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Sample records for dirac equation dispersion

  1. Alternatives to the Dirac equation

    International Nuclear Information System (INIS)

    Girvin, S.M.; Brownstein, K.R.

    1975-01-01

    Recent work by Biedenharn, Han, and van Dam (BHvD) has questioned the uniqueness of the Dirac equation. BHvD have obtained a two-component equation as an alternate to the Dirac equation. Although they later show their alternative to be unitarily equivalent to the Dirac equation, certain physical differences were claimed. BHvD attribute the existence of this alternate equation to the fact that their factorizing matrices were position-dependent. To investigate this, we factor the Klein-Gordon equation in spherical coordinates allowing the factorizing matrices to depend arbitrarily upon theta and phi. It is shown that despite this additional freedom, and without involving any relativistic covariance, the conventional four-component Dirac equation is the only possibility

  2. A fractional Dirac equation and its solution

    International Nuclear Information System (INIS)

    Muslih, Sami I; Agrawal, Om P; Baleanu, Dumitru

    2010-01-01

    This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit α → 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics.

  3. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  4. The Dirac equation for accountants

    International Nuclear Information System (INIS)

    Ord, G.N.

    2006-01-01

    In the context of relativistic quantum mechanics, derivations of the Dirac equation usually take the form of plausibility arguments based on experience with the Schroedinger equation. The primary reason for this is that we do not know what wavefunctions physically represent, so derivations have to rely on formal arguments. There is however a context in which the Dirac equation in one dimension is directly related to a classical generating function. In that context, the derivation of the Dirac equation is an exercise in counting. We provide this derivation here and discuss its relationship to quantum mechanics

  5. Dirac equations for generalised Yang-Mills systems

    International Nuclear Information System (INIS)

    Lechtenfeld, O.; Nahm, W.; Tchrakian, D.H.

    1985-06-01

    We present Dirac equations in 4p dimensions for the generalised Yang-Mills (GYM) theories introduced earlier. These Dirac equations are related to the self-duality equations of the GYM and are checked to be elliptic in a 'BPST' background. In this background these Dirac equations are integrated exactly. The possibility of imposing supersymmetry in the GYM-Dirac system is investigated, with negative results. (orig.)

  6. The Dirac equation and its solutions

    CERN Document Server

    Bagrov, Vladislav G

    2014-01-01

    Dirac equations are of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly.In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

  7. The Dirac equation and its solutions

    International Nuclear Information System (INIS)

    Bagrov, Vladislav G.; Gitman, Dmitry; P.N. Lebedev Physical Institute, Moscow; Tomsk State Univ., Tomsk

    2013-01-01

    The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

  8. The Dirac equation and its solutions

    Energy Technology Data Exchange (ETDEWEB)

    Bagrov, Vladislav G. [Tomsk State Univ., Tomsk (Russian Federation). Dept. of Quantum Field Theroy; Gitman, Dmitry [Sao Paulo Univ. (Brazil). Inst. de Fisica; P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Univ., Tomsk (Russian Federation). Faculty of Physics

    2013-07-01

    The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

  9. Dirac equation on a curved surface

    Energy Technology Data Exchange (ETDEWEB)

    Brandt, F.T., E-mail: fbrandt@usp.br; Sánchez-Monroy, J.A., E-mail: antosan@usp.br

    2016-09-07

    The dynamics of Dirac particles confined to a curved surface is examined employing the thin-layer method. We perform a perturbative expansion to first-order and split the Dirac field into normal and tangential components to the surface. In contrast to the known behavior of second order equations like Schrödinger, Maxwell and Klein–Gordon, we find that there is no geometric potential for the Dirac equation on a surface. This implies that the non-relativistic limit does not commute with the thin-layer method. Although this problem can be overcome when second-order terms are retained in the perturbative expansion, this would preclude the decoupling of the normal and tangential degrees of freedom. Therefore, we propose to introduce a first-order term which rescues the non-relativistic limit and also clarifies the effect of the intrinsic and extrinsic curvatures on the dynamics of the Dirac particles. - Highlights: • The thin-layer method is employed to derive the Dirac equation on a curved surface. • A geometric potential is absent at least to first-order in the perturbative expansion. • The effects of the extrinsic curvature are included to rescue the non-relativistic limit. • The resulting Dirac equation is consistent with the Heisenberg uncertainty principle.

  10. New exact solutions of the Dirac equation. 8

    International Nuclear Information System (INIS)

    Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Sukhomlin, N.B.; Shapovalov, V.N.

    1978-01-01

    The paper continues the investigation into the exact solutions of the Dirac, Klein-Gordon, and Lorentz equations for a charge in an external electromagnetic field. The fields studied do not allow for separation of variables in the Dirac equation, but solutions to the Dirac equation are obtained

  11. Scalar potentials and the Dirac equation

    International Nuclear Information System (INIS)

    Bergerhoff, B.; Soff, G.

    1994-01-01

    The Dirac equation is solved for various types of scalar potentials. Energy eigenvalues and normalized bound-state wave functions are calculated analytically for a scalar 1/r-potential as well as for a mixed scalar and Coulomb 1/r-potential. Also continuum wave functions for positive and negative energies are derived. Similarly, we investigate the solutions of the Dirac equation for a scalar square-well potential. Relativistic wave functions for scalar Yukawa and exponential potentials are determined numerically. Finally, we also discuss solutions of the Dirac equation for scalar linear and quadratic potentials which are frequently used to simulate quark confinement. (orig.)

  12. New solitons connected to the Dirac equation

    International Nuclear Information System (INIS)

    Grosse, H.

    1984-01-01

    Imposing isospectral invariance for the one dimensional Dirac operator leads to systems of nonlinear partial differential equations. By constructing reflectionless potentials of the Dirac equation we obtain a new type of solitons for a system of modified Korteweg-de Vries equations. (Author)

  13. Generalized Lorentz-Dirac Equation for a Strongly Coupled Gauge Theory

    Science.gov (United States)

    Chernicoff, Mariano; García, J. Antonio; Güijosa, Alberto

    2009-06-01

    We derive a semiclassical equation of motion for a “composite” quark in strongly coupled large-Nc N=4 super Yang-Mills theory, making use of the anti-de Sitter space/conformal field theory correspondence. The resulting nonlinear equation incorporates radiation damping, and reduces to the standard Lorentz-Dirac equation for external forces that are small on the scale of the quark Compton wavelength, but has no self-accelerating or preaccelerating solutions. From this equation one can read off a nonstandard dispersion relation for the quark, as well as a Lorentz-covariant formula for its radiation rate.

  14. Generalized Lorentz-Dirac Equation for a Strongly Coupled Gauge Theory

    International Nuclear Information System (INIS)

    Chernicoff, Mariano; Garcia, J. Antonio; Gueijosa, Alberto

    2009-01-01

    We derive a semiclassical equation of motion for a 'composite' quark in strongly coupled large-N c N=4 super Yang-Mills theory, making use of the anti-de Sitter space/conformal field theory correspondence. The resulting nonlinear equation incorporates radiation damping, and reduces to the standard Lorentz-Dirac equation for external forces that are small on the scale of the quark Compton wavelength, but has no self-accelerating or preaccelerating solutions. From this equation one can read off a nonstandard dispersion relation for the quark, as well as a Lorentz-covariant formula for its radiation rate.

  15. The Dirac equation

    International Nuclear Information System (INIS)

    Thaller, B.

    1992-01-01

    This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics

  16. Dirac equation in magnetic-solenoid field

    Energy Technology Data Exchange (ETDEWEB)

    Gavrilov, S.P. [Dept. Fisica e Quimica, UNESP, Campus de Guaratingueta (Brazil); Gitman, D.M.; Smirnov, A.A. [Instituto de Fisica, Universidade de Sao Paulo (Brazil)

    2004-07-01

    We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid. (orig.)

  17. Maxwell-Like Equations for Free Dirac Electrons

    Science.gov (United States)

    Bruce, S. A.

    2018-03-01

    In this article, we show that the wave equation for a free Dirac electron can be represented in a form that is analogous to Maxwell's electrodynamics. The electron bispinor wavefunction is explicitly expressed in terms of its real and imaginary components. This leads us to incorporate into it appropriate scalar and pseudo-scalar fields in advance, so that a full symmetry may be accomplished. The Dirac equation then takes on a form similar to that of a set of inhomogeneous Maxwell's equations involving a particular self-source. We relate plane wave solutions of these equations to waves corresponding to free Dirac electrons, identifying the longitudinal component of the electron motion, together with the corresponding Zitterbewegung ("trembling motion").

  18. Dirac equation in low dimensions: The factorization method

    Energy Technology Data Exchange (ETDEWEB)

    Sánchez-Monroy, J.A., E-mail: antosan@if.usp.br [Instituto de Física, Universidade de São Paulo, 05508-090, São Paulo, SP (Brazil); Quimbay, C.J., E-mail: cjquimbayh@unal.edu.co [Departamento de Física, Universidad Nacional de Colombia, Bogotá, D. C. (Colombia); CIF, Bogotá (Colombia)

    2014-11-15

    We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two Klein–Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials. - Highlights: • The low-dimensional Dirac equation in the presence of static potentials is solved. • The factorization method is generalized for energy-dependent Hamiltonians. • The shape invariance is generalized for energy-dependent Hamiltonians. • The stability of the Dirac sea is related to the existence of supersymmetric partner Hamiltonians.

  19. Dirac's equation and the nature of quantum field theory

    International Nuclear Information System (INIS)

    Plotnitsky, Arkady

    2012-01-01

    This paper re-examines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.

  20. The Lorentz-Dirac equation in light of quantum theory

    International Nuclear Information System (INIS)

    Nikishov, A.I.

    1996-01-01

    To high accuracy, an electron in ultrarelativistic motion 'sees' an external field in its rest frame as a crossed field (E=H, E·H=0). In this case, quantum expressions allow the introduction of a local intensity of the radiation, which determines the radiative term of the force of radiative reaction. For γ=(1-v2)-1/2>> 1 this term is much larger than the mass term, i.e., the term with xd3do. Under these conditions, the reduced Lorentz-Dirac equation, which is obtained from the full Lorentz-Dirac equation by eliminating the terms xd3do and xe on the right side using the equation of motion without taking into account the force of radiative reaction, is equivalent to good accuracy to the original Lorentz-Dirac equation. Exact solutions to the reduced Lorentz-Dirac equation are obtained for a constant field and the field of a plane wave. For γ∼1 a local expression for the radiative term cannot be obtained quantitatively from the quantum expressions. In this case the mass (Lorentz-Dirac) terms in the original and reduced Lorentz-Dirac equations are not small compared to the radiative term. The predictions of these equations, which depend appreciably on the mass terms, are therefore less reliable

  1. Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations

    KAUST Repository

    Lorz, Alexander

    2011-01-17

    Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the limiting concentration points and of the weights of the Dirac masses? What is the long time asymptotics of these Dirac masses? Can several Dirac masses coexist? We will explain how these questions relate to the so-called "constrained Hamilton-Jacobi equation" and how a form of canonical equation can be established. This equation has been established assuming smoothness. Here we build a framework where smooth solutions exist and thus the full theory can be developed rigorously. We also show that our form of canonical equation comes with a kind of Lyapunov functional. Numerical simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.

  2. New exact solutions of the Dirac equation

    International Nuclear Information System (INIS)

    Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Lavrov, P.M.; Shapovalov, V.N.

    1980-01-01

    Search for new exact solutions of the Dirac and Klein-Gordon equations are in progress. Considered are general properties of the Dirac equation solutions for an electron in a purely magnetic field, in combination with a longitudinal magnetic and transverse electric fields. New solutions for the equations of charge motion in an electromagnetic field of axial symmetry and in a nonstationary field of a special form have been found for potentials selected concretely

  3. Multi-component bi-Hamiltonian Dirac integrable equations

    Energy Technology Data Exchange (ETDEWEB)

    Ma Wenxiu [Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700 (United States)], E-mail: mawx@math.usf.edu

    2009-01-15

    A specific matrix iso-spectral problem of arbitrary order is introduced and an associated hierarchy of multi-component Dirac integrable equations is constructed within the framework of zero curvature equations. The bi-Hamiltonian structure of the obtained Dirac hierarchy is presented be means of the variational trace identity. Two examples in the cases of lower order are computed.

  4. The Dirac equation in classical statistical mechanics

    International Nuclear Information System (INIS)

    Ord, G.N.

    2002-01-01

    The Dirac equation, usually obtained by 'quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic continuation, making the model 'self-quantizing'. This provides a new context for the Dirac equation, distinct from its usual context in relativistic quantum mechanics

  5. Spinor-electron wave guided modes in coupled quantum wells structures by solving the Dirac equation

    International Nuclear Information System (INIS)

    Linares, Jesus; Nistal, Maria C.

    2009-01-01

    A quantum analysis based on the Dirac equation of the propagation of spinor-electron waves in coupled quantum wells, or equivalently coupled electron waveguides, is presented. The complete optical wave equations for Spin-Up (SU) and Spin-Down (SD) spinor-electron waves in these electron guides couplers are derived from the Dirac equation. The relativistic amplitudes and dispersion equations of the spinor-electron wave-guided modes in a planar quantum coupler formed by two coupled quantum wells, or equivalently by two coupled slab electron waveguides, are exactly derived. The main outcomes related to the spinor modal structure, such as the breaking of the non-relativistic degenerate spin states, the appearance of phase shifts associated with the spin polarization and so on, are shown.

  6. Wave Functions for Time-Dependent Dirac Equation under GUP

    Science.gov (United States)

    Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

    2018-04-01

    In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

  7. An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like

    International Nuclear Information System (INIS)

    Pierantozzi, T.; Vazquez, L.

    2005-01-01

    Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case

  8. Solvable linear potentials in the Dirac equation

    International Nuclear Information System (INIS)

    Dominguez-Adame, F.; Gonzalez, M.A.

    1990-01-01

    The Dirac equation for some linear potentials leading to Schroedinger-like oscillator equations for the upper and lower components of the Dirac spinor have been solved. Energy levels for the bound states appear in pairs, so that both particles and antiparticles may be bound with the same energy. For weak coupling, the spacing between levels is proportional to the coupling constant while in the strong limit those levels are depressed compared to the nonrelativistic ones

  9. Remarks about singular solutions to the Dirac equation

    International Nuclear Information System (INIS)

    Uhlir, M.

    1975-01-01

    In the paper singular solutions of the Dirac equation are investigated. They are derived in the Lorentz-covariant way of functions proportional to static multipole fields of scalar and (or) electromagnetic fields and of regular solutions of the Dirac equations. The regularization procedure excluding divergences of total energy, momentum and angular momentum of the spinor field considered is proposed

  10. Special function solutions of the free particle Dirac equation

    International Nuclear Information System (INIS)

    Strange, P

    2012-01-01

    The Dirac equation is one of the fundamental equations in physics. Here we present and discuss two novel solutions of the free particle Dirac equation. These solutions have an exact analytical form in terms of Airy or Mathieu functions and exhibit unexpected properties including an enhanced Doppler effect, accelerating wavefronts and solutions with a degree of localization. (paper)

  11. The Dirac equation in the Lobachevsky space-time

    International Nuclear Information System (INIS)

    Paramonov, D.V.; Paramonova, N.N.; Shavokhina, N.S.

    2000-01-01

    The product of the Lobachevsky space and the time axis is termed the Lobachevsky space-time. The Lobachevsky space is considered as a hyperboloid's sheet in the four-dimensional pseudo-Euclidean space. The Dirac-Fock-Ivanenko equation is reduced to the Dirac equation in two special forms by passing from Lame basis in the Lobachevsky space to the Cartesian basis in the enveloping pseudo-Euclidean space

  12. Derivation of equations for scalar and fermion fields using properties of dispersion-codispersion operators

    International Nuclear Information System (INIS)

    Raoelina Andriambololona; Ranaivoson, R.T.R; Hanitriarivo, R.; Harison, V.

    2014-01-01

    We establish equations for scalar and fermion fields using results obtained from a study on a phase space representation of quantum theory that we have performed in a previous work. Our approaches are similar to the historical ones to obtain Klein-Gordon and Dirac equations but the main difference is that ours are based on the use of properties of operators called dispersion-codispersion operators. We begin with a brief recall about the dispersion-codispersion operators. Then, introducing a mass operator with its canonical conjugate coordinate and applying rules of quantization, based on the use of dispersion - codispersion operators , we deduce a second order differential operator relation from the relativistic expression relying energy, momentum and mass. Using Dirac matrices, we derive from this second order differential operator relation a first order one. The application of the second order differential operator relation on a scalar function gives the equation for the scalar field and the use of the first order differential operator relation leads to the equation for fermion field.

  13. Kinks and the Dirac equation

    International Nuclear Information System (INIS)

    Skyrme, T.H.R.

    1994-01-01

    In a model quantum theory of interacting mesons, the motion of certain conserved particle-like structures is discussed. It is shown how collective coordinates may be introduced to describe them, leading, in lowest approximation, to a Dirac equation. (author)

  14. New correct solutions of the Dirac equation. 5

    International Nuclear Information System (INIS)

    Bagrov, V.G.; Byzov, N.N.; Gitman, D.M.; Klimenko, Yu.I.; Meshkov, A.G.; Shapovalov, V.N.; Shakhmatov, V.M.

    1975-01-01

    Some exact solutions for the Dirac equation, Klein-Gordon equation and classical relativistic equations of motion of an electron in external electromagnetic fields of a special type are considered. When fields E vector and H vector are related by the expression H vector=[n vector E vector]+n vector H 3 , where n vector is a constant unit vector, it turns out that among fields permitting the separation of variables in the Klein-Gordon equation more than half satisfy this relationship. For such fields the solution of the Dirac equation may be simplified considerably. Four specific kinds of fields are examined. The character of electron motion in such fields is peculiar but in the mathematical aspect, part of the problem is reduced to those considered previously

  15. Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations

    Energy Technology Data Exchange (ETDEWEB)

    Zabadal, Jorge R.; Borges, Volnei, E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio, E-mail: marciophd@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Centro de Estudos Interdisciplinares

    2015-07-01

    This work presents a new analytical method for solving Klein-Gordon type equations via Backlund transformations. The method consists in mapping the Klein-Gordon model into a first order system of partial differential equations, which contains a generalized velocity field instead of the Dirac matrices. This system is a tensor model for quantum field theory whose space solution is wider than the Dirac model in the original form. Thus, after finding analytical expressions for the wave functions, the Maxwell field can be readily obtained from the Dirac equations, furnishing a self-consistent field solution for the Maxwell-Dirac system. Analytical and numerical results are reported. (author)

  16. Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations

    International Nuclear Information System (INIS)

    Hong Jialin; Li Chun

    2006-01-01

    In this paper, we consider the multi-symplectic Runge-Kutta (MSRK) methods applied to the nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi-symplecticity of the equation. In particular, the conservation of energy, momentum and charge under MSRK discretizations is investigated by means of numerical experiments and numerical comparisons with non-MSRK methods. Numerical experiments presented reveal that MSRK methods applied to the nonlinear Dirac equation preserve exactly conservation laws of charge and momentum, and conserve the energy conservation in the corresponding numerical accuracy to the method utilized. It is verified numerically that MSRK methods are stable and convergent with respect to the conservation laws of energy, momentum and charge, and MSRK methods preserve not only the inner geometric structure of the equation, but also some crucial conservative properties in quantum physics. A remarkable advantage of MSRK methods applied to the nonlinear Dirac equation is the precise preservation of charge conservation law

  17. Particlelike solutions of the Einstein-Dirac equations

    Science.gov (United States)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    1999-05-01

    The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of solitonlike solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well behaved even for strong coupling.

  18. Basic quantum mechanics for three Dirac equations in a curved spacetime

    International Nuclear Information System (INIS)

    Arminjon, Mayeul

    2010-01-01

    We study the basic quantum mechanics for a fully general set of Dirac matrices in a curved spacetime by extending Pauli's method. We further extend this study to three versions of the Dirac equation: the standard (Dirac-Fock-Weyl or DFW) equation, and two alternative versions, both of which are based on the recently proposed linear tensor representations of the Dirac field (TRD). We begin with the current conservation: we show that the latter applies to any solution of the Dirac equation, if the field of Dirac matrices γμ satisfies a specific PDE. This equation is always satisfied for DFW with its restricted choice for the γμ matrices. It similarly restricts the choice of the γμ matrices for TRD. However, this restriction can be achieved. The frame dependence of a general Hamiltonian operator is studied. We show that in any given reference frame with minor restrictions on the spacetime metric, the axioms of quantum mechanics impose a unique form for the Hilbert space scalar product. Finally, the condition for the general Dirac Hamiltonian operator to be Hermitian is derived in a general curved spacetime. For DFW, the validity of this hermeticity condition depends on the choice of the γμ matrices. (author)

  19. Considerations concering the generalization of the Dirac equations to unstable fermions

    International Nuclear Information System (INIS)

    Kniehl, Bernd A.; Sirlin, Alberto

    2014-08-01

    We discuss the generalization of the Dirac equations and spinors in momentum space to free unstable spin-1/2 fermions taking into account the fundamental requirement of Lorentz covariance. We derive the generalized adjoint Dirac equations and spinors, and explain the very simple relation that exists, in our formulation, between the unstable and stable cases. As an application of the generalized spinors, we evaluate the probability density. We also discuss the behavior of the generalized Dirac equations under time reversal.

