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Showing 1 to 17 of 17 for “"The Dirac equation"”.
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Solving the Dirac equation in a two-dimensional spacetime background with a kink
In the following paper, I study the Dirac equation in curved spacetime and solve this equation in two-dimensional spacetime backgrounds discovered by Jackiw et al[4], [5]. I will first discuss flat spacetime and introduce the Dirac equation, which describes the relativistic wavefunctions of …
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Continuum structure in strong electromagnetic fields
[Pages missing ] In this chapter, the Dirac equation for spherically symmetric potentials is closely examined. Analytical solutions are found for a square well potential, the properties of which will be used later when the equation is solved for arbitrary potentials using numerical methods. The …
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A Dirac all-electron basis and spin-orbit coupled projector implementation of the Projector Augmented Wave Method for atomic systems
The Projector Augmented Wave Method (PAW) [1] provides accurate numerical approximations to the exact eigenfunctions and eigenvalues of the Kohn-Sham equations for large-scale ab-initio electronic structure calculations of molecules and solids, for which exact calculations are impractical. …
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The bound states of Dirac equation with a scalar potential
"We study the bound states of the 1+1 dimensional Dirac equation with a scalar potential, which can also be interpreted as a position dependent ""mass'', analytically as well as numerically. We derive a Prüfer-like representation for the Dirac equation, which can be used to derive a condition for …
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Self-adjoint extensions to the Dirac Coulomb Hamiltonian
The Dirac equation is the relativistic generalization of the Schrödinger equation for spin 1/2 particles. It is written in the form -ihc -ihac OXIa+t' Omc 29 = ih-o (1.1) where V) is a four component Dirac spinor and the coefficients a and # are 4 x 4 matrices. Like the Schrödinger equation, the …
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On the parallels between the Maxwell and Dirac equations
… methods, and intuitions from one domain to another, often revealing hidden connections and sparking creative breakthroughs, as exemplified by Hamilton's seminal analogy between classical mechanics and geometric optics---a correspondence that ultimately seeded the development of quantum …
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Bound states of heavy and light quarks in the framework of quantum chromodynamics
The spectra of the D, F, B and E mesons have been calculated using the MIT bag model together with a static potential related to the Fourier transform of the "dressed" gluon propagator. The heavy quark has been assumed to coincide with the centre of the bag, while the Light antiquark was treated …
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Introduction of a Fully Relativistic Capable Basis Set in the ab initio Orthogonalized Linear Combination of Atomic Orbitals Method
… simulation cell sizes, relativistic effects, and the need to correctly model excited state properties are major impediments to the accurate prediction of the optical properties of candidate materials for solid-state laser crystal and luminescent applications. To overcome these challenges, new …
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Relativistic theory of low energy electron diffraction
In view of investigating the role of spin polarization and further relativistic effects in the diffraction of low energy electrons (LEED) by crystals composed of heavy atoms, a relativistic dynamical theory is developed for calculating LEED intensities and spin polarizations. The presentation of …
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Nuclear charge distribution of ¹⁸¹Ta
<p>The energies of the x rays emitted by the muonic atom of <sup>181</sup>Ta were measured by a Ge(Li) solid state detector. From the clustering of these gamma rays it was possible to identify the transitions of the muonic atom which produced them. When a form is chosen for the nuclear charge …
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Relativistic dynamics and Dirac particles in graphene
… hexagonal lattice of carbon, has jumped to the forefront of condensed matter research in the past few years as a high quality two-dimensional electron system with intriguing scientific and practical applications. Both the monolayer and bilayer allotropes are of tremendous theoretical …
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Transport properties of quantum dot molecules and electronic structure of graphene quantum dot qubits
… candidates for nanoelectronics, spintronics, thermoelectrics, and quantum computing applications. The knowledge in the transport and electronic properties of QDMs is important in making progress toward practical devices. We use many-body equation of motion method for Hubbard-Anderson model to …
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Synthesis and characterization of graphene: a raman study of the effect of electromagnetic and proton irradiations on graphene
… of only 0.34 nm, exhibits unique properties. The current interest in graphene can be attributed to three main reasons. Firstly, various forms of graphite, nanotubes, buckyballs and others can all be viewed as derivatives of graphene. Secondly, the scalability of graphene devices to …
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Geometric algebras in physics: Eigenspinors and Dirac theory
The foundations of quantum theory are closely tied to a formulation of classical relativistic physics. In Clifford's geometric algebra classical relativistic physics has a spinorial formulation that is closely related to the standard Dirac equation. The algebra of physical space, APS, gives clear …
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Theoretical Study of Carbon-Based Materials and Their Applications in Nanoelectronics
… scaling down of silicon device, which is the main driving force in device performance enhancement, is not sustainable as we approach the physical limits of silicon and it is foreseen that new materials and novel device structures will be required for future device improvements. In this …
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High temperature quantum transport in graphene/hexagonal-boron nitride heterostructures
The past decade has seen a new paradigm in solid state physics, where a new class of layered crystals can be thinned down to a monolayer and exhibit drastic changes in their electronic and optical properties in comparison to their bulk counterpart. Graphene was the first, and certainly most …
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Topological phases, non-equilibrium dynamics and parallels of black hole phenomena in condensed matter
… chain and parallels of black hole phenomena in the quantum Hall effect. Majorana modes in topological superconductors are of fundamental importance as realizations of real solutions to the Dirac equation and for their anyonic exchange statistics. They are realised as zero energy edge modes in …