In Westminster Abbey, in a nave near to Newton's monument, lies a memorial stone to Paul Dirac. The inscription on the stone includes the relativistic wave equation for an electron: the Dirac equation. At the turn of the 21st century, it…
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the…
The Nielsen-Ninomiya theorem, dubbed `fermion-doubling', poses a problem for the naive discretization of a single (massless) Dirac cone on a two-dimensional surface. The inevitable appearance of an additional, unphysical fermionic mode can,…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…
Microscopic quantum theory of nonlinear stimulated scattering of 2D Dirac particles in doped graphene on Coulomb field of impurity ions at the presence of an external strong coherent electromagnetic radiation is developed. We consider high…
This paper is devoted to a study of relativistic eigenstates of Dirac particles which are simultaneously bound by a static Coulomb potential and added linear confining potentials. It has recently been shown that, despite the addition of…
Since the discovery of topological insulators (TIs)1,2, the peculiar nature of their chiral surface states has been experimentally demonstrated both in bulk and in film materials with open boundaries3,4. Closed boundary on a TI surface may…
We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on…
Functional defects in periodic media confine waves - acoustic, electromagnetic, electronic, spin, etc. - in various dimensions, depending on the structure of the defect. While defects are usually modelled by a superlattice with a typical…