  20. New exact solutions of the Dirac equation. 11

    International Nuclear Information System (INIS)

    Bagrov, V.G.; Noskov, M.D.

    1984-01-01

    Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found

  1. Dirac equation and optical wave propagation in one dimension

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez, Gabriel [Catedras CONACYT, Universidad Autonoma de San Luis Potosi (Mexico); Coordinacion para la Innovacion y la Aplicacion de la Ciencia y la Tecnologia, Universidad Autonoma de San Luis Potosi (Mexico)

    2018-02-15

    We show that the propagation of transverse electric (TE) polarized waves in one-dimensional inhomogeneous settings can be written in the form of the Dirac equation in one space dimension with a Lorentz scalar potential, and consequently perform photonic simulations of the Dirac equation in optical structures. In particular, we propose how the zero energy state of the Jackiw-Rebbi model can be generated in an optical set-up by controlling the refractive index landscape, where TE-polarized waves mimic the Dirac particles and the soliton field can be tuned by adjusting the refractive index. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  2. Inverse scattering scheme for the Dirac equation at fixed energy

    International Nuclear Information System (INIS)

    Leeb, H.; Lehninger, H.; Schilder, C.

    2001-01-01

    Full text: Based on the concept of generalized transformation operators a new hierarchy of Dirac equations with spherical symmetric scalar and fourth component vector potentials is presented. Within this hierarchy closed form expressions for the solutions, the potentials and the S-matrix can be given in terms of solutions of the original Dirac equation. Using these transformations an inverse scattering scheme has been constructed for the Dirac equation which is the analog to the rational scheme in the non-relativistic case. The given method provides for the first time an inversion scheme with closed form expressions for the S-matrix for non-relativistic scattering problems with central and spin-orbit potentials. (author)

  3. Expressing Solutions of the Dirac Equation in Terms of Feynman Path Integral

    CERN Document Server

    Hose, R D

    2006-01-01

    Using the separation of the variables technique, the free particle solutions of the Dirac equation in the momentum space are shown to be actually providing the definition of Delta function for the Schr dinger picture. Further, the said solution is shown to be derivable on the sole strength of geometrical argument that the Dirac equation for free particle is an equation of a plane in momentum space. During the evolution of time in the Schr dinger picture, the normal to the said Dirac equation plane is shown to be constantly changing in direction due to the uncertainty principle and thereby, leading to a zigzag path for the Dirac particle in the momentum space. Further, the time evolution of the said Delta function solutions of the Dirac equation is shown to provide Feynman integral of all such zigzag paths in the momentum space. Towards the end of the paper, Feynman path integral between two fixed spatial points in the co-ordinate space during a certain time interv! al is shown to be composed, in time sequence...

  4. New symmetries for the Dirac equation

    International Nuclear Information System (INIS)

    Linhares, C.A.; Mignaco, J.A.

    1990-01-01

    The Dirac equation in four dimension is studied describing fermions, both as 4 x 4 matrices and differential forms. It is discussed in both formalisms its properties under transformations of the group SU(4). (A.C.A.S.) [pt

  5. An integrodifferential Dirac equation with quantized charge in one space dimension

    International Nuclear Information System (INIS)

    Ranada, A.F.

    1985-01-01

    An integrodifferential Dirac equation in one space dimension is proposed, such that there is a close correspondence between its solutions and a subset of those of the sine-Gordon equation. It has solitonic solutions, quantized charge and positive definite energy density, so that it can be considered a spinorial version of sine-Gordon. Accordingly, it could be named the sine-Dirac equation. (orig.)

  6. Relativistic Spinning Particle without Grassmann Variables and the Dirac Equation

    Directory of Open Access Journals (Sweden)

    A. A. Deriglazov

    2011-01-01

    Full Text Available We present the relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. Classical equations for the spin tensor are the same as those of the Barut-Zanghi model of spinning particle.

  7. Relativistic two-body equation for one Dirac and one Duffin-Kemmer particle

    International Nuclear Information System (INIS)

    Krolikowski, W.

    1983-01-01

    A new relativistic two-body wave equation is proposed for one spin-1/2 and one spin-0 or spin-1 particle which, if isolated from each other, are described by the Dirac and the Duffin-Kemmer equation, respectively. For a static mutual interaction this equation splits into two equations: a two-body wave equation for one Dirac and one Klein-Gordon particle (which was introduced by the author previously) and a new two-body wave equation for one Dirac and one Proca particle. The proposed equation may be applied in particular to the quark-diquark system. In Appendix, however, an alternative approach is sketched, where the diquark is described as the point limit of a very close Breit system rather than a Duffin-Kemmer particle. (Author)

  8. The Dirac equation in external fields: Variable separation in Cartesian coordinates

    International Nuclear Information System (INIS)

    Shishkin, G.V.; Cabos, W.D.

    1991-01-01

    The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors [J. Math. Phys. 30, 2132 (1989)] is developed for the complete set of interactions of the Dirac particle. The essence of the method consists of the separation of the first-order matrix differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with or between the operator of the equation is not assumed. This approach, which is perfectly justified in the presence of gravitational [Theor. Math. Phys. 70, 204 (1987)] or vector fields [J. Math. Phys. 30, 2132 (1989)], permits one to find all the possibilities of separation of variables in the Dirac equation in the case of the most general set of external fields. The complete set of interactions of the Dirac particle is determined by the symmetry group of equations, namely, viz. the SU(4) group. The interactions are scalar, vector, tensor, pseudovector and pseudoscalar. The analysis in this article is limited to Cartesian coordinates. The corresponding results for the general curvilinear coordinates will be presented in a future paper

  9. Probabilistic solution of the Dirac equation

    International Nuclear Information System (INIS)

    Blanchard, P.; Combe, P.

    1985-01-01

    Various probabilistic representations of the 2, 3 and 4 dimensional Dirac equation are given in terms of expectation with respect to stochastic jump processes and are used to derive the nonrelativistic limit even in the presence of an external electromagnetic field. (orig.)

  10. New and old symmetries of the Maxwell and Dirac equations

    International Nuclear Information System (INIS)

    Fushchich, V.I.; Nikitin, A.G.

    1983-01-01

    The symmetry properties of Maxwell's equations for the electromagnetic field and also of the Dirac and Kemmer-Duffin-Petiau equations are analyzed. In the framework of a ''non-Lie'' approach it is shown that, besides the well-known invariance with respect to the conformal group and the Heaviside-Larmor-Rainich transformations, Maxwell's equations have an additional symmetry with respect to the group U(2)xU(2) and with respect to the 23-dimensional Lie algebra A 23 . The transformations of the additional symmetry are given by nonlocal (integro-differential) operators. The symmetry of the Dirac equation in the class of differential and integro-differential transformations is investigated. It is shown that this equation is invariant with respect to an 18-parameter group, which includes the Poincare group as a subgroup. A 28-parameter invariance group of the Kemmer-Duffin-Petiau equation is found. Finite transformations of the conformal group for a massless field with arbitrary spin are obtained. The explicit form of conformal transformations for the electromagnetic field and also for the Dirac and Weyl fields is given

  11. The square root of the Dirac operator on superspace and the Maxwell equations

    Science.gov (United States)

    Bzdak, Adam; Hadasz, Leszek

    2004-02-01

    We re-consider the procedure of "taking a square root of the Dirac equation" on superspace and show that it leads to the well-known superfield Wα and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation.

  12. Imaginary Time Step Method to Solve the Dirac Equation with Nonlocal Potential

    International Nuclear Information System (INIS)

    Zhang Ying; Liang Haozhao; Meng Jie

    2009-01-01

    The imaginary time step (ITS) method is applied to solve the Dirac equation with nonlocal potentials in coordinate space. Taking the nucleus 12 C as an example, even with nonlocal potentials, the direct ITS evolution for the Dirac equation still meets the disaster of the Dirac sea. However, following the recipe in our former investigation, the disaster can be avoided by the ITS evolution for the corresponding Schroedinger-like equation without localization, which gives the convergent results exactly the same with those obtained iteratively by the shooting method with localized effective potentials.

  13. The square root of the Dirac operator on superspace and the Maxwell equations

    International Nuclear Information System (INIS)

    Bzdak, Adam; Hadasz, Leszek

    2004-01-01

    We re-consider the procedure of 'taking a square root of the Dirac equation' on superspace and show that it leads to the well-known superfield W α and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation

  14. P A M Dirac meets M G Krein: matrix orthogonal polynomials and Dirac's equation

    International Nuclear Information System (INIS)

    Duran, Antonio J; Gruenbaum, F Alberto

    2006-01-01

    The solution of several instances of the Schroedinger equation (1926) is made possible by using the well-known orthogonal polynomials associated with the names of Hermite, Legendre and Laguerre. A relativistic alternative to this equation was proposed by Dirac (1928) involving differential operators with matrix coefficients. In 1949 Krein developed a theory of matrix-valued orthogonal polynomials without any reference to differential equations. In Duran A J (1997 Matrix inner product having a matrix symmetric second order differential operator Rocky Mt. J. Math. 27 585-600), one of us raised the question of determining instances of these matrix-valued polynomials going along with second order differential operators with matrix coefficients. In Duran A J and Gruenbaum F A (2004 Orthogonal matrix polynomials satisfying second order differential equations Int. Math. Res. Not. 10 461-84), we developed a method to produce such examples and observed that in certain cases there is a connection with the instance of Dirac's equation with a central potential. We observe that the case of the central Coulomb potential discussed in the physics literature in Darwin C G (1928 Proc. R. Soc. A 118 654), Nikiforov A F and Uvarov V B (1988 Special Functions of Mathematical Physics (Basle: Birkhauser) and Rose M E 1961 Relativistic Electron Theory (New York: Wiley)), and its solution, gives rise to a matrix weight function whose orthogonal polynomials solve a second order differential equation. To the best of our knowledge this is the first instance of a connection between the solution of the first order matrix equation of Dirac and the theory of matrix-valued orthogonal polynomials initiated by M G Krein

  15. The square root of the Dirac operator on superspace and the Maxwell equations

    Energy Technology Data Exchange (ETDEWEB)

    Bzdak, Adam; Hadasz, Leszek

    2004-02-26

    We re-consider the procedure of 'taking a square root of the Dirac equation' on superspace and show that it leads to the well-known superfield W{sub {alpha}} and to the proper equations of motion for the components, i.e., the Maxwell equations and the massless Dirac equation.

  16. On new and old symmetries of Maxwell and Dirac equations

    International Nuclear Information System (INIS)

    Fushchich, V.I.; Nikitin, A.G.

    1983-01-01

    Symmetry properties of the Maxwell equation for the electromagnetic field are analysed as well as of the Dirac and Kemmer-Duffin-Petiau one. In the frame of the non-geometrical approach it is demonstrated, that besides to the well-known invariance under the conformal group and Heaviside-Larmor-Rainich transformation, Maxwell equation possess the additional symmetry under the group U(2)xU(2) and under the 23-dimensional Lie algebra A 23 . The additional symmetry transformations are realized by the non-local (integro-differential) operators. The symmetry of the Dirac. equation under the differential and integro-differential transformations is investio.ated. It is shown that this equation is invariant under the 18-parametrical group, which includes the Poincare group as a subgroup. The 28-parametrical invariance group of the Kemmer-Duffin-Petiau equation is found. The finite conformal group transformations for a massless field of any spin are obtained. The explicit form of the conformal transformations for the electromagnetic field as well as for the Dirac and Weyl fields is given

  17. Rigid particle revisited: Extrinsic curvature yields the Dirac equation

    Energy Technology Data Exchange (ETDEWEB)

    Deriglazov, Alexei, E-mail: alexei.deriglazov@ufjf.edu.br [Depto. de Matemática, ICE, Universidade Federal de Juiz de Fora, MG (Brazil); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk, Lenin Ave. 30 (Russian Federation); Nersessian, Armen, E-mail: arnerses@ysu.am [Yerevan State University, 1 Alex Manoogian St., Yerevan 0025 (Armenia); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk, Lenin Ave. 30 (Russian Federation)

    2014-03-01

    We reexamine the model of relativistic particle with higher-derivative linear term on the first extrinsic curvature (rigidity). The passage from classical to quantum theory requires a number of rather unexpected steps which we report here. We found that, contrary to common opinion, quantization of the model in terms of so(3.2)-algebra yields massive Dirac equation. -- Highlights: •New way of canonical quantization of relativistic rigid particle is proposed. •Quantization made in terms of so(3.2) angular momentum algebra. •Quantization yields massive Dirac equation.

  18. The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials

    International Nuclear Information System (INIS)

    Contreras-Astorga, Alonso; Schulze-Halberg, Axel

    2014-01-01

    We introduce the confluent version of the quantum-mechanical supersymmetry formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to spectral problems is discussed, regularity conditions for the transformed potentials are derived, and normalizability of the transformed solutions is established. Our findings extend and complement former results [L. M. Nieto, A. A. Pecheritsin, and B. F. Samsonov, “Intertwining technique for the one-dimensional stationary Dirac equation,” Ann. Phys. 305, 151–189 (2003)

  19. The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials

    Energy Technology Data Exchange (ETDEWEB)

    Contreras-Astorga, Alonso, E-mail: aloncont@iun.edu; Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)

    2014-10-15

    We introduce the confluent version of the quantum-mechanical supersymmetry formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to spectral problems is discussed, regularity conditions for the transformed potentials are derived, and normalizability of the transformed solutions is established. Our findings extend and complement former results [L. M. Nieto, A. A. Pecheritsin, and B. F. Samsonov, “Intertwining technique for the one-dimensional stationary Dirac equation,” Ann. Phys. 305, 151–189 (2003)].

  20. Two-body Dirac equations for nucleon-nucleon scattering

    International Nuclear Information System (INIS)

    Liu Bin; Crater, Horace

    2003-01-01

    We investigate the nucleon-nucleon interaction by using the meson exchange model and the two-body Dirac equations of constraint dynamics. This approach to the two-body problem has been successfully tested for QED and QCD relativistic bound states. An important question we wish to address is whether or not the two-body nucleon-nucleon scattering problem can be reasonably described in this approach as well. This test involves a number of related problems. First we must reduce our two-body Dirac equations exactly to a Schroedinger-like equation in such a way that allows us to use techniques to solve them already developed for Schroedinger-like systems in nonrelativistic quantum mechanics. Related to this, we present a new derivation of Calogero's variable phase shift differential equation for coupled Schroedinger-like equations. Then we determine if the use of nine meson exchanges in our equations gives a reasonable fit to the experimental scattering phase shifts for n-p scattering. The data involve seven angular momentum states including the singlet states 1 S 0 , 1 P 1 , 1 D 2 and the triplet states 3 P 0 , 3 P 1 , 3 S 1 , 3 D 1 . Two models that we have tested give us a fairly good fit. The parameters obtained by fitting the n-p experimental scattering phase shift give a fairly good prediction for most of the p-p experimental scattering phase shifts examined (for the singlet states 1 S 0 , 1 D 2 and triplet states 3 P 0 , 3 P 1 ). Thus the two-body Dirac equations of constraint dynamics present us with a fit that encourages the exploration of a more realistic model. We outline generalizations of the meson exchange model for invariant potentials that may possibly improve the fit

  1. Dirac equation in Kerr space-time

    Energy Technology Data Exchange (ETDEWEB)

    Iyer, B R; Kumar, Arvind [Bombay Univ. (India). Dept. of Physics

    1976-06-01

    The weak-field low-velocity approximation of Dirac equation in Kerr space-time is investigated. The interaction terms admit of an interpretation in terms of a 'dipole-dipole' interaction in addition to coupling of spin with the angular momentum of the rotating source. The gravitational gyro-factor for spin is identified. The charged case (Kerr-Newman) is studied using minimal prescription for electromagnetic coupling in the locally intertial frame and to the leading order the standard electromagnetic gyro-factor is retrieved. A first order perturbation calculation of the shift of the Schwarzchild energy level yields the main interesting result of this work: the anomalous Zeeman splitting of the energy level of a Dirac particle in Kerr metric.

  2. The square root of the Dirac operator on the superspace and the Maxwell equations

    OpenAIRE

    Bzdak, Adam; Hadasz, Leszek

    2003-01-01

    We re-consider the procedure of ``taking a square root of the Dirac equation'' on the superspace and show that it leads to the well known superfield W_\\alpha and to the proper equations of motion for the components, i.e. the Maxwell equations and the massless Dirac equation.

  3. SU(4) properties of the Dirac equation

    International Nuclear Information System (INIS)

    Linhares, C.A.; Mignaco, J.A.

    1988-01-01

    The Dirac equation in four dimensions has an intimate connection with the representations of the group SU(4). This connection is shown in detail and subsequente properties are displayed in the continuum as well as in the lattice description. (author) [pt

  4. SU(4) proprerties of the Dirac equation

    International Nuclear Information System (INIS)

    Linhares, C.A.; Mignaco, J.A.

    1985-09-01

    The Dirac equation in four dimensions has an intimate connection with the representations of the group SU(4). This connection is shown in detail and subsequent properties are displayed in the continuum as well as in the lattice description [pt

  5. Relativistic Photoionization Computations with the Time Dependent Dirac Equation

    Science.gov (United States)

    2016-10-12

    Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6795--16-9698 Relativistic Photoionization Computations with the Time Dependent Dirac... Photoionization Computations with the Time Dependent Dirac Equation Daniel F. Gordon and Bahman Hafizi Naval Research Laboratory 4555 Overlook Avenue, SW...Unclassified Unlimited Unclassified Unlimited 22 Daniel Gordon (202) 767-5036 Tunneling Photoionization Ionization of inner shell electrons by laser

  6. Relativistic quantum vorticity of the quadratic form of the Dirac equation

    International Nuclear Information System (INIS)

    Asenjo, Felipe A; Mahajan, Swadesh M

    2015-01-01

    We explore the fluid version of the quadratic form of the Dirac equation, sometimes called the Feynman–Gell-Mann equation. The dynamics of the quantum spinor field is represented by equations of motion for the fluid density, the velocity field, and the spin field. In analogy with classical relativistic and non-relativistic quantum theories, the fully relativistic fluid formulation of this equation allows a vortex dynamics. The vortical form is described by a total tensor field that is the weighted combination of the inertial, electromagnetic and quantum forces. The dynamics contrives the quadratic form of the Dirac equation as a total vorticity free system. (paper)

  7. Symmetry Breaking in Photonic Crystals: On-Demand Dispersion from Flatband to Dirac Cones.

    Science.gov (United States)

    Nguyen, H S; Dubois, F; Deschamps, T; Cueff, S; Pardon, A; Leclercq, J-L; Seassal, C; Letartre, X; Viktorovitch, P

    2018-02-09

    We demonstrate that symmetry breaking opens a new degree of freedom to tailor energy-momentum dispersion in photonic crystals. Using a general theoretical framework in two illustrative practical structures, we show that breaking symmetry enables an on-demand tuning of the local density of states of the same photonic band from zero (Dirac cone dispersion) to infinity (flatband dispersion), as well as any constant density over an adjustable spectral range. As a proof of concept, we demonstrate experimentally the transformation of the very same photonic band from a conventional quadratic shape to a Dirac dispersion, a flatband dispersion, and a multivalley one. This transition is achieved by finely tuning the vertical symmetry breaking of the photonic structures. Our results provide an unprecedented degree of freedom for optical dispersion engineering in planar integrated photonic devices.

  8. P A M Dirac meets M G Krein: matrix orthogonal polynomials and Dirac's equation

    Energy Technology Data Exchange (ETDEWEB)

    Duran, Antonio J [Departamento de Analisis Matematico, Universidad de Sevilla, Apdo (PO BOX) 1160, 41080 Sevilla (Spain); Gruenbaum, F Alberto [Department of Mathematics, University of California, Berkeley, CA 94720 (United States)

    2006-04-07

    The solution of several instances of the Schroedinger equation (1926) is made possible by using the well-known orthogonal polynomials associated with the names of Hermite, Legendre and Laguerre. A relativistic alternative to this equation was proposed by Dirac (1928) involving differential operators with matrix coefficients. In 1949 Krein developed a theory of matrix-valued orthogonal polynomials without any reference to differential equations. In Duran A J (1997 Matrix inner product having a matrix symmetric second order differential operator Rocky Mt. J. Math. 27 585-600), one of us raised the question of determining instances of these matrix-valued polynomials going along with second order differential operators with matrix coefficients. In Duran A J and Gruenbaum F A (2004 Orthogonal matrix polynomials satisfying second order differential equations Int. Math. Res. Not. 10 461-84), we developed a method to produce such examples and observed that in certain cases there is a connection with the instance of Dirac's equation with a central potential. We observe that the case of the central Coulomb potential discussed in the physics literature in Darwin C G (1928 Proc. R. Soc. A 118 654), Nikiforov A F and Uvarov V B (1988 Special Functions of Mathematical Physics (Basle: Birkhauser) and Rose M E 1961 Relativistic Electron Theory (New York: Wiley)), and its solution, gives rise to a matrix weight function whose orthogonal polynomials solve a second order differential equation. To the best of our knowledge this is the first instance of a connection between the solution of the first order matrix equation of Dirac and the theory of matrix-valued orthogonal polynomials initiated by M G Krein.

