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Showing 1 to 20 of 28 for “"Dirac equation"”.
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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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Topological solitons of the nonlinear Dirac equation in 2+1 dimensional space time
… of this thesis is a presentation of nonlinear Dirac-type models with the primary focus being on planar, (2 + 1) dimensional nonlinear Dirac models.We study a (2 + 1) dimensional extension of the (2 + 0) dimensional reduction the complex sine-Gordon. This is a tachyonic nonlinear 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
… 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. Relativistic and spin-orbit effects are significant for valence electrons of magnetic and semimetal …
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On the parallels between the Maxwell and Dirac equations
… deeply the similarity between the Maxwell and Dirac equations. We reformulate the Dirac equation in an \emph{exact} form of the Maxwell equations, which we refer to as the ``electronic Maxwell equations.'' In this formulation, the standard free Maxwell equations emerge as a special case …
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Relativistic theory of low energy electron diffraction
… value problem for the mixed-representation Dirac equation is followed by the construction of a relativistic KKRZ-type electron-ion-core pseudopotential. The solution of the Dirac equation inside a model crystal that consists of this potential plus a bulk and surf ace optical potential is …
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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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Aspects of twistors and tractors in field theory
… action on the Fefferman-Graham space whose equations of motion descend to a conformally coupled scalar on the base manifold. We present also a novel Fefferman-Graham worldline action for the massless Dirac equation and demonstrate that it descents to a Dirac spinor on the base manifold. …
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Motion of charged particles in pulsar magnetospheres
… axes we solve a fluid version of the Lorentz-Dirac equation, in the Landau approximation, for a two-component plasma. We start from an approximately force-free initial condition and numerically integrate the equations of motion for a time equal to 1.6% of one stellar rotation period. We find …
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Bound states of heavy and light quarks in the framework of quantum chromodynamics
… antiquark was treated relativistically using the Dirac equation. The spectra obtained are compared with experimental data as well as with the results of other models of these Qq mesons. The ratio mb/mc obtained in the fit to experimentally known states is compared with the result expected from the …
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Introduction of a Fully Relativistic Capable Basis Set in the ab initio Orthogonalized Linear Combination of Atomic Orbitals Method
… Hamiltonian which bypasses directly solving the Dirac equation has been explicated. The orbital description improvements are tested against YAG, YBCO, SnO2 and BiF3. The improvements to the basis set reflect an improvement in both computational speed and accuracy
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Geometric algebras in physics: Eigenspinors and Dirac theory
… that is closely related to the standard Dirac equation. The algebra of physical space, APS, gives clear insight into the quantum/classical interface. Here, APS is compared to other formulations of relativistic quantum theory, especially the Dirac equation. These formulations are shown to …
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Nuclear charge distribution of ¹⁸¹Ta
… for vacuum polarization, is used in the Dirac equation. Then the electric quadrupole interaction term is diagonalized in the basis formed by the Dirac solutions and the nuclear wave functions. This prescription assumes a nuclear rotational model to be valid and takes no account of the …
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Tensorial spacetime geometries and background-independent quantum field theory
… off the geometry of spacetime from Maxwell's equations. Today, we take this geometry that serious that our fundamental theory of matter, the standard model of particle physics, is based on it. However, it seems that there is a gap in our understanding if it comes to the physics outside of the …
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Relativistic dynamics and Dirac particles in graphene
… fields and use the Lorentz symmetry of the Dirac equation to solve for magnetoconductance. Next, we proceed to study monolayer quasiparticles in a deconfining potential and a magnetic field. The twodimensional nature of graphene allows us to study competition between the two external fields. …
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Effects of Radiation Damping in Extreme Ultra-intense Laser-Plasma Interaction
… problem we developed a code to solve a set of equations describing the evolution of a strong electromagnetic wave interacting with a single electron. Usually the equation of motion of an electron including radiation damping under the influence of electromagnetic fields is derived from the …
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Modeling and Numerics for Two Partial Differential Equation Systems Arising From Nanoscale Physics
… field of analysis of partial differential equations has undergone rapid changes in recent years. Consistent improvement of mathematical computation allows more and more questions to be addressed in the form of numerical simulations. At the same time, novel materials arising from advances in …
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Transport properties of quantum dot molecules and electronic structure of graphene quantum dot qubits
… toward practical devices. We use many-body equation of motion method for Hubbard-Anderson model to study non-equilibrium charge and thermal transport properties of QDMs connected to metallic electrodes in the Coulomb blockade regime. An exterior algebra method is developed to construct the …
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Defects, topology, and the geometric phase in condensed matter physics
… as well as the solutions of the continuum Dirac equation. We demonstrated \cite{roygraph} that these two approaches as well as bare numerical computation could be made consistent once one took into account boundary conditions at the defect site. For example, the continuum model considers …
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