A Finite and Discrete Model for Single Fermion Mass Renormalization: Derivation of the free particle Dirac equation
Explore the source record for details and available documents.
Noyes, H.↗
SEARCH · Engineering Papers
Results for “DIRAC EQUATION”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Discrete Physics and the Dirac Equation
Explore the source record for details and available documents.
Kauffman, L.↗
The equation-transform model for Dirac–Morse problem including Coulomb tensor interaction
The approximate solutions of Dirac equation with Morse potential in the presence of Coulomb-like tensor potential are obtained by using Laplace transform (LT) approach. The energy eigenvalue equation of the Dirac particles is found and some numerical results are obtained. By using convolution integral, the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. -- Highlights: •The Dirac equation with tensor interaction is solved by using Laplace transform. •For solving this equation, we introduce the equation-transform model. •Numerical results and plots for pseudospin and spin symmetric solutions are given. •The obtained numerical results by using transform method are compared with orthogonal polynomial method.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Auxiliary-Field Quantum Monte Carlo Simulations of Strongly-Correlated Systems, the Final Report
In this final report, we present preliminary results of ground state phases of interacting spinless Dirac fermions. The name "Dirac fermion" originates from the fact that low-energy excitations of electrons hopping on the honeycomb lattice are described by a relativistic Dirac equation. Dirac fermions have received much attention particularly after the seminal work of Haldale1 which shows that the quantum Hall physics can be realized on the honeycomb lattice without magnetic fields. Haldane's work later becomes the foundation of topological insulators (TIs). While the physics of TIs is based largely on spin-orbit coupled non-interacting electrons, it was conjectured that topological insulators can be induced by strong correlations alone.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Characteristics of level-spacing statistics in chaotic graphene billiards
A fundamental result in nonrelativistic quantum nonlinear dynamics is that the spectral statistics of quantum systems that possess no geometric symmetry, but whose classical dynamics are chaotic, are described by those of the Gaussian orthogonal ensemble (GOE) or the Gaussian unitary ensemble (GUE), in the presence or absence of time-reversal symmetry, respectively. For massless spin-half particles such as neutrinos in relativistic quantum mechanics in a chaotic billiard, the seminal work of Berry and Mondragon established the GUE nature of the level-spacing statistics, due to the combination of the chirality of Dirac particles and the confinement, which breaks the time-reversal symmetry. A question is whether the GOE or the GUE statistics can be observed in experimentally accessible, relativistic quantum systems. We demonstrate, using graphene confinements in which the quasiparticle motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are persistently those of GOE random matrices. We present extensive numerical evidence obtained from the tight-binding approach and a physical explanation for the GOE statistics. We also find that the presence of a weak magnetic field switches the statistics to those of GUE. For a strong magnetic field, Landau levels become influential, causing the level-spacing distribution to deviate markedly from the random-matrix predictions. Issues addressed also include the effects of a number of realistic factors on level-spacing statistics such as next nearest-neighbor interactions, different lattice orientations, enhanced hopping energy for atoms on the boundary, and staggered potential due to graphene-substrate interactions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Inequivalent solutions for Dirac spin-(1/2) particles under conservation of parity II
By law of conservation of parity we show that Dirac equation in an electromagnetic field can be split up into two uncoupled two-component equations. As a result, we shall find twice as many as the conventional solutions. For free particles four linearly independent plane wave solutions which hold for E > 0 and also for E < 0 can be established. In a Coulomb field we shall easily find the stationary solutions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Pseudospin symmetry for a new oscillatory ring-shaped noncentral potential
A new oscillatory ring-shaped noncentral potential is proposed and the pseudospin symmetry for this potential is investigated by solving the Dirac equation with equally mixed scalar and vector potentials with opposite signs. The spinor wave functions and the energy spectrum for the bound states are obtained by using the Nikiforov-Uvarov method. The effect of angle-dependent part on the radial solutions and the algebraic property of the energy equation are discussed.
97 MATHEMATICS AND COMPUTING↗
Electron-positron pair creation induced by quantum-mechanical tunneling
We study the creation of electron-positron pairs from the vacuum induced by two spatially displaced static electric fields. The strength and spatial width of each localized field is less than required for pair creation. If, however, the separation between the fields is less than the quantum-mechanical tunneling length associated with the corresponding quantum scattering system, the system produces a steady flux of electron-positron pairs. We compute the time dependence of the pair-creation probability by solving the Dirac equation numerically for various external field sequences. For the special case of two very narrow fields we provide an analytical expression for the pair-creation rate in the long-time limit.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Causality and relativistic localization in one-dimensional Hamiltonians
We compare the relativistic time evolution of an initially localized quantum particle obtained from the relativistic Schroedinger, the Klein-Gordon and the Dirac equations. By computing the amount of the spatial probability density that evolves outside the light cone we quantify the amount of causality violation for the relativistic Schroedinger Hamiltonian. We comment on the relationship between quantum field theoretical transition amplitudes, commutators of the fields and their bilinear combinations outside the light cone as indicators of a possible causality violation. We point out the relevance of the relativistic localization problem to this discussion and comment on ideas about the supposed role of quantum field theory as a vehicle of making a theory causal by introducing antiparticles.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Relativistic ionization characteristics of laser-driven hydrogenlike ions