  9. From a world-sheet supersymmetry to the Dirac equation

    International Nuclear Information System (INIS)

    Mankoc Borstnik, N.

    1991-10-01

    Starting from a classical action for a point particle with a local world-sheet supersymmetry, the Dirac equation follows with operators α-vector, β-vector γ-vector being defined in the Grassmann space as differential operators and having all the properties of the corresponding Dirac matrices except that α-vector and β-vector are anti-Hermitian rather than Hermitian. Such a particle interacts with an external field as expected. (author). 7 refs

  10. Nuclear structure information studied through Dirac equation with deformed mean fields

    International Nuclear Information System (INIS)

    Dudek, J.

    2000-01-01

    Complete text of publication follows. Relativistic mean-field theory provides a formal expression for the Dirac equation for the nucleonic motion in an atomic nucleus. The 'potentials' within such a formalism are given in terms of the meson fields, the latter obtained through a coupled system of equations of the Klein-Grodon type. Usually the whole system is being solved by using a Hartree approximation by employing an iterative selfonsistent algorithms. On a more phenomenological level one can parametrize the potentials that enter into a Dirac equation rather than obtain the selfconsistently; such a simplification was suggested some time ago by the Munich group. We introduce a Woods-Saxon type parametrisation and verify by a non-linear search routine what are the 'best fit potential parameters' that reproduce the single particle excitations in the double-magic spherical nuclei as well as the band-head properties in some hundreds of deformed nuclei. Next, by introducing a low-energy reduction of the Dirac equation, one may obtain in a natural way a Pauli Schrodinger type equation with a position dependent effective mass. The role of the corresponding term in a description of single particle energies of the nucleons is illustrated and the implications for the cranking equation are discussed in some detail. (author)

  11. Generalized Solutions of the Dirac Equation, W Bosons, and Beta Decay

    International Nuclear Information System (INIS)

    Okniński, Andrzej

    2016-01-01

    We study the 7×7 Hagen-Hurley equations describing spin 1 particles. We split these equations, in the interacting case, into two Dirac equations with nonstandard solutions. It is argued that these solutions describe decay of a virtual W boson in beta decay.

  12. On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons

    Directory of Open Access Journals (Sweden)

    Eckart Marsch

    2015-04-01

    Full Text Available We revisit the charge-conjugation operation for the Dirac equation in its chiral representation. A new decomposition of the Dirac spinor field is suggested and achieved by means of projection operators based on charge conjugation, which is discussed here in a non-standard way. Thus, two separate two-component Majorana-type field equations for the eigenfields of the charge-conjugation operator are obtained. The corresponding free fields are entirely separated without a gauge field, but remain mixed and coupled together through an electromagnetic field term. For fermions that are charged and, thus, subjected to the gauge field of electrodynamics, these two Majorana fields can be reassembled into a doublet, which is equivalent to a standard four-component Dirac spinor field. In this way, the Dirac equation is retained in a new guise, which is fully equivalent to that equation in its chiral form.

  13. On the solution of the Dirac equation in de Sitter space

    International Nuclear Information System (INIS)

    Klishevich, V V; Tyumentsev, V A

    2005-01-01

    It is shown that the maximal number of first-order symmetry operators for the Dirac equation (including spin symmetries), both in arbitrary signature flat space and in de Sitter space, is equal. The isomorphic representation of 11-dimensional nonlinear symmetry algebra (W-algebra) of first-order operators for the Dirac operator in flat space and de Sitter space is considered. The algebra is an extension of the Lie algebra of the group of pseudo-orthogonal rotations and this extension is unique. We have found all linear Lie subalgebras in the nonlinear algebra that satisfy the conditions of the noncommutative integration theorem. Using one subalgebra we have integrated the Dirac equation in the generalized spherical system of coordinates and have constructed the complete class of exact solutions. The solution is found by a method that differs from the variable separation method and is new in the literature. The massive particle spectrum, models of particle into antiparticle transmutation, the disappearance of particles and the quantization conditions of the motion are discussed. One can use the results of the paper to pose the boundary problem for the Dirac equation in de Sitter space if the interval is used in the boundary condition. As an example, we consider a model of asymptotically flat space that is glued from the de Sitter space and flat space. We interpret the model as a gravitational well or barrier

  14. Noncommutativity into Dirac Equation with mass dependent on the position

    International Nuclear Information System (INIS)

    Bastos, Samuel Batista; Almeida, Carlos Alberto Santos; Nunes, Luciana Angelica da Silva

    2013-01-01

    Full text: In recent years, there is growing interest in the study of theories in non-commutative spaces. Non-commutative fields theories are related with compactifications of M theory, string theory and the quantum Hall effect. Moreover, the role of the non-commutativity of theories of a particle finds large applications when analyzed in scenarios of quantum mechanics and relativistic quantum mechanics. In these contexts investigations on the Schrodinger and Dirac equations with mass depending on the position (MDP) has attracted much attention in the literature. Systems endowed with MDP models are useful for the study of many physical problems. In particular, they are used to study the energy density in problems of many bodies, determining the electronic properties of semiconductor heterostructures and also to describe the properties of heterojunctions and quantum dots. In particular, the investigation of relativistic effects it is important for systems containing heavy atoms or doping by heavy ions. For these types of materials, the study of the properties of the Dirac equation, in the case where the mass becomes variable is of great interest. In this paper, we seek for the non-relativistic limit of the Dirac Hamiltonian in the context of a theory of effective mass, through a Foldy-Wouthuysen transformation. We analyse the Dirac equation with mass dependent on the position, in a smooth step shape mass distribution, in non-commutative space (NC). This potential type kink was recently discussed by several authors in the commutative context and now we present our results in the non-commutative context. (author)

  15. How (not) to teach Lorentz covariance of the Dirac equation

    International Nuclear Information System (INIS)

    Nikolić, Hrvoje

    2014-01-01

    In the textbook proofs of the Lorentz covariance of the Dirac equation, one treats the wave function as a spinor and gamma matrices as scalars, leading to a quite complicated formalism with several pedagogic drawbacks. As an alternative, I propose to teach the Dirac equation and its Lorentz covariance by using a much simpler, but physically equivalent formalism, in which these drawbacks do not appear. In this alternative formalism, the wave function transforms as a scalar and gamma matrices as components of a vector, such that the standard physically relevant bilinear combinations do not change their transformation properties. The alternative formalism allows also a natural construction of some additional non-standard bilinear combinations with well-defined transformation properties. (paper)

  16. Particle-like solutions of the Einstein-Dirac-Maxwell equations

    Science.gov (United States)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    1999-08-01

    We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the ground state solutions are discussed for different values of the electromagnetic coupling constant. We find solutions even when the electromagnetic coupling is so strong that the total interaction is repulsive in the Newtonian limit. Our solutions are regular and well-behaved; this shows that the combined electromagnetic and gravitational self-interaction of the Dirac particles is finite.

  17. General method for reducing the two-body Dirac equation

    International Nuclear Information System (INIS)

    Galeao, A.P.; Ferreira, P.L.

    1992-01-01

    A semi relativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schroedinger-type equations is also discussed. (author)

  18. Invariance properties of the Dirac equation with external electro ...

    Indian Academy of Sciences (India)

    . Introduction. The objective of this short paper is to investigate the invariance properties of the Dirac equation with external electro-magnetic field. There exists a large number of literatures on the problem beginning almost from the formulation ...

  19. Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

    Energy Technology Data Exchange (ETDEWEB)

    Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)

    2015-10-15

    Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.

  20. Dispersive estimates for massive Dirac operators in dimension two

    Science.gov (United States)

    Erdoğan, M. Burak; Green, William R.; Toprak, Ebru

    2018-05-01

    We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the t-1 decay rate holds in the L1 →L∞ setting if the threshold energies are regular. We also show these bounds hold in the presence of s-wave resonances at the threshold. We further show that, if the threshold energies are regular then a faster decay rate of t-1(log ⁡ t) - 2 is attained for large t, at the cost of logarithmic spatial weights. The free Dirac equation does not satisfy this bound due to the s-wave resonances at the threshold energies.

  1. New experimental proposals for testing Dirac equation

    International Nuclear Information System (INIS)

    Camacho, Abel; Macias, Alfredo

    2004-01-01

    The advent of phenomenological quantum gravity has ushered us in the search for experimental tests of the deviations from general relativity predicted by quantum gravity or by string theories, and as a by-product of this quest the possible modifications that some field equations, for instance, the motion equation of spin-1/2-particles, have already been considered. In the present Letter a modified Dirac equation, whose extra term embraces a second-order time derivative, is taken as mainstay, and three different experimental proposals to detect it are put forward. The novelty in these ideas is that two of them do not fall within the extant approaches in this context, to wit, red-shift, atomic interferometry, or Hughes-Drever type-like experiments

  2. Survey on Dirac equation in general relativity theory

    International Nuclear Information System (INIS)

    Paillere, P.

    1984-10-01

    Starting from an infinitesimal transformation expressed with a Killing vector and using systematically the formalism of the local tetrades, we show that, in the area of the general relativity, the Dirac equation may be formulated only versus the four local vectors which determine the gravitational potentials, their gradients and the 4-vector potential of the electromagnetic field [fr

  3. Two-body Dirac equation and its wave function at the origin

    International Nuclear Information System (INIS)

    Ito, Hitoshi

    1998-01-01

    We propose a relativistic bound state equation for the Dirac particles interacting through an Abelian gauge field. It reduces to the (one body) Dirac equation in the infinite limit of one of the masses and is invariant under the PCT transformation. This invariance is a consequence of a modification of the Stueckelberg-Feynman boundary condition for propagation of the negative-energy two-body states, by which the some effect of the crossed diagram is taken in the lowest ladder equation. We can correct back the modification in perturbative calculations of the weak-coupling theory by adding a counter correction term in the interaction kernel. The equation can be used for the phenomenology of the heavy flavored mesons. We get good behavior of the wave function at the origin (WFO), with which the annihilation amplitude of the pseudoscalar meson becomes finite. Some comments are mentioned for the application in the heavy quark effective theory. The talk was based on a preprint

  4. Exact solution of the N-dimensional generalized Dirac-Coulomb equation

    International Nuclear Information System (INIS)

    Tutik, R.S.

    1992-01-01

    An exact solution to the bound state problem for the N-dimensional generalized Dirac-Coulomb equation, whose potential contains both the Lorentz-vector and Lorentz-scalar terms of the Coulomb form, is obtained. 24 refs. (author)

  5. Bound state solution of Dirac equation for Hulthen plus trigonometric Rosen Morse non-central potential using Romanovski polynomial

    Energy Technology Data Exchange (ETDEWEB)

    Suparmi, A., E-mail: suparmiuns@gmail.com; Cari, C., E-mail: suparmiuns@gmail.com [Physics Department, Post Graduate Study, Sebelas Maret University (Indonesia); Angraini, L. M. [Physics Department, Mataram University (Indonesia)

    2014-09-30

    The bound state solutions of Dirac equation for Hulthen and trigonometric Rosen Morse non-central potential are obtained using finite Romanovski polynomials. The approximate relativistic energy spectrum and the radial wave functions which are given in terms of Romanovski polynomials are obtained from solution of radial Dirac equation. The angular wave functions and the orbital quantum number are found from angular Dirac equation solution. In non-relativistic limit, the relativistic energy spectrum reduces into non-relativistic energy.

  6. Dirac equation in noncommutative space for hydrogen atom

    International Nuclear Information System (INIS)

    Adorno, T.C.; Baldiotti, M.C.; Chaichian, M.; Gitman, D.M.; Tureanu, A.

    2009-01-01

    We consider the energy levels of a hydrogen-like atom in the framework of θ-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S 1/2 , 2P 1/2 and 2P 3/2 is lifted completely, such that new transition channels are allowed.

  7. Universal behavior of a dispersive Dirac cone in gradient-index plasmonic metamaterials

    Science.gov (United States)

    Maier, Matthias; Mattheakis, Marios; Kaxiras, Efthimios; Luskin, Mitchell; Margetis, Dionisios

    2018-01-01

    We demonstrate analytically and numerically that the dispersive Dirac cone emulating an epsilon-near-zero (ENZ) behavior is a universal property within a family of plasmonic crystals consisting of two-dimensional (2D) metals. Our starting point is a periodic array of 2D metallic sheets embedded in an inhomogeneous and anisotropic dielectric host that allows for propagation of transverse-magnetic (TM) polarized waves. By invoking a systematic bifurcation argument for arbitrary dielectric profiles in one spatial dimension, we show how TM Bloch waves experience an effective dielectric function that averages out microscopic details of the host medium. The corresponding effective dispersion relation reduces to a Dirac cone when the conductivity of the metallic sheet and the period of the array satisfy a critical condition for ENZ behavior. Our analytical findings are in excellent agreement with numerical simulations.

  8. Solution of Dirac equation for modified Poschl Teller plus trigonometric Scarf potential using Romanovsky polynomials method

    International Nuclear Information System (INIS)

    Prastyaningrum, I.; Cari, C.; Suparmi, A.

    2016-01-01

    The approximation analytical solution of Dirac equation for Modified Poschl Teller plus Trigonometric Scarf Potential are investigated numerically in terms of finite Romanovsky Polynomial. The combination of two potentials are substituted into Dirac Equation then the variables are separated into radial and angular parts. The Dirac equation is solved by using Romanovsky Polynomial Method. The equation that can reduce from the second order of differential equation into the differential equation of hypergeometry type by substituted variable method. The energy spectrum is numerically solved using Matlab 2011. Where the increase in the radial quantum number nr and variable of modified Poschl Teller Potential causes the energy to decrease. The radial and the angular part of the wave function also visualized with Matlab 2011. The results show, by the disturbance of a combination between this potential can change the wave function of the radial and angular part. (paper)

  9. Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function

    Science.gov (United States)

    Durmus, Aysen

    2018-03-01

    The time independent Dirac equation is solved analytically for equal scalar and vector hyperbolic potential function in the presence of Greene and Aldrich approximation scheme. The bound state energy equation and spinor wave functions expressed by the hypergeometric function have been obtained in detail with asymptotic iteration approach. In order to indicate the accuracy of this different approach proposed to solve second order linear differential equations, we present that in the non-relativistic limit, analytical solutions of the Dirac equation converge to those of the Schrödinger one. We introduce numerical results of the theoretical analysis for hyperbolic potential function. Bound states corresponding to arbitrary values of n and l are reported for potential parameters covering a wide range of interaction. Also, we investigate relativistic vibrational energy spectra of alkali metal diatomic molecules in the different electronic states. It is observed that theoretical vibrational energy values are consistent with experimental Rydberg-Klein-Rees (RKR) results and vibrational energies of NaK, K_2 and KRb diatomic molecules interacting with hyperbolic potential smoothly converge to the experimental dissociation limit D_e=2508cm^{-1}, 254cm^{-1} and 4221cm^{-1}, respectively.

  10. Overcritical PT-symmetric square well potential in the Dirac equation

    OpenAIRE

    Cannata, Francesco; Ventura, Alberto

    2007-01-01

    We study scattering properties of a PT-symmetric square well potential with real depth larger than the threshold of particle-antiparticle pair production as the time component of a vector potential in the (1+1)-dimensional Dirac equation.

  11. Solution of the Lorentz-Dirac equation based on a new momentum expression

    CERN Document Server

    Yan, C C

    1998-01-01

    The Lorentz-Dirac equation is solved based on a new momentum expression given by p sup a =1/c sup 2 (u submu p supmu)u sup a +k du sup a /d tau. This new momentum expression is the form proposed by Barut modified to satisfy the condition imposed by Dirac. The solution turns out to be well behaved without violating causality or causing runaway. (author)

  12. Spinors, tensors and the covariant form of Dirac's equation

    International Nuclear Information System (INIS)

    Chen, W.Q.; Cook, A.H.

    1986-01-01

    The relations between tensors and spinors are used to establish the form of the covariant derivative of a spinor, making use of the fact that certain bilinear combinations of spinors are vectors. The covariant forms of Dirac's equation are thus obtained and examples in specific coordinate systems are displayed. (author)

  13. A rational interpretation of the Dirac equation for the electron

    International Nuclear Information System (INIS)

    Koga, T.

    1975-01-01

    Rationalization of the interpretation of the Dirac equation for the electron lies beyond the conventional scope of quantum mechanics. This difficulty motivates a revision of the system of quantum mechanics through which the indeterministic trait is eliminated from the system. (author)

  14. Dirac equation in noncommutative space for hydrogen atom

    Energy Technology Data Exchange (ETDEWEB)

    Adorno, T.C., E-mail: tadorno@nonada.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Chaichian, M., E-mail: Masud.Chaichian@helsinki.f [Department of Physics, University of Helsinki and Helsinki Institute of Physics, PO Box 64, FIN-00014 Helsinki (Finland); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Tureanu, A., E-mail: Anca.Tureanu@helsinki.f [Department of Physics, University of Helsinki and Helsinki Institute of Physics, PO Box 64, FIN-00014 Helsinki (Finland)

    2009-11-30

    We consider the energy levels of a hydrogen-like atom in the framework of theta-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S{sub 1/2}, 2P{sub 1/2} and 2P{sub 3/2} is lifted completely, such that new transition channels are allowed.

  15. Reactimeter dispersion equation

    OpenAIRE

    A.G. Yuferov

    2016-01-01

    The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...

  16. First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals

    KAUST Repository

    Mei, Jun; Wu, Ying; Chan, C. T.; Zhang, Zhao-Qing

    2012-01-01

    By using the k•p method, we propose a first-principles theory to study the linear dispersions in phononic and photonic crystals. The theory reveals that only those linear dispersions created by doubly degenerate states can be described by a reduced Hamiltonian that can be mapped into the Dirac Hamiltonian and possess a Berry phase of -π. Linear dispersions created by triply degenerate states cannot be mapped into the Dirac Hamiltonian and carry no Berry phase, and, therefore should be called Dirac-like cones. Our theory is capable of predicting accurately the linear slopes of Dirac and Dirac-like cones at various symmetry points in a Brillouin zone, independent of frequency and lattice structure. © 2012 American Physical Society.

  17. First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals

    KAUST Repository

    Mei, Jun

    2012-07-24

    By using the k•p method, we propose a first-principles theory to study the linear dispersions in phononic and photonic crystals. The theory reveals that only those linear dispersions created by doubly degenerate states can be described by a reduced Hamiltonian that can be mapped into the Dirac Hamiltonian and possess a Berry phase of -π. Linear dispersions created by triply degenerate states cannot be mapped into the Dirac Hamiltonian and carry no Berry phase, and, therefore should be called Dirac-like cones. Our theory is capable of predicting accurately the linear slopes of Dirac and Dirac-like cones at various symmetry points in a Brillouin zone, independent of frequency and lattice structure. © 2012 American Physical Society.

  18. Analytical evaluation of the plasma dispersion function for a Fermi Dirac distribution

    International Nuclear Information System (INIS)

    Mamedov, B.A.

    2012-01-01

    An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi—Dirac distribution is proposed. The new method has been developed using the binomial expansion theorem and the Gamma functions. The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function. The resulting series present better convergence rates. Several acceleration techniques are combined to further improve the efficiency. The obtained results for the plasma dispersion function are in good agreement with the known numerical data. (physics of gases, plasmas, and electric discharges)

  19. Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics

    International Nuclear Information System (INIS)

    Ni Guang-Jiong; Xu Jian-Jun; Lou Sen-Yue

    2011-01-01

    Based on the accurate experimental data of energy-level differences in hydrogen-like atoms, especially the 1S—2S transitions of hydrogen and deuterium, the necessity of introducing a reduced Dirac equation with reduced mass as the substitution of original electron mass is stressed. Based on new cognition about the essence of special relativity, we provide a reasonable argument for the reduced Dirac equation to have two symmetries, the invariance under the (newly defined) space-time inversion and that under the pure space inversion, in a noninertial frame. By using the reduced Dirac equation and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bound electron staying in an off-mass-shell state—-a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity. (general)

  20. Covariant differential calculus on quantum Minkowski space and the q-analogue of Dirac equation

    International Nuclear Information System (INIS)

    Song Xingchang; Academia Sinica, Beijing

    1992-01-01

    The covariant differential calculus on the quantum Minkowski space is presented with the help of the generalized Wess-Zumino method and the quantum Pauli matrices and quantum Dirac matrices are constructed parallel to those in the classical case. Combining these two aspects a q-analogue of Dirac equation follows directly. (orig.)

  1. Algebraic solution for the vector potential in the Dirac equation

    Energy Technology Data Exchange (ETDEWEB)

    Booth, H.S. [School of Mathematics and Physics, University of Tasmania, Hobart Tas (Australia); Centre for Mathematics and its Applications, Australian National University (Australia)]. E-mail: hbooth@wintermute.anu.edu.au; Legg, G.; Jarvis, P.D. [School of Mathematics and Physics, University of Tasmania, Hobart Tas (Australia)

    2001-07-20

    The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford's method of algebraically solving for the vector potential is reviewed, with attention to the additional constraints arising from non-maximality of the rank. The extension of the method to general spacetimes is illustrated by examples in diverse dimensions with both c- and a-number wavefunctions. (author)

  2. An asymptotic formula for Weyl solutions of the dirac equations

    International Nuclear Information System (INIS)

    Misyura, T.V.

    1995-01-01

    In the spectral analysis of differential operators and its applications an important role is played by the investigation of the behavior of the Weyl solutions of the corresponding equations when the spectral parameter tends to infinity. Elsewhere an exact asymptotic formula for the Weyl solutions of a large class of Sturm-Liouville equations has been obtained. A decisve role in the proof of this formula has been the semiboundedness property of the corresponding Sturm-Liouville operators. In this paper an analogous formula is obtained for the Weyl solutions of the Dirac equations

  3. Wave-equation dispersion inversion

    KAUST Repository

    Li, Jing

    2016-12-08

    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

  4. Paul Dirac

    Science.gov (United States)

    Pais, Abraham; Jacob, Maurice; Olive, David I.; Atiyah, Michael F.

    2005-09-01

    Preface Peter Goddard; Dirac memorial address Stephen Hawking; 1. Paul Dirac: aspects of his life and work Abraham Pais; 2. Antimatter Maurice Jacob; 3. The monopole David Olive; 4. The Dirac equation and geometry Michael F. Atiyah.

  5. Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

    International Nuclear Information System (INIS)

    Arum Sari, Resita; Suparmi, A; Cari, C

    2016-01-01

    The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation, then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number n r causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function. (paper)

  6. A novel quantum-mechanical interpretation of the Dirac equation

    Science.gov (United States)

    K-H Kiessling, M.; Tahvildar-Zadeh, A. S.

    2016-04-01

    A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr-Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit G\\to 0, where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.

  7. Spin-curvature interaction from curved Dirac equation: Application to single-wall carbon nanotubes

    Science.gov (United States)

    Zhang, Kai; Zhang, Erhu; Chen, Huawei; Zhang, Shengli

    2017-06-01

    The spin-curvature interaction (SCI) and its effects are investigated based on curved Dirac equation. Through the low-energy approximation of curved Dirac equation, the Hamiltonian of SCI is obtained and depends on the geometry and spinor structure of manifold. We find that the curvature can be considered as field strength and couples with spin through Zeeman-like term. Then, we use dimension reduction to derive the local Hamiltonian of SCI for cylinder surface, which implies that the effective Hamiltonian of single-wall carbon nanotubes results from the geometry and spinor structure of lattice and includes two types of interactions: one does not break any symmetries of the lattice and only shifts the Dirac points for all nanotubes, while the other one does and opens the gaps except for armchair nanotubes. At last, analytical expressions of the band gaps and the shifts of their positions induced by curvature are given for metallic nanotubes. These results agree well with experiments and can be verified experimentally.

  8. Dirac Equation in (1 +1 )-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model

    Science.gov (United States)

    Pedernales, J. S.; Beau, M.; Pittman, S. M.; Egusquiza, I. L.; Lamata, L.; Solano, E.; del Campo, A.

    2018-04-01

    We introduce an exact mapping between the Dirac equation in (1 +1 )-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1 +1 )-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1 +1 )-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.

  9. Non-existence of time-periodic solutions of the Dirac equation in a Reissner-Nordström black hole background

    Science.gov (United States)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    2000-04-01

    It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner-Nordström black hole background; in particular, there are no static solutions of the Dirac equation in such a background metric. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.

  10. Single-site Green function of the Dirac equation for full-potential electron scattering

    Energy Technology Data Exchange (ETDEWEB)

    Kordt, Pascal

    2012-05-30

    I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)

  11. Single-site Green function of the Dirac equation for full-potential electron scattering

    International Nuclear Information System (INIS)

    Kordt, Pascal

    2012-01-01

    I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)

  12. Geometric discretization of the multidimensional Dirac delta distribution - Application to the Poisson equation with singular source terms

    Science.gov (United States)

    Egan, Raphael; Gibou, Frédéric

    2017-10-01

    We present a discretization method for the multidimensional Dirac distribution. We show its applicability in the context of integration problems, and for discretizing Dirac-distributed source terms in Poisson equations with constant or variable diffusion coefficients. The discretization is cell-based and can thus be applied in a straightforward fashion to Quadtree/Octree grids. The method produces second-order accurate results for integration. Superlinear convergence is observed when it is used to model Dirac-distributed source terms in Poisson equations: the observed order of convergence is 2 or slightly smaller. The method is consistent with the discretization of Dirac delta distribution for codimension one surfaces presented in [1,2]. We present Quadtree/Octree construction procedures to preserve convergence and present various numerical examples, including multi-scale problems that are intractable with uniform grids.

  13. Orbiting the moons of Pluto complex solutions to the Einstein, Maxwell, Schroedinger and Dirac equations

    CERN Document Server

    Rauscher, Elizabeth A

    2011-01-01

    The Maxwell, Einstein, Schrödinger and Dirac equations are considered the most important equations in all of physics. This volume aims to provide new eight- and twelve-dimensional complex solutions to these equations for the first time in order to reveal

  14. Analysis of D Dimensional Dirac equation for q -deformed Posch-Teller combined with q -deformed trigonometric Manning Rosen Non-Central potential using Asymptotic Iteration Method (AIM)

    International Nuclear Information System (INIS)

    Alam, Y.; Suparmi; Cari; Anwar, F.

    2016-01-01

    In this study, we used asymptotic iteration method (AIM) to obtain the relativistic energy spectra and wavefunctions for D Dimensional Dirac equation. Solution of the D Dimensional Dirac equation using asymptotic iteration method was done by four steps. The first step, we substitutied q deformed Poschl-Teller potential plus q-deformed Manning Rosen Non-Central potential into D dimensional Dirac equation. And then, general term of D dimensioanl Dirac equation for q deformed Poschl-Teller potential plus q-deformed Manning Rosen Non-Central potential was reduced into one dimensioanal Dirac equation, consist of radial part and angular part. The second step, both of one dimensional part must be reduced to hypergeometric type differential equation by suitable parameter change. And then, hypergeometric type differential equation was transformed into AIM type differential equation. For the last step, AIM type differential equation can be solved to obtain the relativistic energy and wavefunctions of Dirac equation. Relativistic energy and wavefunctions were visualized by using Matlab software. (paper)

  15. Bound state solution of Dirac equation for 3D harmonics oscillator plus trigonometric scarf noncentral potential using SUSY QM approach

    Energy Technology Data Exchange (ETDEWEB)

    Cari, C., E-mail: carinln@yahoo.com; Suparmi, A., E-mail: carinln@yahoo.com [Physics Department, Sebelas Maret University, Jl. Ir. Sutami no 36A Kentingan Surakarta 57126 (Indonesia)

    2014-09-30

    Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.

  16. Potential scattering of Dirac particles

    International Nuclear Information System (INIS)

    Thaller, B.

    1981-01-01

    A quantum mechanical interpretation of the Dirac equation for particles in external electromagnetic potentials is discussed. It is shown that a consequent development of the Stueckelberg-Feynman theory into a probabilistic interpretation of the Dirac equation corrects some prejudices concerning negative energy states, Zitterbewegung and bound states in repulsive potentials and yields the connection between propagator theory and scattering theory. Limits of the Dirac equation, considered as a wave mechanical equation, are considered. (U.K.)

  17. Wave-equation dispersion inversion

    KAUST Repository

    Li, Jing; Feng, Zongcai; Schuster, Gerard T.

    2016-01-01

    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained

  18. Fermion unification model based on the intrinsic SU(8 symmetry of a generalized Dirac equation

    Directory of Open Access Journals (Sweden)

    Eckart eMarsch

    2015-10-01

    Full Text Available A natural generalization of the original Dirac spinor into a multi-component spinor is achieved, which corresponds to the single lepton and the three quarks of the first family of the standard model of elementary particle physics. Different fermions result from similarity transformations of the Dirac equation, but apparently there can be no more fermions according to the maximal multiplicity revealed in this study. Rotations in the fermion state space are achieved by the unitary generators of the U(1 and the SU(3 groups, corresponding to quantum electrodynamics (QED based on electric charge and chromodynamics (QCD based on colour charge. In addition to hypercharge the dual degree of freedom of hyperspin emerges, which occurs due to the duplicity implied by the two related (Weyl and Dirac representations of the Dirac equation. This yields the SU(2 symmetry of the weak interaction, which can be married to U(1 to generate the unified electroweak interaction as in the standard model. Therefore, the symmetry group encompassing all the three groups mentioned above is SU(8, which can accommodate and unify the observed eight basic stable fermions.

  19. Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

    Energy Technology Data Exchange (ETDEWEB)

    Koke, Christian, E-mail: christian.koke@stud.uni-heidelberg.de [Institut für theoretische Physik, Philosophenweg 16, D-69120 Heidelberg (Germany); Noh, Changsuk, E-mail: changsuk@kias.re.kr [Korea Institute for Advanced Study, 85 Hoegiro, Seoul 130-722 (Korea, Republic of); Angelakis, Dimitris G., E-mail: dimitris.angelakis@gmail.com [Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117542 (Singapore); School of Electronic and Computer Engineering, Technical University of Crete, Chania, Crete, 73100 (Greece)

    2016-11-15

    When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogical introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.

  20. Solution of Effective-Mass Dirac Equation with Scalar-Vector and Pseudoscalar Terms for Generalized Hulthén Potential

    Directory of Open Access Journals (Sweden)

    Altuğ Arda

    2017-01-01

    Full Text Available We find the exact bound state solutions and normalization constant for the Dirac equation with scalar-vector-pseudoscalar interaction terms for the generalized Hulthén potential in the case where we have a particular mass function m(x. We also search the solutions for the constant mass where the obtained results correspond to the ones when the Dirac equation has spin and pseudospin symmetry, respectively. After giving the obtained results for the nonrelativistic case, we search then the energy spectra and corresponding upper and lower components of Dirac spinor for the case of PT-symmetric forms of the present potential.

  1. D-Dimensional Dirac Equation for Energy-Dependent Pseudoharmonic and Mie-type Potentials via SUSYQM

    International Nuclear Information System (INIS)

    Ikot, A.N.; Hassanabadi, H.; Maghsoodi, E.; Zarrinkamar, S.

    2014-01-01

    We investigate the approximate solution of the Dirac equation for energy-dependent pseudoharmonic and Mie-type potentials under the pseudospin and spin symmetries using the supersymmetry quantum mechanics. We obtain the bound-state energy equation in an analytical manner and comment on the system behavior via various figures and tables

  2. Dirac charge dynamics in graphene by infrared spectroscopy

    International Nuclear Information System (INIS)

    Martin, Michael C; Li, Z.Q.; Henriksen, E.A.; Jiang, Z.; Hao, Z.; Martin, Michael C; Kim, P.; Stormer, H.L.; Basov, Dimitri N.

    2008-01-01

    A remarkable manifestation of the quantum character of electrons in matter is offered by graphene, a single atomic layer of graphite. Unlike conventional solids where electrons are described with the Schroedinger equation, electronic excitations in graphene are governed by the Dirac hamiltonian. Some of the intriguing electronic properties of graphene, such as massless Dirac quasiparticles with linear energy-momentum dispersion, have been confirmed by recent observations. Here, we report an infrared spectromicroscopy study of charge dynamics in graphene integrated in gated devices. Our measurements verify the expected characteristics of graphene and, owing to the previously unattainable accuracy of infrared experiments, also uncover significant departures of the quasiparticle dynamics from predictions made for Dirac fermions in idealized, free-standing graphene. Several observations reported here indicate the relevance of many-body interactions to the electromagnetic response of graphene

  3. Dirac equation of spin particles and tunneling radiation from a Kinnersly black hole

    Energy Technology Data Exchange (ETDEWEB)

    Li, Guo-Ping; Zu, Xiao-Tao [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Feng, Zhong-Wen [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); China West Normal University, College of Physics and Space Science, Nanchong (China); Li, Hui-Ling [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Shenyang Normal University, College of Physics Science and Technology, Shenyang (China)

    2017-04-15

    In curved space-time, the Hamilton-Jacobi equation is a semi-classical particle equation of motion, which plays an important role in the research of black hole physics. In this paper, starting from the Dirac equation of spin 1/2 fermions and the Rarita-Schwinger equation of spin 3/2 fermions, respectively, we derive a Hamilton-Jacobi equation for the non-stationary spherically symmetric gravitational field background. Furthermore, the quantum tunneling of a charged spherically symmetric Kinnersly black hole is investigated by using the Hamilton-Jacobi equation. The result shows that the Hamilton-Jacobi equation is helpful to understand the thermodynamic properties and the radiation characteristics of a black hole. (orig.)

  4. Path space measures for Dirac and Schroedinger equations: Nonstandard analytical approach

    International Nuclear Information System (INIS)

    Nakamura, T.

    1997-01-01

    A nonstandard path space *-measure is constructed to justify the path integral formula for the Dirac equation in two-dimensional space endash time. A standard measure as well as a standard path integral is obtained from it. We also show that, even for the Schroedinger equation, for which there is no standard measure appropriate for a path integral, there exists a nonstandard measure to define a *-path integral whose standard part agrees with the ordinary path integral as defined by a limit from time-slice approximant. copyright 1997 American Institute of Physics

  5. Exact solutions of time-dependent Dirac equations and the quantum-classical correspondence

    International Nuclear Information System (INIS)

    Zhang Zhiguo

    2006-01-01

    Exact solutions to the Dirac equations with a time-dependent mass and a static magnetic field or a time-dependent linear potential are given. Matrix elements of the coordinate, momentum and velocity operator are calculated. In the large quantum number limit, these matrix elements give the classical solution

  6. Quantum oscillations and Dirac dispersion in the BaZnBi2 semimetal guaranteed by local Zn vacancy order

    Science.gov (United States)

    Zhao, K.; Golias, E.; Zhang, Q. H.; Krivenkov, M.; Jesche, A.; Gu, L.; Rader, O.; Mazin, I. I.; Gegenwart, P.

    2018-03-01

    We have synthesized single crystals of Dirac semimetal candidates A ZnBi2 with A =Ba and Sr. In contrast to A =Sr , the Ba material displays a local Zn vacancy ordering, which makes the observation of quantum oscillations in out-of-plane magnetic fields possible. As a Dirac semimetal candidate, BaZnBi2 exhibits a small cyclotron electron mass, high quantum mobility, and nontrivial Berry phases. Three Dirac dispersions are observed by angle-resolved photoemission spectroscopy and identified by first-principles band-structure calculations. Compared to A Mn(Bi/Sb) 2 systems which host Mn magnetic moments, BaZnBi2 acts as a nonmagnetic analog to investigate the intrinsic properties of Dirac fermions in this structure family.

  7. Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations

    International Nuclear Information System (INIS)

    Esteban, M.J.; Georgiev, V.; Sere, E.

    1995-01-01

    The Maxwell-Dirac system describes the interaction of an electron with its own electromagnetic field. We prove the existence of soliton-like solutions of Maxwell-Dirac in (3+1)-Minkowski space-time. The solutions obtained are regular, stationary in time, and localized in space. They are found by a variational method, as critical points of an energy functional. This functional is strongly indefinite and presents a lack of compactness. We also find soliton-like solutions for the Klein-Gordon-Dirac system, arising in the Yukawa model. (author). 32 refs

  8. Semi-Dirac points in phononic crystals

    KAUST Repository

    Zhang, Xiujuan

    2014-01-01

    A semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. It was originally discovered in electron systems, in which the associated quasi-particles are massless along one direction, like those in graphene, but effective-mass-like along the other. It was reported that a semi-Dirac point is associated with the topological phase transition between a semi-metallic phase and a band insulator. Very recently, the classical analogy of a semi-Dirac cone has been reported in an electromagnetic system. Here, we demonstrate that, by accidental degeneracy, two-dimensional phononic crystals consisting of square arrays of elliptical cylinders embedded in water are also able to produce the particular dispersion relation of a semi-Dirac cone in the center of the Brillouin zone. A perturbation method is used to evaluate the linear slope and to affirm that the dispersion relation is a semi-Dirac type. If the scatterers are made of rubber, in which the acoustic wave velocity is lower than that in water, the semi-Dirac dispersion can be characterized by an effective medium theory. The effective medium parameters link the semi-Dirac point to a topological transition in the iso-frequency surface of the phononic crystal, in which an open hyperbola is changed into a closed ellipse. This topological transition results in drastic change in wave manipulation. On the other hand, the theory also reveals that the phononic crystal is a double-zero-index material along the x-direction and photonic-band-edge material along the perpendicular direction (y-direction). If the scatterers are made of steel, in which the acoustic wave velocity is higher than that in water, the effective medium description fails, even though the semi-Dirac dispersion relation looks similar to that in the previous case. Therefore different wave transport behavior is expected. The semi-Dirac points in phononic crystals described in

  9. Full utilization of semi-Dirac cones in photonics

    Science.gov (United States)

    Yasa, Utku G.; Turduev, Mirbek; Giden, Ibrahim H.; Kurt, Hamza

    2018-05-01

    In this study, realization and applications of anisotropic zero-refractive-index materials are proposed by exposing the unit cells of photonic crystals that exhibit Dirac-like cone dispersion to rotational symmetry reduction. Accidental degeneracy of two Bloch modes in the Brillouin zone center of two-dimensional C2-symmetric photonic crystals gives rise to the semi-Dirac cone dispersion. The proposed C2-symmetric photonic crystals behave as epsilon-and-mu-near-zero materials (ɛeff≈ 0 , μeff≈ 0 ) along one propagation direction, but behave as epsilon-near-zero material (ɛeff≈ 0 , μeff≠ 0 ) for the perpendicular direction at semi-Dirac frequency. By extracting the effective medium parameters of the proposed C4- and C2-symmetric periodic media that exhibit Dirac-like and semi-Dirac cone dispersions, intrinsic differences between isotropic and anisotropic materials are investigated. Furthermore, advantages of utilizing semi-Dirac cone materials instead of Dirac-like cone materials in photonic applications are demonstrated in both frequency and time domains. By using anisotropic transmission behavior of the semi-Dirac materials, photonic application concepts such as beam deflectors, beam splitters, and light focusing are proposed. Furthermore, to the best of our knowledge, semi-Dirac cone dispersion is also experimentally demonstrated for the first time by including negative, zero, and positive refraction states of the given material.

  10. Plasma dispersion function for a Fermi-Dirac distribution

    International Nuclear Information System (INIS)

    Melrose, D. B.; Mushtaq, A.

    2010-01-01

    A plasma dispersion function (PDF) is defined for a nonrelativistic Fermi-Dirac distribution and its properties are explored. The degree of degeneracy is described by a parameter ξ=e μ e /T e , for electrons, with μ e /T e large and negative in the nondegenerate limit, and large and positive in the completely degenerate limit. The PDF is denoted Z(y,ξ), where the variable y=ω/√(2)kV e , is the argument of the conventional PDF, Z(y)=Z(y,0), for a Maxwellian distribution. In the completely degenerate limit, Z(y,ξ) approaches a logarithmic function that depends on the Fermi temperature and is independent of T e . Analytic approximations to Z(y,ξ) are derived in terms of polylogarithmic functions for y 2 >>1 and for y 2 <<1.

  11. Wigner function for the Dirac oscillator in spinor space

    International Nuclear Information System (INIS)

    Ma Kai; Wang Jianhua; Yuan Yi

    2011-01-01

    The Wigner function for the Dirac oscillator in spinor space is studied in this paper. Firstly, since the Dirac equation is described as a matrix equation in phase space, it is necessary to define the Wigner function as a matrix function in spinor space. Secondly, the matrix form of the Wigner function is proven to support the Dirac equation. Thirdly, by solving the Dirac equation, energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained. (authors)

  12. Quasi-classical derivation of the Dirac and one-particle Schroedinger equations

    International Nuclear Information System (INIS)

    Wignall, J.W.G.

    1990-08-01

    The quasi-classical approach, in which particles are regarded as extended periodic excitations of a classical nonlinear field, is for the first time applied quantitatively in the quantum domain. It is shown that the twofold intrinsic 'spin' degree of freedom possessed by an electron can be interpreted in a purely classical way, and that the Lorentz covariant incorporation of this degree of freedom requires that the spacetime evolution of an electron excitation in a prescribed external field be given by the Dirac equation and hence, in the nonrelativistic limit, by the Pauli or Schroedinger one-particle equations. 17 refs

  13. Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

    International Nuclear Information System (INIS)

    Onate, C.A.; Onyeaju, M.C.; Ikot, A.N.

    2016-01-01

    The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.

  14. Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential

    Energy Technology Data Exchange (ETDEWEB)

    Onate, C.A., E-mail: oaclems14@physicist.net [Physics Department, University of Benin (Nigeria); Onyeaju, M.C.; Ikot, A.N. [Theoretical Physics Group, Physics Department, University of Port Harcourt (Nigeria)

    2016-12-15

    The approximate analytical solutions of the Dirac equation with Hellmann–Frost–Musulin potential have been studied by using the generalized parametric Nikiforov–Uvarov (NU) method for arbitrary spin–orbit quantum number k under the spin and pseudospin symmetries. The Hellmann–Frost–Musulin potential is a superposition potential that consists of Yukawa potential, Coulomb potential, and Frost–Musulin potential. As a particular case, we found the energy levels of the non-relativistic limit of the spin symmetry. The energy equation of Yukawa potential, Coulomb potential, Hellmann potential and Frost–Musulin potential are obtained. Energy values are generated for some diatomic molecules.