In this contribution, we investigate the relativistic ionization characteristics of highly charged hydrogenlike ions in short intense laser pulses as a function of the laser pulse parameters by means of the numerical solution of the time-dependent Dirac equation and the time-dependent Klein-Gordon equation as well as by the classical phase-space averaging method. For this purpose, we generalize the phase-space averaging method such that it is applicable to relativistically driven particles in arbitrary central potentials. If the ionization probability is not too small, quantum mechanical and classical methods give similar results for laser wavelengths in the range from the near-infrared to soft x-ray radiation. We find that ionization in few-cycle intense laser pulses depends sensitively on the pulses' peak intensity but little on the pulse tails and on the pulse energy. The ionization probability is shown to be strongly linked to the peak intensity allowing for an estimation of the laser intensity via ionization yields.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Vortex and gap generation in gauge models of graphene
Effective quantum field theoretical continuum models for graphene are investigated. The models include a complex scalar field and a vector gauge field. Different gauge theories are considered and their gap patterns for the scalar, vector, and fermion excitations are investigated. Different gauge groups lead to different relations between the gaps, which can be used to experimentally distinguish the gauge theories. In this class of models the fermionic gap is a dynamic quantity. The finite-energy vortex solutions of the gauge models have the flux of the ''magnetic field'' quantized, making the Bohm-Aharonov effect active even when external electromagnetic fields are absent. The flux comes proportional to the scalar field angular momentum quantum number. The zero modes of the Dirac equation show that the gauge models considered here are compatible with fractionalization.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Nonlinear propagation of light in Dirac matter
The nonlinear interaction between intense laser light and a quantum plasma is modeled by a collective Dirac equation coupled with the Maxwell equations. The model is used to study the nonlinear propagation of relativistically intense laser light in a quantum plasma including the electron spin-1/2 effect. The relativistic effects due to the high-intensity laser light lead, in general, to a downshift of the laser frequency, similar to a classical plasma where the relativistic mass increase leads to self-induced transparency of laser light and other associated effects. The electron spin-1/2 effects lead to a frequency upshift or downshift of the electromagnetic (EM) wave, depending on the spin state of the plasma and the polarization of the EM wave. For laboratory solid density plasmas, the spin-1/2 effects on the propagation of light are small, but they may be significant in superdense plasma in the core of white dwarf stars. We also discuss extensions of the model to include kinetic effects of a distribution of the electrons on the nonlinear propagation of EM waves in a quantum plasma.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Spin and the Honeycomb Lattice: Lessons from Graphene
A model of electrons hopping from atom to atom in graphene's honeycomb lattice gives low-energy electronic excitations that obey a relation formally identical to a 2+1 dimensional Dirac equation. Graphene's spin equivalent, 'pseudospin', arises from the degeneracy introduced by the honeycomb lattice's two inequivalent atomic sites per unit cell. Previously it has been thought that the usual electron spin and the pseudospin indexing the graphene sublattice state are merely analogues. Here we show that the pseudospin is also a real angular momentum. This identification explains the suppression of electron backscattering in carbon nanotubes and the angular dependence of light absorption by graphene. Furthermore, it demonstrates that half-integer spin like that carried by the quarks and leptons can derive from hidden substructure, not of the particles themselves, but rather of the space in which these particles live.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Quantum Electron Self-Interaction in a Strong Laser Field
The quantum state of an electron in a strong laser field is altered if the interaction of the electron with its own electromagnetic field is taken into account. Starting from the Schwinger-Dirac equation, we determine the states of an electron in a plane-wave field with inclusion, at leading order, of its electromagnetic self-interaction. On the one hand, the electron states show a pure quantum contribution to the electron quasimomentum, conceptually different from the conventional classical one arising from the quiver motion of the electron. On the other hand, the electron self-interaction induces a distinct dynamics of the electron spin, whose effects are shown to be measurable in principle with available technology.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The Hamiltonian structure of Dirac's equation in tensor form and its Fermi quantization
Currently, there is some interest in studying the tensor forms of the Dirac equation to elucidate the possibility of the constrained tensor fields admitting Fermi quantization. We demonstrate that the bispinor and tensor Hamiltonian systems have equivalent Fermi quantizations. Although the tensor Hamiltonian system is noncanonical, representing the tensor Poisson brackets as commutators for the Heisenberg operators directly leads to Fermi quantization without the use of bispinors.
Reifler, Frank↗
Quantum simulations of hydrodynamics via the Madelung transformation
Developing numerical methods to simulate efficiently nonlinear fluid dynamics on universal quantum computers is a challenging problem. In this paper, a generalization of the Madelung transform is defined to solve quantum relativistic charged fluid equations interacting with external electromagnetic forces via the Dirac equation. The Dirac equation is discretized into discrete-time quantum walks which can be efficiently implemented on universal quantum computers. A variant of this algorithm is proposed to implement simulations using current noisy intermediate scale quantum (NISQ) devices in the case of homogeneous external forces. High resolution (up to N=2 17 grid points) numerical simulations of relativistic and nonrelativistic hydrodynamical shocks on current IBM NISQs are performed with this algorithm. Here, this paper demonstrates that fluid dynamics can be simulated on NISQs, and opens the door to simulating other fluids, including plasmas, with more general quantum walks and quantum automata.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Homogeneous quantum electrodynamic turbulence
The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.
Shebalin, John V.↗
Coherent quantum states of a relativistic particle in an electromagnetic plane wave and a parallel magnetic field
We analyze the solutions of the Klein–Gordon and Dirac equations describing a charged particle in an electromagnetic plane wave combined with a magnetic field parallel to the direction of propagation of the wave. It is shown that the Klein–Gordon equation admits coherent states as solutions, while the corresponding solutions of the Dirac equation are superpositions of coherent and displaced-number states. Particular attention is paid to the resonant case in which the motion of the particle is unbounded. -- Highlights: •We study a relativistic electron in a particular electromagnetic field configuration. •New exact solutions of the Klein–Gordon and Dirac equations are obtained. •Coherent and displaced number states can describe a relativistic particle.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