  15. Investigation of the Dirac Equation by Using the Conformable Fractional Derivative

    Science.gov (United States)

    Mozaffari, F. S.; Hassanabadi, H.; Sobhani, H.; Chung, W. S.

    2018-05-01

    In this paper,the Dirac equation is constructed using the conformable fractional derivative so that in its limit for the fractional parameter, the normal version is recovered. Then, the Cornell potential is considered as the interaction of the system. In this case, the wave function and the energy eigenvalue equation are derived with the aim of the bi-confluent Heun functions. use of the conformable fractional derivative is proven to lead to a branching treatment for the energy of the system. Such a treatment is obvious for small values of the fractional parameter, and a united value as the fractional parameter approaches unity.

  16. Exact solutions of the Dirac equation with a Coulomb plus scalar potential in 2 + 1 dimensions

    International Nuclear Information System (INIS)

    Dong, Shihai; Gu, Xiaoyan; Ma, Zhongqi; Dong, Shishan

    2002-01-01

    The exact solutions of the (2+1)-dimensional Dirac equation with a Coulomb potential and a scalar one are analytically presented by studying the second-order differential equations obtained from a pair of coupled first-order ones. The eigenvalues are studied in some detail. (author)

  17. A new approach to the I/N-expansion for the Dirac equation

    International Nuclear Information System (INIS)

    Stepanov, S.S.; Tutik, R.S.

    1991-01-01

    The difficulties associated with application of the I/N-expansion to the Dirac equation have been resolved by applying the method of (h/2π)-expansion. This technique does not involve converting the initial equation into the Schroedinger-like or Klein-Gordon-like form. Obtained recurrence formulae have a simple form and allow one to find the I/N-corrections of an arbitrary order in any of the I/N-expansion scheme. The method restores the exact results for the Coulomb potential. 17 refs. (author)

  18. The Schroedinger and Dirac free particle equations without quantum mechanics

    International Nuclear Information System (INIS)

    Ord, G.N.

    1996-01-01

    Einstein close-quote s theory of Brownian Movement has provided a well accepted microscopic model of diffusion for many years. Until recently the relationship between this model and Quantum Mechanics has been completely formal. Brownian motion provides a microscopic model for diffusion, but quantum mechanics and diffusion are related by a formal analytic continuation, so the relationship between Brownian motion and Quantum Mechanics has been correspondingly vague. Some recent work has changed this picture somewhat and here we show that a random walk model of Brownian motion produces the diffusion equation or the telegraph equations as a descriptions of particle densities, while at the same time the correlations in the space-time geometry of these same Brownian particles obey the Schroedinger and Dirac equations respectively. This is of interest because the equations of Quantum Mechanics appear here naturally in a classical context without the problems of interpretation they have in the usual context. copyright 1996 Academic Press, Inc

  19. Some spectral properties of the one-dimensional disordered Dirac equation

    International Nuclear Information System (INIS)

    Bocquet, Marc

    1999-01-01

    We study spectral properties of a one-dimensional Dirac equation with various disorder. We use replicas to calculate the exact density of state and typical localization length of a Dirac particle in several cases. We show that they can be calculated, in quite a simple fashion, in any type of disorder obeying a Gaussian white noise distribution. In addition to cases involving pure types of disorder, we study a mixed disorder case where the Dyson singularity is destroyed by the mixing. We also clarify the supersymmetric alternative derivation, even though it proves less efficient than the replica treatment for such thermodynamic quantities. We show that the smallest dynamical algebra in the Hamiltonian formalism is u(1,1), preferably to u(n,n) in the replica derivation or u(1, 1 vertical bar 2) in the supersymmetric alternative. Finally, we discuss symmetries in the disorder fields and show that there exists a non-trivial mapping between the electric potential disorder and the magnetic (or mass) disorder

  20. Dirac, Weyl, Majorana, a review

    International Nuclear Information System (INIS)

    Uschersohn, J.

    1982-05-01

    The Dirac equation and the properties of Dirac matrices are presented and discussed. A large number of representations of the Dirac matrices is identified. Special emphasis is put on aspects rarely treated or neglected in textbooks

  1. Algebraic inversion of the Dirac equation for the vector potential in the non-Abelian case

    International Nuclear Information System (INIS)

    Inglis, S M; Jarvis, P D

    2012-01-01

    We study the Dirac equation for spinor wavefunctions minimally coupled to an external field, from the perspective of an algebraic system of linear equations for the vector potential. By analogy with the method in electromagnetism, which has been well-studied, and leads to classical solutions of the Maxwell–Dirac equations, we set up the formalism for non-Abelian gauge symmetry, with the SU(2) group and the case of four-spinor doublets. An extended isospin-charge conjugation operator is defined, enabling the hermiticity constraint on the gauge potential to be imposed in a covariant fashion, and rendering the algebraic system tractable. The outcome is an invertible linear equation for the non-Abelian vector potential in terms of bispinor current densities. We show that, via application of suitable extended Fierz identities, the solution of this system for the non-Abelian vector potential is a rational expression involving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial vector current densities, albeit in the non-closed form of a Neumann series. (paper)

  2. Interpretation of the evolution parameter of the Feynman parametrization of the Dirac equation

    International Nuclear Information System (INIS)

    Aparicio, J.P.; Garcia Alvarez, E.T.

    1995-01-01

    The Feynman parametrization of the Dirac equation is considered in order to obtain an indefinite mass formulation of relativistic quantum mechanics. It is shown that the parameter that labels the evolution is related to the proper time. The Stueckelberg interpretation of antiparticles naturally arises from the formalism. ((orig.))

  3. Introduction to nonlinear dispersive equations

    CERN Document Server

    Linares, Felipe

    2015-01-01

    This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...

  4. Dirac delta representation by exact parametric equations.. Application to impulsive vibration systems

    Science.gov (United States)

    Chicurel-Uziel, Enrique

    2007-08-01

    A pair of closed parametric equations are proposed to represent the Heaviside unit step function. Differentiating the step equations results in two additional parametric equations, that are also hereby proposed, to represent the Dirac delta function. These equations are expressed in algebraic terms and are handled by means of elementary algebra and elementary calculus. The proposed delta representation complies exactly with the values of the definition. It complies also with the sifting property and the requisite unit area and its Laplace transform coincides with the most general form given in the tables. Furthermore, it leads to a very simple method of solution of impulsive vibrating systems either linear or belonging to a large class of nonlinear problems. Two example solutions are presented.

  5. The supersymmetric Dirac equation the application to hydrogenic atoms

    CERN Document Server

    Hirshfeld, Allen

    2012-01-01

    The solution of the Dirac equation for an electron in a Coulomb field is systematically treated here by utilizing new insights provided by supersymmetry. It is shown that each of the concepts has its analogue in the non-relativistic case. Indeed, the non-relativistic case is developed first, in order to introduce the new concepts in a familiar context. The symmetry of the non-relativistic model is already present in the classical limit, so the classical Kepler problem is first discussed in order to bring out the role played by the Laplace vector, one of the central concepts of the whole book.

  6. Relativistic energy eigenvalues for the Dirac equation in the presence of vector and scalar potentials via the simple similarity transformation

    International Nuclear Information System (INIS)

    Barakat, T

    2012-01-01

    Based on the simple similarity transformation, we were able to transform the Dirac equation whose potential contains vector V (r) = -A/r + B 1 r and scalar S(r) = B 2 r types into a form nearly identical to the Schrödinger equation. The transformed equation is so simple that one can solve it by means of the asymptotic iteration method. Moreover, within the same framework we were able to obtain the relativistic energy eigenvalues for the Dirac equation with vector Coulomb plus scalar linear, and with pure scalar linear potentials; V (r) = -A/r, S(r) = B 2 r, and V (r) = 0, S(r) = B 2 r, respectively.

  7. Meson spectra from two-body dirac equations with minimal interactions

    International Nuclear Information System (INIS)

    Crater, H.W.; Becker, R.L.; Wong, C.Y.

    1991-01-01

    Many authors have used two-body relativistic wave equations with spin in nonperturbative numerical quark model calculations of the meson spectrum. Usually, they adopt a truncation of the Bethe-Salpeter equation of QED and/or scalar. QED and replace the static Coulomb interactions of those field theories with a semiphenomenological Q bar Q potential whose insertion in the Breit terms give the corresponding spin corrections. However, the successes of these wave equations in QED have invariably depended on perturbative treatment of the terms in each beyond the Coulomb terms. There have been no successful nonperturbative numerical test of two-body quantum wave equations in QED, because in most equations the effective potentials beyond the Coulomb are singular and can only be treated perturbatively. This is a glaring omission that we rectify here for the case of the two-body Dirac equations of constraint dynamics. We show in this paper that a nonperturbative numerical treatment of these equations for QED yields the same spectral results as a perturbative treatment of them which in turn agrees with the standard spectral results for positronium and muonium. This establishes that the vector and scalar interaction structures of our equations accurately incorporate field theoretic interactions in a bone fide relativistic wave equation. The last portion of this work will report recent quark model calculations using these equations with the Adler-Piran static Q bar Q potential

  8. The Dirac equation in the local representation - contributions to the quantum electrodynamics of strong fields

    International Nuclear Information System (INIS)

    Schlueter, P.

    1985-05-01

    In this work three topics related to the theory of positron creation in heavy ion collisions are investigated. The first of these is concerned with the local representation of the Dirac matrices. It consists of a space dependent similarity transformation of the Dirac matrices which is chosen in such a way that for certain orthogonal coordinate systems the Dirac equation assumes a simple standardized form. This form is well suited for analytical as well as numerical calculations. For all generally used coordinate systems the transformation can be given in closed form. The application of this idea is not restricted to the solution of the two-centre Dirac equation but may be used also for different electro-magnetic potentials. In the second of the above mentioned problems, the question is discussed, whether the recently observed peak structures in positron spectra from U-U collisions can originate from nuclear conversion processes. It is demonstrated that, taking this hypothesis at face value, in the photon or delta-electron spectrum corresponding structures should be observed. Moreover, rather large nuclear excitation probabilities in the order of percents are needed to make this explanation plausible. Finally, the third topic is concerned with a more fundamental question: May it be possible that the interaction of the strongly bound electrons in a critical electric field with the radiation field leads to an energy shift which is big enough to prevent the diving of the 1s-state into the negative energy continuum. (orig./HSI) [de

  9. Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis

    International Nuclear Information System (INIS)

    Fillion-Gourdeau, F.; Lorin, E.; Bandrauk, A.D.

    2016-01-01

    A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.

  10. Approximate Solutions to the Dirac Equation with Effective Mass for the Manning-Rosen Potential in N Dimensions

    International Nuclear Information System (INIS)

    Bahar, M.K.; Yasuk, F.

    2012-01-01

    The solutions of the effective mass Dirac equation for the Manning-Rosen potential with the centrifugal term are studied approximately in N dimension. The relativistic energy spectrum and two-component spinor eigenfunctions are obtained by the asymptotic iteration method. We have also investigated eigenvalues of the effective mass Dirac-Manning-Rosen problem for α = 0 or α = 1. In this case, the Manning-Rosen potential reduces to the Hulthen potential. (author)

  11. Application of a Lorentz transformation in six dimensions to an extension of dirac equation

    International Nuclear Information System (INIS)

    Sabry, A.A.

    2000-01-01

    On applying a six dimensional Lorentz transformation (by adding three time components to the usual 3 space components) a covariant extended Dirac equation in this six dimensional space is suggested. From the free field solution of the extended equation we obtained four solutions for E , the first component of energy which depends on very big masses M and M 0 . The observed masses of the leptons and their corresponding neutrinos satisfying the same free field equation, can then be obtained on using second quantisation procedures on the field operators

  12. The nonlinear Dirac equation and the study of effective many-particle interactions in QED

    International Nuclear Information System (INIS)

    Ionescu, D.C.

    1987-12-01

    The starting point of the discussion was extended Lagrangian density for the classical Dirac field. The considered additional terms we had thereby interpreted as effective interactions because the corresponding field theory was not renormalizable. A scalar coupling as well as a vectorial coupling were put into calculation. The equation of motion for the system was thereby a one-particle equation which separated for s 1/2 and p 1/2 states and led to a system of coupled differential equations for the radial part. The derived radial equations were studied on three different levels. First we considered ordinary systems from atomic physics with ordinal numbers Z ≤ 110 in order to obtain from precision experiments of quantum electrodynamics upper bounds for the coupling constants. Second we have studied the influence of these additional interactions on the energy levels of the superheavy systems with ordinal numbers 110 ≤ Z ≤ 190. Third we have searched for bound states of a nonlinear Dirac equation which should exist only because of the effective interaction. In the further study we have then changed to a field-quantized consideration because our hitherto analysis was purely classical. In this connection we have studied the (e + e - ) 2 system with a (anti ΨΓΨ) 2 interaction. From the corresponding many-particle equation we have then by means of the Hartree-Fock method derived the one-particle equation of the system. Finally we had studied the electron-positron interaction by exchange of a massive intermediate vector boson. (orig./HSI) [de

  13. Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

    Energy Technology Data Exchange (ETDEWEB)

    Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com [Physics Department, Faculty of Mathematics and Science, Sebelas Maret University, Jl. Ir. Sutami 36A Kentingan Surakarta 57126 (Indonesia); Deta, U. A. [Physics Department, Faculty of Science and Mathematics Education and Teacher Training, Surabaya State University, Surabaya (Indonesia)

    2016-02-08

    The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy. The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.

  14. Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets

    International Nuclear Information System (INIS)

    Cariglia, Marco; Krtous, Pavel; Kubiznak, David

    2011-01-01

    In this paper we derive the most general first-order symmetry operator commuting with the Dirac operator in all dimensions and signatures. Such an operator splits into Clifford even and Clifford odd parts which are given in terms of odd Killing-Yano and even closed conformal Killing-Yano inhomogeneous forms, respectively. We study commutators of these symmetry operators and give necessary and sufficient conditions under which they remain of the first-order. In this specific setting we can introduce a Killing-Yano bracket, a bilinear operation acting on odd Killing-Yano and even closed conformal Killing-Yano forms, and demonstrate that it is closely related to the Schouten-Nijenhuis bracket. An important nontrivial example of vanishing Killing-Yano brackets is given by Dirac symmetry operators generated from the principal conformal Killing-Yano tensor [hep-th/0612029]. We show that among these operators one can find a complete subset of mutually commuting operators. These operators underlie separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions [arXiv:0711.0078].

  15. Topological insulators Dirac equation in condensed matter

    CERN Document Server

    Shen, Shun-Qing

    2017-01-01

    This new edition presents a unified description of these insulators from one to three dimensions based on the modified Dirac equation. It derives a series of solutions of the bound states near the boundary, and describes the current status of these solutions. Readers are introduced to topological invariants and their applications to a variety of systems from one-dimensional polyacetylene, to two-dimensional quantum spin Hall effect and p-wave superconductors, three-dimensional topological insulators and superconductors or superfluids, and topological Weyl semimetals, helping them to better understand this fascinating field. To reflect research advances in topological insulators, several parts of the book have been updated for the second edition, including: Spin-Triplet Superconductors, Superconductivity in Doped Topological Insulators, Detection of Majorana Fermions and so on. In particular, the book features a new chapter on Weyl semimetals, a topic that has attracted considerable attention and has already b...

  16. Topological Insulators Dirac Equation in Condensed Matters

    CERN Document Server

    Shen, Shun-Qing

    2012-01-01

    Topological insulators are insulating in the bulk, but process metallic states around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, Topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological in...

  17. Paul Dirac: the purest soul in physics

    International Nuclear Information System (INIS)

    Berry, M.

    1998-01-01

    Paul Dirac published the first of his papers on ''The Quantum Theory of the Electron'' seventy years ago this month. Published in the Proceedings of the Royal Society (London) in February and March 1928, the papers contained one of the greatest leaps of imagination in 20th century physics. The Dirac equation, derived in those papers, is one of the most important equations in physics. Dirac showed that the simplest wave satisfying the requirements of quantum mechanics and relativity was not a simple number but had four components. He found that the logic that led to the theory was, although deeply sophisticated, in a sense beautifully simple. Much later, when someone asked him ''How did you find the Dirac equation?'' he is said to have replied: ''I found it beautiful''. In addition to explaining the magnetic and spin properties of the electron, the equation also predicts the existence of antimatter. Because Dirac was a quiet man - famously quiet, indeed - he is not well known outside physics, although this is slowly changing. In 1995 a plaque to Dirac was unveiled at Westminster Abbey in London and last year Institute of Physics Publishing, which is based in Bristol, named its new building Dirac House. In this article the author recalls the achievements of the greatest physicists of the 20th century. (UK)

  18. Photoconductivity in Dirac materials

    International Nuclear Information System (INIS)

    Shao, J. M.; Yang, G. W.

    2015-01-01

    Two-dimensional (2D) Dirac materials including graphene and the surface of a three-dimensional (3D) topological insulator, and 3D Dirac materials including 3D Dirac semimetal and Weyl semimetal have attracted great attention due to their linear Dirac nodes and exotic properties. Here, we use the Fermi’s golden rule and Boltzmann equation within the relaxation time approximation to study and compare the photoconductivity of Dirac materials under different far- or mid-infrared irradiation. Theoretical results show that the photoconductivity exhibits the anisotropic property under the polarized irradiation, but the anisotropic strength is different between 2D and 3D Dirac materials. The photoconductivity depends strongly on the relaxation time for different scattering mechanism, just like the dark conductivity

  19. Optical analogue of relativistic Dirac solitons in binary waveguide arrays

    Energy Technology Data Exchange (ETDEWEB)

    Tran, Truong X., E-mail: truong.tran@mpl.mpg.de [Department of Physics, Le Quy Don University, 236 Hoang Quoc Viet str., 10000 Hanoi (Viet Nam); Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); Longhi, Stefano [Department of Physics, Politecnico di Milano and Istituto di Fotonica e Nanotecnologie del Consiglio Nazionale delle Ricerche, Piazza L. da Vinci 32, I-20133 Milano (Italy); Biancalana, Fabio [Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); School of Engineering and Physical Sciences, Heriot-Watt University, EH14 4AS Edinburgh (United Kingdom)

    2014-01-15

    We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An optical analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.

  20. Numerical implementation of the Dirac equation on hypercube multicomputers

    International Nuclear Information System (INIS)

    Wells, J.C.

    1991-01-01

    Motivated by an interest in nonperturbative electromagnetic lepton-pair production in relativistic heavy-ion collisions, we discuss the numerical methods used in implementing a lattice solution of the time-dependent Dirac equation in three-dimensional Cartesian coordinates. Discretization is obtained using the lattice basis-spline collocation method, in which quantum-state vectors and coordinate-space operators are expressed in terms of basis-spline functions, and represented on a spatial lattice. All numerical procedures reduce to a series of matrix-vector operations which we perform on the Intel iPSC/860 hypercube multicomputer. We discuss solutions to the problems of limited node memory and node-to-node communication overhead inherent in using distributed-memory, multiple-instruction, multiple-data parallel computers

  1. Dirac equation in 5- and 6-dimensional curved space-time manifolds

    International Nuclear Information System (INIS)

    Vladimirov, Yu.S.; Popov, A.D.

    1984-01-01

    The program of plotting unified multidimensional theory of gravitation, electromagnetism and electrically charged matter with transition from 5-dimensional variants to 6-dimensional theory possessing signature (+----+) is developed. For recording the Dirac equation in 5- and 6-dimensional curved space-time manifolds the tetrad formalism and γ-matrix formulation of the General Relativity Theory are used. It is shown that the 6-dimensional theory case unifies the two private cases of 5-dimensional theory and corresponds to two possibilities of the theory developed by Kadyshevski

  2. Bound states of the Dirac equation with some physical potentials by the Nikiforov-Uvarov method

    Energy Technology Data Exchange (ETDEWEB)

    Setare, Mohammad R; Haidari, S [Department of Physics, University of Kurdistan, Pasdaran Avenue, Sanandaj (Iran, Islamic Republic of)], E-mail: rezakord@ipm.ir, E-mail: heidary.somayeh@gmail.com

    2010-01-15

    Exact analytical solutions for the s-wave Dirac equation with the reflectionless-type, Rosen-Morse and Manning-Rosen potentials are obtained, under the condition of spin symmetry. We obtained bound state energy eigenvalues and corresponding spinor wave function in the framework of the Nikiforov-Uvarov (NU) method.

  3. Semi-Dirac points in phononic crystals

    KAUST Repository

    Zhang, Xiujuan; Wu, Ying

    2014-01-01

    of rubber, in which the acoustic wave velocity is lower than that in water, the semi-Dirac dispersion can be characterized by an effective medium theory. The effective medium parameters link the semi-Dirac point to a topological transition in the iso

  4. On the confinement of a Dirac particle to a two-dimensional ring

    International Nuclear Information System (INIS)

    Bakke, K.; Furtado, C.

    2012-01-01

    In this contribution, we propose a new model for studying the confinement of a spin-half particle to a two-dimensional quantum ring for systems described by the Dirac equation by introducing a new coupling into the Dirac equation. We show that the introduction of this new coupling into the Dirac equation yields a generalization of the two-dimensional quantum ring model proposed by Tan and Inkson [W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11 (1996) 1635] for relativistic spin-half quantum particles. -- Highlights: ► Two-dimensional ring model for condensed matter systems described by the Dirac equation. ► Exact solutions of the Dirac equation. ► Persistent currents for Dirac-like systems confined to a two-dimensional quantum ring.

  5. A Dirac algebraic approach to supersymmetry

    International Nuclear Information System (INIS)

    Guersey, F.

    1984-01-01

    The power of the Dirac algebra is illustrated through the Kaehler correspondence between a pair of Dirac spinors and a 16-component bosonic field. The SO(5,1) group acts on both the fermion and boson fields, leading to a supersymmetric equation of the Dirac type involving all these fields. (author)

  6. Skeletonized wave equation of surface wave dispersion inversion

    KAUST Repository

    Li, Jing; Schuster, Gerard T.

    2016-01-01

    We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel

  7. Dirac matter

    CERN Document Server

    Rivasseau, Vincent; Fuchs, Jean-Nöel

    2017-01-01

    This fifteenth volume of the Poincare Seminar Series, Dirac Matter, describes the surprising resurgence, as a low-energy effective theory of conducting electrons in many condensed matter systems, including graphene and topological insulators, of the famous equation originally invented by P.A.M. Dirac for relativistic quantum mechanics. In five highly pedagogical articles, as befits their origin in lectures to a broad scientific audience, this book explains why Dirac matters. Highlights include the detailed "Graphene and Relativistic Quantum Physics", written by the experimental pioneer, Philip Kim, and devoted to graphene, a form of carbon crystallized in a two-dimensional hexagonal lattice, from its discovery in 2004-2005 by the future Nobel prize winners Kostya Novoselov and Andre Geim to the so-called relativistic quantum Hall effect; the review entitled "Dirac Fermions in Condensed Matter and Beyond", written by two prominent theoreticians, Mark Goerbig and Gilles Montambaux, who consider many other mater...

  8. Particle resonance in the Dirac equation in the presence of a delta interaction and a perturbative hyperbolic potential

    International Nuclear Information System (INIS)

    Villalba, Victor M.; Gonzalez-Diaz, Luis A.

    2009-01-01

    We show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing weak electric field associated with a hyperbolic tangent potential. We solve the Dirac equation in terms of Gauss hyper-geometric functions and show explicitly how the resonant behavior depends on the strength of the electric field evaluated at the support of the point interaction. We derive an approximate expression for the value of the resonances and compare the results calculated for the hyperbolic potential with those obtained for a linear perturbative potential. Finally, we characterize the resonances with the help of the phase shift and the Wigner delay time. (orig.)

  9. Skeletonized wave equation of surface wave dispersion inversion

    KAUST Repository

    Li, Jing

    2016-09-06

    We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel-time inversion, the complicated surface-wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the (kx,ω) domain. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D velocity models. This procedure, denoted as wave equation dispersion inversion (WD), does not require the assumption of a layered model and is less prone to the cycle skipping problems of full waveform inversion (FWI). The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distribution in laterally heterogeneous media.

  10. Dirac Magnons in Honeycomb Ferromagnets

    Directory of Open Access Journals (Sweden)

    Sergey S. Pershoguba

    2018-01-01

    Full Text Available The discovery of the Dirac electron dispersion in graphene [A. H. Castro Neto, et al., The Electronic Properties of Graphene, Rev. Mod. Phys. 81, 109 (2009RMPHAT0034-686110.1103/RevModPhys.81.109] led to the question of the Dirac cone stability with respect to interactions. Coulomb interactions between electrons were shown to induce a logarithmic renormalization of the Dirac dispersion. With a rapid expansion of the list of compounds and quasiparticle bands with linear band touching [T. O. Wehling, et al., Dirac Materials, Adv. Phys. 63, 1 (2014ADPHAH0001-873210.1080/00018732.2014.927109], the concept of bosonic Dirac materials has emerged. We consider a specific case of ferromagnets consisting of van der Waals-bonded stacks of honeycomb layers, e.g., chromium trihalides CrX_{3} (X=F, Cl, Br and I, that display two spin wave modes with energy dispersion similar to that for the electrons in graphene. At the single-particle level, these materials resemble their fermionic counterparts. However, how different particle statistics and interactions affect the stability of Dirac cones has yet to be determined. To address the role of interacting Dirac magnons, we expand the theory of ferromagnets beyond the standard Dyson theory [F. J. Dyson, General Theory of Spin-Wave Interactions, Phys. Rev. 102, 1217 (1956PHRVAO0031-899X10.1103/PhysRev.102.1217, F. J. Dyson, Thermodynamic Behavior of an Ideal Ferromagnet, Phys. Rev. 102, 1230 (1956PHRVAO0031-899X10.1103/PhysRev.102.1230] to the case of non-Bravais honeycomb layers. We demonstrate that magnon-magnon interactions lead to a significant momentum-dependent renormalization of the bare band structure in addition to strongly momentum-dependent magnon lifetimes. We show that our theory qualitatively accounts for hitherto unexplained anomalies in nearly half-century-old magnetic neutron-scattering data for CrBr_{3} [W. B. Yelon and R. Silberglitt, Renormalization of Large-Wave-Vector Magnons in

  11. Dirac Magnons in Honeycomb Ferromagnets

    Science.gov (United States)

    Pershoguba, Sergey S.; Banerjee, Saikat; Lashley, J. C.; Park, Jihwey; Ågren, Hans; Aeppli, Gabriel; Balatsky, Alexander V.

    2018-01-01

    The discovery of the Dirac electron dispersion in graphene [A. H. Castro Neto, et al., The Electronic Properties of Graphene, Rev. Mod. Phys. 81, 109 (2009), 10.1103/RevModPhys.81.109] led to the question of the Dirac cone stability with respect to interactions. Coulomb interactions between electrons were shown to induce a logarithmic renormalization of the Dirac dispersion. With a rapid expansion of the list of compounds and quasiparticle bands with linear band touching [T. O. Wehling, et al., Dirac Materials, Adv. Phys. 63, 1 (2014), 10.1080/00018732.2014.927109], the concept of bosonic Dirac materials has emerged. We consider a specific case of ferromagnets consisting of van der Waals-bonded stacks of honeycomb layers, e.g., chromium trihalides CrX3 (X =F , Cl, Br and I), that display two spin wave modes with energy dispersion similar to that for the electrons in graphene. At the single-particle level, these materials resemble their fermionic counterparts. However, how different particle statistics and interactions affect the stability of Dirac cones has yet to be determined. To address the role of interacting Dirac magnons, we expand the theory of ferromagnets beyond the standard Dyson theory [F. J. Dyson, General Theory of Spin-Wave Interactions, Phys. Rev. 102, 1217 (1956), 10.1103/PhysRev.102.1217, F. J. Dyson, Thermodynamic Behavior of an Ideal Ferromagnet, Phys. Rev. 102, 1230 (1956), 10.1103/PhysRev.102.1230] to the case of non-Bravais honeycomb layers. We demonstrate that magnon-magnon interactions lead to a significant momentum-dependent renormalization of the bare band structure in addition to strongly momentum-dependent magnon lifetimes. We show that our theory qualitatively accounts for hitherto unexplained anomalies in nearly half-century-old magnetic neutron-scattering data for CrBr3 [W. B. Yelon and R. Silberglitt, Renormalization of Large-Wave-Vector Magnons in Ferromagnetic CrBr3 Studied by Inelastic Neutron Scattering: Spin-Wave Correlation

  12. Non-relativistic correspondence of Dirac equation with external electromagnetic field and space-time torsion

    International Nuclear Information System (INIS)

    Goncalves, Bruno; Dias Junior, Mario Marcio

    2013-01-01

    Full text: The discussion of experimental manifestations of torsion at low energies is mainly related to the torsion-spin interaction. In this respect the behavior of Dirac field and the spinning particle in an external torsion field deserves and received very special attention. In this work, we consider the combined action of torsion and magnetic field on the massive spinor field. In this case, the Dirac equation is not straightforward solved. We suppose that the spinor has two components. The equations have mixed terms between the two components. The electromagnetic field is introduced in the action by the usual gauge transformation. The torsion field is described by the field S μ . The main purpose of the work is to get an explicit form to the equation of motion that shows the possible interactions between the external fields and the spinor in a Hamiltonian that is independent to each component. We consider that S 0 is constant and is the unique non-vanishing term of S μ . This simplification is taken just to simplify the algebra, as our main point is not to describe the torsion field itself. In order to get physical analysis of the problem, we consider the non-relativistic approximation. The final result is a Hamiltonian that describes a half spin field in the presence of electromagnetic and torsion external fields. (author)

  13. Solutions of the Dirac Equation with the Shifted DENG-FAN Potential Including Yukawa-Like Tensor Interaction

    Science.gov (United States)

    Yahya, W. A.; Falaye, B. J.; Oluwadare, O. J.; Oyewumi, K. J.

    2013-08-01

    By using the Nikiforov-Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng-Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schr\\"{o}dinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.

  14. Approximate analytical solution of the Dirac equation for pseudospin symmetry with modified Po schl-Teller potential and trigonometric Scarf II non-central potential using asymptotic iteration method

    International Nuclear Information System (INIS)

    Pratiwi, B N; Suparmi, A; Cari, C; Yunianto, M; Husein, A S

    2016-01-01

    We apllied asymptotic iteration method (AIM) to obtain the analytical solution of the Dirac equation in case exact pseudospin symmetry in the presence of modified Pcischl- Teller potential and trigonometric Scarf II non-central potential. The Dirac equation was solved by variables separation into one dimensional Dirac equation, the radial part and angular part equation. The radial and angular part equation can be reduced into hypergeometric type equation by variable substitution and wavefunction substitution and then transform it into AIM type equation to obtain relativistic energy eigenvalue and wavefunctions. Relativistic energy was calculated numerically by Matlab software. And then relativistic energy spectrum and wavefunctions were visualized by Matlab software. The results show that the increase in the radial quantum number n_r causes decrease in the relativistic energy spectrum. The negative value of energy is taken due to the pseudospin symmetry limit. Several quantum wavefunctions were presented in terms of the hypergeometric functions. (paper)

  15. Non-existence of black-hole solutions for the electroweak Einstein-Dirac-Yang/Mills equations

    International Nuclear Information System (INIS)

    Bernard, Yann

    2006-01-01

    We consider a static, spherically symmetric system of a Dirac particle interacting with classical gravity and an electroweak Yang-Mills field. It is shown that the only black-hole solutions of the corresponding coupled equations must be the extreme Reissner-Nordstroem solutions, locally near the event horizon. This work generalizes a series of papers published by F Finster, J Smoller and S-T Yau

  16. Time-dependent massless Dirac fermions in graphene

    Energy Technology Data Exchange (ETDEWEB)

    Khantoul, Boubakeur, E-mail: bobphys@gmail.com [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom); Department of Physics, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel (Algeria); Fring, Andreas, E-mail: a.fring@city.ac.uk [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom)

    2015-10-30

    Using the Lewis–Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent vector potential. The eigenvalue equations for the two spinor components of the Lewis–Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians. - Highlights: • An explicit analytical solution for a massless 2+1 dimensional time-dependent Dirac equation is found. • All steps of the Lewis–Riesenfeld method have been carried out.

  17. Bound-state Dirac eigenvalues for scalar potentials

    International Nuclear Information System (INIS)

    Ram, B.; Arafah, M.

    1981-01-01

    The Dirac equation is solved with a linear and a quadratic scalar potential using an approach in which the Dirac equation is first transformed to a one-dimensional Schroedinger equation with an effective potential. The WKB method is used to obtain the energy eigenvalues. The eigenvalues for the quadratic scalar potential are real just as they are for the linear potential. The results with the linear potential agree well with those obtained by Critchfield. (author)

  18. Axial anomaly and index theorem for Dirac-Kaehler fermions

    International Nuclear Information System (INIS)

    Fonseca Junior, C.A.L. da.

    1985-02-01

    Some aspects of topological influence on gauge field theory are analysed, considering the geometry and differential topology methods. A review of concepts of differential forms, fibered spaces, connection and curvature, showing an interpretation of gauge theory in this context, is presented. The question of fermions, analysing in details the Dirac-Kaehler which fermionic particle is considered a general differential form, is studied. It is shown how the explicit expressions in function of the Dirac spinor components vary with the Dirac matrix representation. The Dirac-Kahler equation contains 4 times (in 4 dimensions) the Dirac equation, each particle being associated an ideal at left of the algebra of general differential forms. These ideals and the SU(4) symmetry among them are also studied on the point of view of spinors and, the group of reduction to one of the ideals is identified as the Cartan subalgebra of this SU(4). Finally, the axial anomaly is calculated through the functional determinant given by the Dirac-Kaehler operator. The regularization method is the Seeley's coefficients. From that results a comparison of the index theorems for the twisted complexes of signature and spin, which proportionality is given by the number of the algebra ideals contained in the Dirac-Kaehler equation and which also manifests in the respective axial anomaly equations. (L.C.) [pt

  19. Predictive equation of state method for heavy materials based on the Dirac equation and density functional theory

    Science.gov (United States)

    Wills, John M.; Mattsson, Ann E.

    2012-02-01

    Density functional theory (DFT) provides a formally predictive base for equation of state properties. Available approximations to the exchange/correlation functional provide accurate predictions for many materials in the periodic table. For heavy materials however, DFT calculations, using available functionals, fail to provide quantitative predictions, and often fail to be even qualitative. This deficiency is due both to the lack of the appropriate confinement physics in the exchange/correlation functional and to approximations used to evaluate the underlying equations. In order to assess and develop accurate functionals, it is essential to eliminate all other sources of error. In this talk we describe an efficient first-principles electronic structure method based on the Dirac equation and compare the results obtained with this method with other methods generally used. Implications for high-pressure equation of state of relativistic materials are demonstrated in application to Ce and the light actinides. Sandia National Laboratories is a multi-program laboratory managed andoperated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

  20. Dirac equation in very special relativity for hydrogen atom

    Energy Technology Data Exchange (ETDEWEB)

    Maluf, R.V., E-mail: r.v.maluf@fisica.ufc.br [Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Caixa Postal 6030, 60455-760 Fortaleza, Ceará (Brazil); Silva, J.E.G., E-mail: euclides@fisica.ufc.br [Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Caixa Postal 6030, 60455-760 Fortaleza, Ceará (Brazil); Cruz, W.T., E-mail: wilamicruz@gmail.com [Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE), Campus Juazeiro do Norte, 63040-000 Juazeiro do Norte, Ceará (Brazil); Almeida, C.A.S., E-mail: carlos@fisica.ufc.br [Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Caixa Postal 6030, 60455-760 Fortaleza, Ceará (Brazil)

    2014-11-10

    In this work, we study the modified Dirac equation in the framework of very special relativity (VSR). The low-energy regime is accessed and the nonrelativistic Hamiltonian is obtained. It turns out that this Hamiltonian is similar to that achieved from the Standard Model Extension (SME) via coupling of the spinor field to a Lorentz-violating term, but new features arise inherited from the non-local character of the VSR. In addition, the implications of the VSR-modified Lorentz symmetry on the spectrum of a hydrogen atom are determined by calculating the first-order energy corrections in the context of standard quantum mechanics. Among the results, we highlight that the modified Hamiltonian provides non-vanishing corrections which lift the degeneracy of the energy levels and allow us to find an upper bound upon the VSR-parameter.

  1. Relativistic particle in a box: Klein-Gordon versus Dirac equations

    Science.gov (United States)

    Alberto, Pedro; Das, Saurya; Vagenas, Elias C.

    2018-03-01

    The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.

  2. Particles and Dirac-type operators on curved spaces

    International Nuclear Information System (INIS)

    Visinescu, Mihai

    2003-01-01

    We review the geodesic motion of pseudo-classical particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of Killing-Yano tensors. Passing from the spinning spaces to the Dirac equation in curved backgrounds we point out the role of the Killing-Yano tensors in the construction of the Dirac-type operators. The general results are applied to the case of the four-dimensional Euclidean Taub-Newman-Unti-Tamburino space. From the covariantly constant Killing-Yano tensors of this space we construct three new Dirac-type operators which are equivalent with the standard Dirac operator. Finally the Runge-Lenz operator for the Dirac equation in this background is expressed in terms of the fourth Killing-Yano tensor which is not covariantly constant. As a rule the covariantly constant Killing-Yano tensors realize certain square roots of the metric tensor. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a one-parameter Lie group connecting this operator with the standard Dirac one. On the other hand, the not covariantly constant Killing-Yano tensors are important in generating hidden symmetries. The presence of not covariantly constant Killing-Yano tensors implies the existence of non-standard supersymmetries in point particle theories on curved background. (author)

  3. Are Dirac electrons faster than light?

    International Nuclear Information System (INIS)

    De Angelis, G.F.

    1986-01-01

    This paper addresses the problem of path integral solutions of the Dirac equation. The path integral construction of the Dirac propagator which extends Fynman's checkerboard rule in more than one space dimension is discussed. A distinguished feature of such extension is the fact that the speed of a relativistic electron is actually greater than the speed of light when the space has more than one dimension. A technique employed in obtaining an extension to higher space dimension is described which consists in comparing continuity equations of quantum mechanical origin with forward Kolmogorov equations for suitable chosen classes of random processes

  4. Avoid the tsunami of the Dirac sea in the imaginary time step method

    International Nuclear Information System (INIS)

    Zhang, Ying; Liang, Haozhao; Meng, Jie

    2010-01-01

    The discrete single-particle spectra in both the Fermi and Dirac sea have been calculated by the imaginary time step (ITS) method for the Schroedinger-like equation after avoiding the "tsunami" of the Dirac sea, i.e. the diving behavior of the single-particle level into the Dirac sea in the direct application of the ITS method for the Dirac equation. It is found that by the transform from the Dirac equation to the Schroedinger-like equation, the single-particle spectra, which extend from the positive to the negative infinity, can be separately obtained by the ITS evolution in either the Fermi sea or the Dirac sea. Identical results with those in the conventional shooting method have been obtained via the ITS evolution for the equivalent Schroedinger-like equation, which demonstrates the feasibility, practicality and reliability of the present algorithm and dispels the doubts on the ITS method in the relativistic system. (author)

  5. Dirac equation for massive neutrinos in a Schwarzschild-de Sitter spacetime from a 5D vacuum

    International Nuclear Information System (INIS)

    Sánchez, Pablo Alejandro; Anabitarte, Mariano; Bellini, Mauricio

    2011-01-01

    Starting from a Dirac equation for massless neutrino in a 5D Ricci-flat background metric, we obtain the effective 4D equation for massive neutrino in a Schwarzschild-de Sitter (SdS) background metric from an extended SdS 5D Ricci-flat metric. We use the fact that the spin connection is defined to an accuracy of a vector, so that the covariant derivative of the spinor field is strongly dependent of the background geometry. We show that the mass of the neutrino can be induced from the extra space-like dimension.

  6. Hawking radiation of Dirac particles in the hot NUT-Kerr-Newman spacetime

    International Nuclear Information System (INIS)

    Ahmed, M.

    1991-01-01

    The Hawking radiation of charged Dirac particles on the horizons of the hot NUT-Kerr-Newman spacetime is studied in this paper. To this end, we obtain the radial decoupled Dirac equation for the electron in the hot NUT-Kerr-Newman spacetime. Next we solve the Dirac equation near the horizons. Finally, by analytic continuation, the Hawking thermal spectrum formula of Dirac particles is obtained. The problem of the Hawking evaporation of Dirac particles in the hot NUT-Kerr-Newman background is thus solved. (orig.)

  7. Dirac and Weyl semimetals with holographic interactions

    NARCIS (Netherlands)

    Jacobs, V.P.J.

    2015-01-01

    Dirac and Weyl semimetals are states of matter exhibiting the relativistic physics of, respectively, the Dirac and Weyl equation in a three-dimensional bulk material. These three-dimensional semimetals have recently been realized experimentally in various crystals. Theoretically, especially the

  8. Accidental degeneracy of double Dirac cones in a phononic crystal

    KAUST Repository

    Chen, Ze-Guo; Ni, Xu; Wu, Ying; He, Cheng; Sun, Xiao-Chen; Zheng, Li-Yang; Lu, Ming-Hui; Chen, Yan-Feng

    2014-01-01

    Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of the Brillouin zone in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of this quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique properties in wave propagating, such as defect-insensitive propagating character and the Talbot effect.

  9. Accidental degeneracy of double Dirac cones in a phononic crystal

    KAUST Repository

    Chen, Ze-Guo

    2014-04-09

    Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of the Brillouin zone in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of this quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique properties in wave propagating, such as defect-insensitive propagating character and the Talbot effect.

  10. A generalized advection dispersion equation

    Indian Academy of Sciences (India)

    This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.

  11. A CPT-even and Lorentz-Violating nonminimal coupling in the Dirac equation

    Energy Technology Data Exchange (ETDEWEB)

    Ferreira Junior, Manoel; Casana, M.R.; Santos, Frederico E.P. dos; Silva, E.O. [UFMA, Sao Luis (Brazil); Passos, E. [UFCG, Campina Grande, PB (Brazil)

    2013-07-01

    Full text: The Standard Model Extension (SME) has been the usual framework for investigating signals of Lorentz violation in physical systems. It is the natural framework for studying properties of physical systems with Lorentz-violation since it includes Lorentz-violating terms in all sectors of the minimal standard model. The Lorentz-violating (LV) terms are generated as vacuum expectation values of tensors defined in a high energy scale. This framework has inspired a great deal of investigation in recent years. Such works encompass several distinct aspects involving fermion systems and radiative corrections, CPT- probing experiments, the electromagnetic CPT- and Lorentz-odd term, the 19 electromagnetic CPT-even coefficients. Recently, some studies involving higher dimensional operators have also been reported with great interest, including nonminimal interactions. These many contributions have elucidated the effects induced by Lorentz violation and served to set up stringent upper bounds on the LV coefficients. In the present work, we propose a new CPT-even, dimension-five, nonminimal coupling linking the fermionic and gauge fields in the context of the Dirac equation, involving the CPT-even tensor of the gauge term of the SME. By considering the nonrelativistic limit of the modified Dirac equation, we explicitly evaluate the new contributions to the nonrelativistic Hamiltonian. These new terms imply a direct correction on the anomalous magnetic moment, a kind of electrical Zeeman-like effect on the atomic spectrum, and a Rashba-like coupling term. These effects are then used to impose upper bounds on the magnitude of the non minimally coupled LV coefficients at the level of 1 part in 10{sub 16}. (author)

  12. A CPT-even and Lorentz-Violating nonminimal coupling in the Dirac equation

    International Nuclear Information System (INIS)

    Ferreira Junior, Manoel; Casana, M.R.; Santos, Frederico E.P. dos; Silva, E.O.; Passos, E.

    2013-01-01

    Full text: The Standard Model Extension (SME) has been the usual framework for investigating signals of Lorentz violation in physical systems. It is the natural framework for studying properties of physical systems with Lorentz-violation since it includes Lorentz-violating terms in all sectors of the minimal standard model. The Lorentz-violating (LV) terms are generated as vacuum expectation values of tensors defined in a high energy scale. This framework has inspired a great deal of investigation in recent years. Such works encompass several distinct aspects involving fermion systems and radiative corrections, CPT- probing experiments, the electromagnetic CPT- and Lorentz-odd term, the 19 electromagnetic CPT-even coefficients. Recently, some studies involving higher dimensional operators have also been reported with great interest, including nonminimal interactions. These many contributions have elucidated the effects induced by Lorentz violation and served to set up stringent upper bounds on the LV coefficients. In the present work, we propose a new CPT-even, dimension-five, nonminimal coupling linking the fermionic and gauge fields in the context of the Dirac equation, involving the CPT-even tensor of the gauge term of the SME. By considering the nonrelativistic limit of the modified Dirac equation, we explicitly evaluate the new contributions to the nonrelativistic Hamiltonian. These new terms imply a direct correction on the anomalous magnetic moment, a kind of electrical Zeeman-like effect on the atomic spectrum, and a Rashba-like coupling term. These effects are then used to impose upper bounds on the magnitude of the non minimally coupled LV coefficients at the level of 1 part in 10 16 . (author)

  13. Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves

    Science.gov (United States)

    Grava, T.; Klein, C.; Pitton, G.

    2018-02-01

    A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

  14. Dirac Fermions in an Antiferromagnetic Semimetal

    Science.gov (United States)

    Tang, Peizhe; Zhou, Quan; Xu, Gang; Zhang, Shou-Cheng; Shou-Cheng Zhang's Group Team, Prof.

    Analogues of the elementary particles have been extensively searched for in condensed matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low energy excitations in materials now known as Dirac semimetals. All the currently known Dirac semimetals are nonmagnetic with both time-reversal symmetry  and inversion symmetry "". Here we show that Dirac fermions can exist in one type of antiferromagnetic systems, where both  and "" are broken but their combination "" is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyze the robustness of the Dirac points under symmetry protections, and demonstrate its distinctive bulk dispersions as well as the corresponding surface states by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism. We acknowledge the DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-AC02-76SF00515, NSF under Grant No.DMR-1305677 and FAME, one of six centers of STARnet.

  15. Analytical solutions of advection-dispersion equation for varying ...

    African Journals Online (AJOL)

    Analytical solutions are obtained for a one-dimensional advection–dispersion equation with variable coefficients in a longitudinal domain. Two cases are considered. In the first one the solute dispersion is time dependent along a uniform flow in a semi-infinite domain while in the second case the dispersion and the velocity ...

  16. Dirac directional emission in anisotropic zero refractive index photonic crystals.

    Science.gov (United States)

    He, Xin-Tao; Zhong, Yao-Nan; Zhou, You; Zhong, Zhi-Chao; Dong, Jian-Wen

    2015-08-14

    A certain class of photonic crystals with conical dispersion is known to behave as isotropic zero-refractive-index medium. However, the discrete building blocks in such photonic crystals are limited to construct multidirectional devices, even for high-symmetric photonic crystals. Here, we show multidirectional emission from low-symmetric photonic crystals with semi-Dirac dispersion at the zone center. We demonstrate that such low-symmetric photonic crystal can be considered as an effective anisotropic zero-refractive-index medium, as long as there is only one propagation mode near Dirac frequency. Four kinds of Dirac multidirectional emitters are achieved with the channel numbers of five, seven, eleven, and thirteen, respectively. Spatial power combination for such kind of Dirac directional emitter is also verified even when multiple sources are randomly placed in the anisotropic zero-refractive-index photonic crystal.

  17. Drift-free kinetic equations for turbulent dispersion

    Science.gov (United States)

    Bragg, A.; Swailes, D. C.; Skartlien, R.

    2012-11-01

    The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.

  18. Shot noise in systems with semi-Dirac points

    International Nuclear Information System (INIS)

    Zhai, Feng; Wang, Juan

    2014-01-01

    We calculate the ballistic conductance and shot noise of electrons through a two-dimensional stripe system (width W ≫ length L) with semi-Dirac band-touching points. We find that the ratio between zero-temperature noise power and mean current (the Fano factor) is highly anisotropic. When the transport is along the linear-dispersion direction and the Fermi energy is fixed at the semi-Dirac point, the Fano factor has a universal value F = 0.179 while a minimum conductivity exists and scales with L 1∕2 . Along the parabolic dispersion direction, the Fano factor at the semi-Dirac point has a contact-independent limit exceeding 0.9, which varies weakly with L due to the common-path interference of evanescent waves. Our findings suggest a way to discern the type of band-touching points

  19. On an uninterpretated tensor in Dirac's theory

    International Nuclear Information System (INIS)

    Costa de Beauregard, O.

    1989-01-01

    Franz, in 1935, deduced systematically from the Dirac equation 10 tensorial equations, 5 with a mechanical interpretation, 5 with an electromagnetic interpretation, which are also consequences of Kemmer's formalism for spins 1 and 0; Durand, in 1944, operating similarly with the second order Dirac equation, obtained, 10 equations, 5 of which expressing the divergences of the Gordon type tensors. Of these equations, together with the tensors they imply, some are easily interpreted by reference to the classical theories, some other remain uniterpreted. Recently (1988) we proposed a theory of the coupling between Einstein's gravity field and the 5 Franz mechanical equations, yielding as a bonus the complete interpretation of the 5 Franz mechanical equations. This is an incitation to reexamine the 5 electromagnetic equations. We show here that two of these, together with one of the Durand equations, implying the same tensor, remain uninterpreted. This is proposed as a challenge to the reader's sagacity [fr

  20. Electric field driven plasmon dispersion in AlGaN/GaN high electron mobility transistors

    International Nuclear Information System (INIS)

    Tan Ren-Bing; Qin Hua; Zhang Xiao-Yu; Xu Wen

    2013-01-01

    We present a theoretical study on the electric field driven plasmon dispersion of the two-dimensional electron gas (2DEG) in AlGaN/GaN high electron mobility transistors (HEMTs). By introducing a drifted Fermi—Dirac distribution, we calculate the transport properties of the 2DEG in the AlGaN/GaN interface by employing the balance-equation approach based on the Boltzmann equation. Then, the nonequilibrium Fermi—Dirac function is obtained by applying the calculated electron drift velocity and electron temperature. Under random phase approximation (RPA), the electric field driven plasmon dispersion is investigated. The calculated results indicate that the plasmon frequency is dominated by both the electric field E and the angle between wavevector q and electric field E. Importantly, the plasmon frequency could be tuned by the applied source—drain bias voltage besides the gate voltage (change of the electron density)

  1. Counter-diabatic driving for Dirac dynamics

    Science.gov (United States)

    Fan, Qi-Zhen; Cheng, Xiao-Hang; Chen, Xi

    2018-03-01

    In this paper, we investigate the fast quantum control of Dirac equation dynamics by counter-diabatic driving, sharing the concept of shortcut to adiabaticity. We systematically calculate the counter-diabatic terms in different Dirac systems, like graphene and trapped ions. Specially, the fast and robust population inversion processes are achieved in Dirac system, taking into account the quantum simulation with trapped ions. In addition, the population transfer between two bands can be suppressed by counter-diabatic driving in graphene system, which might have potential applications in opt-electric devices.

  2. Radiative heat transfer in 2D Dirac materials

    International Nuclear Information System (INIS)

    Rodriguez-López, Pablo; Tse, Wang-Kong; Dalvit, Diego A R

    2015-01-01

    We compute the radiative heat transfer between two sheets of 2D Dirac materials, including topological Chern insulators and graphene, within the framework of the local approximation for the optical response of these materials. In this approximation, which neglects spatial dispersion, we derive both numerically and analytically the short-distance asymptotic of the near-field heat transfer in these systems, and show that it scales as the inverse of the distance between the two sheets. Finally, we discuss the limitations to the validity of this scaling law imposed by spatial dispersion in 2D Dirac materials. (paper)

  3. A Route to Dirac Liquid Theory: A Fermi Liquid Description for Dirac Materials

    Science.gov (United States)

    Gochan, Matthew; Bedell, Kevin

    Since the pioneering work developed by L.V. Landau sixty years ago, Fermi Liquid Theory has seen great success in describing interacting Fermi systems. While much interest has been generated over the study of non-Fermi Liquid systems, Fermi Liquid theory serves as a formidable model for many systems and offers a rich amount of of results and insight. The recent classification of Dirac Materials, and the lack of a unifying theoretical framework for them, has motivated our study. Dirac materials are a versatile class of materials in which an abundance of unique physical phenomena can be observed. Such materials are found in all dimensions, with the shared property that their low-energy fermionic excitations behave as massless Dirac fermions and are therefore governed by the Dirac equation. The most popular Dirac material, graphene, is the focus of this work. We present our Fermi Liquid description of Graphene. We find many interesting results, specifically in the transport and dynamics of the system. Additionally, we expand on previous work regarding the Virial Theorem and its impact on the Fermi Liquid parameters in graphene. Finally, we remark on viscoelasticity of Dirac Materials and other unusual results that are consequences of AdS-CFT.

  4. Superstatistics of the Klein-Gordon equation in deformed formalism for modified Dirac delta distribution

    Science.gov (United States)

    Sargolzaeipor, S.; Hassanabadi, H.; Chung, W. S.

    2018-04-01

    The Klein-Gordon equation is extended in the presence of an Aharonov-Bohm magnetic field for the Cornell potential and the corresponding wave functions as well as the spectra are obtained. After introducing the superstatistics in the statistical mechanics, we first derived the effective Boltzmann factor in the deformed formalism with modified Dirac delta distribution. We then use the concepts of the superstatistics to calculate the thermodynamics properties of the system. The well-known results are recovered by the vanishing of deformation parameter and some graphs are plotted for the clarity of our results.

  5. Dirac spinors for doubly special relativity and κ-Minkowski noncommutative spacetime

    International Nuclear Information System (INIS)

    Agostini, Alessandra; Amelino-Camelia, Giovanni; Arzano, Michele

    2004-01-01

    We construct a Dirac equation that is consistent with one of the recently-proposed schemes for a 'doubly special relativity', a relativity with both an observer-independent velocity scale (still naturally identified with the speed-of-light constant) and an observer-independent length/momentum scale (possibly given by the Planck length/momentum). We find that the introduction of the second observer-independent scale only induces a mild deformation of the structure of Dirac spinors. We also show that our modified Dirac equation naturally arises in constructing a Dirac equation in the κ-Minkowski noncommutative spacetime. Previous, more heuristic studies had already argued for a possible role of doubly special relativity in κ-Minkowski, but remained vague on the nature of the consistency requirements that should be implemented in order to assure the observer-independence of the two scales. We find that a key role is played by the choice of a differential calculus in κ-Minkowski. A much-studied choice of the differential calculus does lead to our doubly special relativity Dirac equation, but a different scenario is encountered for another popular choice of differential calculus

  6. Factoring the dispersion relation in the presence of Lorentz violation

    International Nuclear Information System (INIS)

    Colladay, Don; McDonald, Patrick; Mullins, David

    2010-01-01

    We produce an explicit formula for the dispersion relation for the Dirac equation in the standard model extension in the presence of Lorentz violation. Our expression is obtained using novel techniques which exploit the algebra of quaternions. The dispersion relation is found to conveniently factor in two special cases that each involve a mutually exclusive set of nonvanishing Lorentz-violating parameters. This suggests that a useful approach to studies of Lorentz-violating models is to split the parameter space into two separate pieces, each of which yields a simple, tractable dispersion relation that can be used for analysis.

  7. Fermi field and Dirac oscillator in a Som-Raychaudhuri space-time

    Science.gov (United States)

    de Montigny, Marc; Zare, Soroush; Hassanabadi, Hassan

    2018-05-01

    We investigate the relativistic dynamics of a Dirac field in the Som-Raychaudhuri space-time, which is described by a Gödel-type metric and a stationary cylindrical symmetric solution of Einstein field equations for a charged dust distribution in rigid rotation. In order to analyze the effect of various physical parameters of this space-time, we solve the Dirac equation in the Som-Raychaudhuri space-time and obtain the energy levels and eigenfunctions of the Dirac operator by using the Nikiforov-Uvarov method. We also examine the behaviour of the Dirac oscillator in the Som-Raychaudhuri space-time, in particular, the effect of its frequency and the vorticity parameter.

  8. The nonlinear dirac equation in Bose-Einstein condensates: vortex solutions and spectra in a weak harmonic trap

    Science.gov (United States)

    Haddad, L. H.; Carr, Lincoln D.

    2015-11-01

    We analyze the vortex solution space of the (2+1)-dimensional nonlinear Dirac equation for bosons in a honeycomb optical lattice at length scales much larger than the lattice spacing. Dirac point relativistic covariance combined with s-wave scattering for bosons leads to a large number of vortex solutions characterized by different functional forms for the internal spin and overall phase of the order parameter. We present a detailed derivation of these solutions which include skyrmions, half-quantum vortices, Mermin-Ho and Anderson-Toulouse vortices for vortex winding {\\ell }=1. For {\\ell }≥slant 2 we obtain topological as well as non-topological solutions defined by the asymptotic radial dependence. For arbitrary values of ℓ the non-topological solutions include bright ring-vortices which explicitly demonstrate the confining effects of the Dirac operator. We arrive at solutions through an asymptotic Bessel series, algebraic closed-forms, and using standard numerical shooting methods. By including a harmonic potential to simulate a finite trap we compute the discrete spectra associated with radially quantized modes. We demonstrate the continuous spectral mapping between the vortex and free particle limits for all of our solutions.

  9. On Huygens' principle for Dirac operators associated to electromagnetic fields

    Directory of Open Access Journals (Sweden)

    CHALUB FABIO A.C.C.

    2001-01-01

    Full Text Available We study the behavior of massless Dirac particles, i.e., solutions of the Dirac equation with m = 0 in the presence of an electromagnetic field. Our main result (Theorem 1 is that for purely real or imaginary fields any Huygens type (in Hadamard's sense Dirac operators is equivalent to the free Dirac operator, equivalence given by changes of variables and multiplication (right and left by nonzero functions.

  10. Leptons as systems of Dirac particles

    International Nuclear Information System (INIS)

    Borstnik, N.M.; Kaluza, M.

    1988-03-01

    Charged leptons are treated as systems of three equal independent Dirac particles in an external static effective potential which has a vector and a scalar term. The potential is constructed to reproduce the experimental mass spectrum of the charged leptons. The Dirac covariant equation for three interacting particles is discussed in order to comment on the magnetic moment of leptons. (author). 9 refs, 2 figs, 4 tabs

  11. Quantum geometry of the Dirac fermions

    International Nuclear Information System (INIS)

    Korchemskij, G.P.

    1989-01-01

    The bosonic path integral formalism is developed for Dirac fermions interacting with a nonabelian gauge field in the D-dimensional Euclidean space-time. The representation for the effective action and correlation functions of interacting fermions as sums over all bosonic paths on the complex projective space CP 2d-1 , (2d=2 [ D 2] is derived where all the spinor structure is absorbed by the one-dimensional Wess-Zumino term. It is the Wess-Zumino term that ensures all necessary properties of Dirac fermions under quantization. i.e., quantized values of the spin, Dirac equation, Fermi statistics. 19 refs

  12. Exact Solution of Klein-Gordon and Dirac Equations with Snyder-de Sitter Algebra

    Science.gov (United States)

    Merad, M.; Hadj Moussa, M.

    2018-01-01

    In this paper, we present the exact solution of the (1+1)-dimensional relativistic Klein-Gordon and Dirac equations with linear vector and scalar potentials in the framework of deformed Snyder-de Sitter model. We introduce some changes of variables, we show that a one-dimensional linear potential for the relativistic system in a space deformed can be equivalent to the trigonometric Rosen-Morse potential in a regular space. In both cases, we determine explicitly the energy eigenvalues and their corresponding eigenfunctions expressed in terms of Romonovski polynomials. The limiting cases are analyzed for α 1 and α 2 → 0 and are compared with those of literature.

  13. On a model for baryons based on a Dirac equation with confining potentials

    International Nuclear Information System (INIS)

    Ferreira, P.L.

    1977-06-01

    An independent particle model for baryons is studied in which the quarks obey a Dirac equation with an average potential of the form V(r) = 1/2 (1 + β)(V 0 + lambda r - γ/r). A numerical solution is obtained for S-waves. Several properties of the 1/2 + baryons such as the ratio (G sub(A)/G sub(V)) sub (N) for nucleons and baryon magnetic moments are analysed in terms of the model. A comparison with the case of a pure linear potential and with a pure harmonic oscillator is made, showing that it is possible to obtain a better agreement with the data in the present case

  14. Phenomenological optical model for p-/sup 4/He elastic scattering. [560 to 1730 MeV: Dirac equation optical model analysis

    Energy Technology Data Exchange (ETDEWEB)

    Mercer, R L [International Business Machines Corp., Yorktown Heights, N.Y. (USA); Arnold, L G; Clark, B C [Ohio State Univ., Columbus (USA). Dept. of Physics

    1978-01-30

    The results of a Dirac equation optical model analysis of p-/sup 4/He elastic scattering data are reported. The optical potential obtained at 1029 MeV reproduces the systematics of p-/sup 4/He data over the energy range from 560 to 1730 MeV.

  15. Dispersion relation and Landau damping of waves in high-energy density plasmas

    International Nuclear Information System (INIS)

    Zhu Jun; Ji Peiyong

    2012-01-01

    We present a theoretical investigation on the propagation of electromagnetic waves and electron plasma waves in high energy density plasmas using the covariant Wigner function approach. Based on the covariant Wigner function and Dirac equation, a relativistic quantum kinetic model is established to describe the physical processes in high-energy density plasmas. With the zero-temperature Fermi–Dirac distribution, the dispersion relation and Landau damping of waves containing the relativistic quantum corrected terms are derived. The relativistic quantum corrections to the dispersion relation and Landau damping are analyzed by comparing our results with those obtained in classical and non-relativistic quantum plasmas. We provide a detailed discussion on the Landau damping obtained in classical plasmas, non-relativistic Fermi plasmas and relativistic Fermi plasmas. The contributions of the Bohm potential, the Fermi statistics pressure and relativistic effects to the dispersion relation and Landau damping of waves are quantitatively calculated with real plasma parameters. (paper)

  16. Quantum mechanics of Yano tensors: Dirac equation in curved spacetime

    International Nuclear Information System (INIS)

    Cariglia, Marco

    2004-01-01

    In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors

  17. Analysis and classification of nonlinear dispersive evolution equations in the potential representation

    International Nuclear Information System (INIS)

    Eichmann, U.A.; Draayer, J.P.; Ludu, A.

    2002-01-01

    A potential representation for the subset of travelling solutions of nonlinear dispersive evolution equations is introduced. The procedure involves reduction of a third-order partial differential equation to a first-order ordinary differential equation. The potential representation allows us to deduce certain properties of the solutions without the actual need to solve the underlying evolution equation. In particular, the paper deals with the so-called K(n, m) equations. Starting from their respective potential representations it is shown that these equations can be classified according to a simple point transformation. As a result, e.g., all equations with linear dispersion join the same equivalence class with the Korteweg-deVries equation being its representative, and all soliton solutions of higher order nonlinear equations are thus equivalent to the KdV soliton. Certain equations with both linear and quadratic dispersions can also be treated within this equivalence class. (author)

  18. Superconductivity in doped Dirac semimetals

    Science.gov (United States)

    Hashimoto, Tatsuki; Kobayashi, Shingo; Tanaka, Yukio; Sato, Masatoshi

    2016-07-01

    We theoretically study intrinsic superconductivity in doped Dirac semimetals. Dirac semimetals host bulk Dirac points, which are formed by doubly degenerate bands, so the Hamiltonian is described by a 4 ×4 matrix and six types of k -independent pair potentials are allowed by the Fermi-Dirac statistics. We show that the unique spin-orbit coupling leads to characteristic superconducting gap structures and d vectors on the Fermi surface and the electron-electron interaction between intra and interorbitals gives a novel phase diagram of superconductivity. It is found that when the interorbital attraction is dominant, an unconventional superconducting state with point nodes appears. To verify the experimental signature of possible superconducting states, we calculate the temperature dependence of bulk physical properties such as electronic specific heat and spin susceptibility and surface state. In the unconventional superconducting phase, either dispersive or flat Andreev bound states appear between point nodes, which leads to double peaks or a single peak in the surface density of states, respectively. As a result, possible superconducting states can be distinguished by combining bulk and surface measurements.

  19. The Dirac equation and the normalization of its solutions in a closed Friedmann- Robertson-Walker universe

    Energy Technology Data Exchange (ETDEWEB)

    Finster, Felix [NWF I-Mathematik, Universitaet Regensburg, D-93040 Regensburg (Germany); Reintjes, Moritz, E-mail: Felix.Finster@mathematik.uni-regensburg.d, E-mail: moritz@math.ucdavis.ed [Mathematics Department, University of California, Davis, CA 95616 (United States)

    2009-05-21

    We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and separate the spatial and time variables. In the case of a closed universe, the spatial dependence is solved explicitly, giving rise to a discrete set of solutions. We compute the probability integral and analyze a spacetime normalization integral. This analysis allows us to introduce the fermionic projector in a closed Friedmann-Robertson-Walker geometry and to specify its global normalization as well as its local form.

  20. The Dirac equation and the normalization of its solutions in a closed Friedmann- Robertson-Walker universe

    International Nuclear Information System (INIS)

    Finster, Felix; Reintjes, Moritz

    2009-01-01

    We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and separate the spatial and time variables. In the case of a closed universe, the spatial dependence is solved explicitly, giving rise to a discrete set of solutions. We compute the probability integral and analyze a spacetime normalization integral. This analysis allows us to introduce the fermionic projector in a closed Friedmann-Robertson-Walker geometry and to specify its global normalization as well as its local form.

  1. Simulation of Zitterbewegung by modelling the Dirac equation in Metamaterials

    OpenAIRE

    Ahrens, Sven; Jiang, Jun; Sun, Yong; Zhu, Shi-Yao

    2015-01-01

    We develop a dynamic description of an effective Dirac theory in metamaterials, in which the wavefunction is modeled by the corresponding electric and magnetic field in the metamaterial. This electro-magnetic field can be probed in the experimental setup, which means that the wavefunction of the effective theory is directly accessible by measurement. Our model is based on a plane wave expansion, which ravels the identification of Dirac spinors with single-frequency excitations of the electro-...

  2. A strong-topological-metal material with multiple Dirac cones

    OpenAIRE

    Ji, Huiwen; Pletikosić, I; Gibson, Q. D.; Sahasrabudhe, Girija; Valla, T.; Cava, R. J.

    2015-01-01

    We report a new, cleavable, strong-topological-metal, Zr2Te2P, which has the same tetradymite-type crystal structure as the topological insulator Bi2Te2Se. Instead of being a semiconductor, however, Zr2Te2P is metallic with a pseudogap between 0.2 and 0.7 eV above the fermi energy (EF). Inside this pseudogap, two Dirac dispersions are predicted: one is a surface-originated Dirac cone protected by time-reversal symmetry (TRS), while the other is a bulk-originated and slightly gapped Dirac cone...

  3. Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

    KAUST Repository

    Zhang, Zhendong

    2016-07-26

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.

  4. A matricial approach for the Dirac-Kahler formalism

    International Nuclear Information System (INIS)

    Goto, M.

    1987-01-01

    A matricial approach for the Dirac-Kahler formalism is considered. It is shown that the matrical approach i) brings a great computational simplification compared to the common use of differential forms and that ii) by an appropriate choice of notation, it can be extended to the lattice, including a matrix Dirac-Kahler equation. (author) [pt

  5. A new formalism for Dirac-like theories with curved space-time

    International Nuclear Information System (INIS)

    Halliday, D.W.

    1992-01-01

    This paper develops a formalism for Dirac-like equations (linear complex differential equations, linear in all derivatives), allowing for general coordinate and open-quotes spin-spaceclose quotes (internal space) transformations. A correspondence principle is also developed by requiring solutions to the Dirac-like equations to be solutions to a Klein-Gordon equation that is likewise generally invariant. Through this treatment, previous generalizations of the Dirac equation are incorporated, and various aspects of these methods are analyzed. Furthermore, the Yang-Mills-like gauge fields allowed, or required, by the formalism are expressed, and found to be associated with much larger symmetries than most would desire, suggesting either there has been much greater symmetry breaking than expected, or else few of the particles accepted as fundamental really are. It is also found that unless the space-time is open-quotes parallelizableclose quotes (so there exist fields that are everywhere parallel transported into themselves, which is not generally the case), or some of the wave function components (and separately some of the Yang-Mills fields) are interdependent, one cannot have the Dirac gamma operators commuting with the momentum operators, while simultaneously having a spin-space metric that is compatible with the Yang-Mills fields

  6. Quantum transport through 3D Dirac materials

    International Nuclear Information System (INIS)

    Salehi, M.; Jafari, S.A.

    2015-01-01

    Bismuth and its alloys provide a paradigm to realize three dimensional materials whose low-energy effective theory is given by Dirac equation in 3+1 dimensions. We study the quantum transport properties of three dimensional Dirac materials within the framework of Landauer–Büttiker formalism. Charge carriers in normal metal satisfying the Schrödinger equation, can be split into four-component with appropriate matching conditions at the boundary with the three dimensional Dirac material (3DDM). We calculate the conductance and the Fano factor of an interface separating 3DDM from a normal metal, as well as the conductance through a slab of 3DDM. Under certain circumstances the 3DDM appears transparent to electrons hitting the 3DDM. We find that electrons hitting the metal-3DDM interface from metallic side can enter 3DDM in a reversed spin state as soon as their angle of incidence deviates from the direction perpendicular to interface. However the presence of a second interface completely cancels this effect

  7. Quantum transport through 3D Dirac materials

    Energy Technology Data Exchange (ETDEWEB)

    Salehi, M. [Department of Physics, Sharif University of Technology, Tehran 11155-9161 (Iran, Islamic Republic of); Jafari, S.A., E-mail: jafari@physics.sharif.edu [Department of Physics, Sharif University of Technology, Tehran 11155-9161 (Iran, Islamic Republic of); Center of Excellence for Complex Systems and Condensed Matter (CSCM), Sharif University of Technology, Tehran 1458889694 (Iran, Islamic Republic of)

    2015-08-15

    Bismuth and its alloys provide a paradigm to realize three dimensional materials whose low-energy effective theory is given by Dirac equation in 3+1 dimensions. We study the quantum transport properties of three dimensional Dirac materials within the framework of Landauer–Büttiker formalism. Charge carriers in normal metal satisfying the Schrödinger equation, can be split into four-component with appropriate matching conditions at the boundary with the three dimensional Dirac material (3DDM). We calculate the conductance and the Fano factor of an interface separating 3DDM from a normal metal, as well as the conductance through a slab of 3DDM. Under certain circumstances the 3DDM appears transparent to electrons hitting the 3DDM. We find that electrons hitting the metal-3DDM interface from metallic side can enter 3DDM in a reversed spin state as soon as their angle of incidence deviates from the direction perpendicular to interface. However the presence of a second interface completely cancels this effect.

  8. The Dirac field in the electromagnetic potential of a charged string; Das Dirac-Feld im elektromagnetischen Potential eines geladenen Strings

    Energy Technology Data Exchange (ETDEWEB)

    Anaguano, L.

    2005-07-01

    According to the theory of Quantum Electrodynamics (QED) the vacuum state will change in the presence of very strong electromagnetic fields. If the external field (in the simplest case purely electrostatic) exceeds a certain critical value the creation of electron-positron pairs will ensue, resulting the the formation of a charged vacuum. This process is characterized by the emergence of electron states with a binding energy larger than twice the electron rest mass. The effect up to now usually was studied for spherically symmetric systems, in particular for the Coulomb potential of a heavy nucleus. In the present thesis we investigate, how this phenomenon changes when passing from spherical to cylindrical geometry. For this, we derive the solutions of the Dirac equation for electrons in the electrostatic potential of a long, thin charged cylinder (a ''charged string'') and study the ensuing supercritical effects. Since the logarithmic potential of an infinitely long string rises indefinitely with growing distance, all electron states should be supercritical (i.e., electrons should be able to tunnel through the particle-antiparticle gap of the Dirac equation). Therefore on may expect that the central charge will surround itself with an oppositely charged sheath of vacuum electrons, leading to neutralization of the string. To develop a quantitative description of this process, we investigate the solutions of the Poisson equation and the Dirac equation in cylindrical symmetry. In the first step a series expansion of the electrostatic potential in the central plane of a homogeneously charge cylinder of finite length and finite radius is derived. Subsequently, we employ the tetrad (vierbein) formalism to separate the Dirac equation in cylindrical coordinates. The resulting radial Dirac equation is transformed to Schroedinger type. The bound states are evaluated using the method of uniform approximation (a version of the WKB approximation). We study

  9. Dirac equation in a de Sitter expansion for massive neutrinos from modern Kaluza-Klein theory

    International Nuclear Information System (INIS)

    Sánchez, Pablo Alejandro; Anabitarte, Mariano; Bellini, Mauricio

    2012-01-01

    Using the modern Kaluza-Klein theory of gravity (or the Induced Matter theory), we study the Dirac equation for massive neutrinos on a de Sitter background metric from a 5D Riemann-flat (and hence Ricci-flat) extended de Sitter metric, on which is defined the vacuum for test massless 1/2-spin neutral fields minimally coupled to gravity and free of any other interactions. We obtain that the effective 4D masses of the neutrinos can only take three possible values, which are related to the (static) foliation of the fifth and noncompact extra dimension.

  10. The neutron's Dirac-equation: Its rigorous solution at slab-like magnetic fields, non-relativistic approximation, energy spectra and statistical characteristics

    International Nuclear Information System (INIS)

    Zhang Yongde.

    1987-03-01

    In this paper, the neutron Dirac-equation is presented. After decoupling it into two equations of the simple spinors, the rigorous solution of this equation is obtained in the case of slab-like uniform magnetic fields at perpendicular incidence. At non-relativistic approximation and first order approximation of weak field (NRWFA), our results have included all results that have been obtained in references for this case up to now. The corresponding transformations of the neutron's spin vectors are given. The single particle spectrum and its approximate expression are obtained. The characteristics of quantum statistics with the approximate expression of energy spectrum are studied. (author). 15 refs

  11. Magnetic moments of confined quarks and baryons in an independent-quark model based on Dirac equation with power-law potential

    International Nuclear Information System (INIS)

    Barik, N.; Das, M.

    1983-01-01

    The effect of confinement on the magnetic moment of a quark has been studied in a simple independent-quark model based on the Dirac equation with a power-law potential. The magnetic moments so obtained for the constituent quarks, which are found to be significantly different from their corresponding Dirac moments, are used in predicting the magnetic moments of baryons in the nucleon octet as well as those in the charmed and b-flavored sectors. We not only get an improved result for the proton magnetic moment, but the calculation for the rest of the nucleon octet also turns out to be in reasonable agreement with experiment. The overall predictions for the charmed and b-flavored baryons are also comparable with other model predictions

  12. The Dirac equation and the normalization of its solutions in a closed Friedmann- Robertson-Walker universe

    Science.gov (United States)

    Finster, Felix; Reintjes, Moritz

    2009-05-01

    We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and separate the spatial and time variables. In the case of a closed universe, the spatial dependence is solved explicitly, giving rise to a discrete set of solutions. We compute the probability integral and analyze a spacetime normalization integral. This analysis allows us to introduce the fermionic projector in a closed Friedmann-Robertson-Walker geometry and to specify its global normalization as well as its local form. First author supported in part by the Deutsche Forschungsgemeinschaft.

  13. Explicit solutions of two nonlinear dispersive equations with variable coefficients

    International Nuclear Information System (INIS)

    Lai Shaoyong; Lv Xiumei; Wu Yonghong

    2008-01-01

    A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is developed to construct the exact solutions for a generalized Camassa-Holm equation and a nonlinear dispersive equation with variable coefficients. It is shown that the variable coefficients of the derivative terms in the equations cause the qualitative change in the physical structures of the solutions

  14. Quantum equations from Brownian motions

    International Nuclear Information System (INIS)

    Rajput, B.S.

    2011-01-01

    Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)

  15. FFT-split-operator code for solving the Dirac equation in 2+1 dimensions

    Science.gov (United States)

    Mocken, Guido R.; Keitel, Christoph H.

    2008-06-01

    provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 474 937 No. of bytes in distributed program, including test data, etc.: 4 128 347 Distribution format: tar.gz Programming language: C++ Computer: Any, but SMP systems are preferred Operating system: Linux and MacOS X are actively supported by the current version. Earlier versions were also tested successfully on IRIX and AIX Number of processors used: Generally unlimited, but best scaling with 2-4 processors for typical problems RAM: 160 Megabytes minimum for the examples given here Classification: 2.7 External routines: FFTW Library [3,4], Gnu Scientific Library [5], bzip2, bunzip2 Nature of problem: The relativistic time evolution of wave functions according to the Dirac equation is a challenging numerical task. Especially for an electron in the presence of high intensity laser beams and/or highly charged ions, this type of problem is of considerable interest to atomic physicists. Solution method: The code employs the split-operator method [1,2], combined with fast Fourier transforms (FFT) for calculating any occurring spatial derivatives, to solve the given problem. An autocorrelation spectral method [6] is provided to generate a bound state for use as the initial wave function of further dynamical studies. Restrictions: The code in its current form is restricted to problems in two spatial dimensions. Otherwise it is only limited by CPU time and memory that one can afford to spend on a particular problem. Unusual features: The code features dynamically adapting position and momentum space grids to keep execution time and memory requirements as small as possible. It employs an object-oriented approach, and it relies on a Clifford algebra class library to represent the mathematical objects of the Dirac formalism which we employ. Besides that it includes a feature (typically called "checkpointing") which allows the resumption of an

  16. On the modification of the Fermi-Dirac distribution function in degenerate semiconductors

    International Nuclear Information System (INIS)

    Chakraborty, P.K.; Biswas, S.K.; Ghatak, K.P.

    2004-01-01

    An attempt is made to study the Fermi-Dirac distribution function in degenerate semiconductors forming band tails (f p ) on the basis of a newly formulated electron dispersion law. It appears, taking n-GaAs as an example, that the influence of the carrier concentration (N i ) on f p is more significant than that of f 0 and f p is more effective than f 0 for higher values of N i . The relative change in Fermi-Dirac function with respect to f0((Δf/f0),Δf=fp-f0) for a fixed value of impurity screening potential, has initially zero value and then decreases with increasing electron energy (E). Thereafter exhibiting the minimum value, the (Δf/f0) increases at a relatively slow rate with increasing E and for higher value of E, f p approaches to f 0 . The present formulation provides us the key to investigate the transport properties of degenerate semiconductors which, in turn, depend on the solution of the Boltzmann transport equation and is expected to agree better with the experiments

  17. Weak cosmic censorship, dyonic Kerr–Newman black holes and Dirac fields

    International Nuclear Information System (INIS)

    Tóth, Gábor Zsolt

    2016-01-01

    It was investigated recently, with the aim of testing the weak cosmic censorship conjecture, whether an extremal Kerr black hole can be converted into a naked singularity by interaction with a massless classical Dirac test field, and it was found that this is possible. We generalize this result to electrically and magnetically charged rotating extremal black holes (i.e. extremal dyonic Kerr–Newman black holes) and massive Dirac test fields, allowing magnetically or electrically uncharged or nonrotating black holes and the massless Dirac field as special cases. We show that the possibility of the conversion is a direct consequence of the fact that the Einstein–Hilbert energy-momentum tensor of the classical Dirac field does not satisfy the null energy condition, and is therefore not in contradiction with the weak cosmic censorship conjecture. We give a derivation of the absence of superradiance of the Dirac field without making use of the complete separability of the Dirac equation in the dyonic Kerr–Newman background, and we determine the range of superradiant frequencies of the scalar field. The range of frequencies of the Dirac field that can be used to convert a black hole into a naked singularity partially coincides with the superradiant range of the scalar field. We apply horizon-penetrating coordinates, as our arguments involve calculating quantities at the event horizon. We describe the separation of variables for the Dirac equation in these coordinates, although we mostly avoid using it. (paper)

  18. Non-Existence of Black Hole Solutionsfor a Spherically Symmetric, Static Einstein-Dirac-Maxwell System

    Science.gov (United States)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.

  19. Classical electromagnetic radiation of the Dirac electron

    Science.gov (United States)

    Lanyi, G.

    1973-01-01

    A wave-function-dependent four-vector potential is added to the Dirac equation in order to achieve conservation of energy and momentum for a Dirac electron and its emitted electromagnetic field. The resultant equation contains solutions which describe transitions between different energy states of the electron. As a consequence it is possible to follow the space-time evolution of such a process. This evolution is shown in the case of the spontaneous emission of an electromagnetic field by an electron bound in a hydrogen-like atom. The intensity of the radiation and the spectral distribution are calculated for transitions between two eigenstates. The theory gives a self-consistent deterministic description of some simple radiation processes without using quantum electrodynamics or the correspondence principle.

  20. Su(4) properties of the Dirac-Kaehler equation

    International Nuclear Information System (INIS)

    Linhares, C.A.; Mignaco, J.A.

    1991-01-01

    We use the Dirac-Kaehler formalism in the space of differential forms (endowed with a Clifford product) to study the SU(4) symmetry related to the description of spin-1/2 particles found previously in the usual matrix treatment. We show that differential forms may be taken as the generators spanning the algebra of the SU(4) group and how the operations of this group can be related to a change of frame of reference in the algebra. We demonstrate that minimal left ideals of the algebra constitute irreducible representations for spin-1/2 particles for Clifford operation from the left, and exhibit how these ideals are related via space inversion, time reversal and their product. We also consider the dual space of minimal right ideals and show how the Dirac-Kaehler differential operator acts from the right, leaving the minimal right ideals invariant. This allows the introduction of an adjoint form and through the definition of a suitable scalar product, of conserved currents. We emphasize the relevance of all these features to the problem of proliferation of fermion species in the continuum limit of the lattice formalism. (author)

  1. Dirac potentials in a coupled channel approach to inelastic scattering

    International Nuclear Information System (INIS)

    Mishra, V.K.; Clark, B.C.; Cooper, E.D.; Mercer, R.L.

    1990-01-01

    It has been shown that there exist transformations that can be used to change the Lorentz transformation character of potentials, which appear in the Dirac equation for elastic scattering. We consider the situation for inelastic scattering described by coupled channel Dirac equations. We examine a two-level problem where both the ground and excited states are assumed to have zero spin. Even in this simple case we have not found an appropriate transformation. However, if the excited state has zero excitation energy it is possible to find a transformation

  2. Spin correlations and spin-wave excitations in Dirac-Weyl semimetals

    Science.gov (United States)

    Araki, Yasufumi; Nomura, Kentaro

    We study correlations among magnetic dopants in three-dimensional Dirac and Weyl semimetals. Effective field theory for localized magnetic moments is derived by integrating out the itinerant electron degrees of freedom. We find that spin correlation in the spatial direction parallel to local magnetization is more rigid than that in the perpendicular direction, reflecting spin-momentum locking nature of the Dirac Hamiltonian. Such an anisotropy becomes stronger for Fermi level close to the Dirac points, due to Van Vleck paramagnetism triggered by spin-orbit coupling. One can expect topologically nontrivial spin textures under this anisotropy, such as a hedgehog around a single point, or a radial vortex around an axis, as well as a uniform ferromagnetic order. We further investigate the characteristics of spin waves in the ferromagnetic state. Spin-wave dispersion also shows a spatial anisotropy, which is less dispersed in the direction transverse to the magnetization than that in the longitudinal direction. The spin-wave dispersion anisotropy can be traced back to the rigidity and flexibility of spin correlations discussed above. This work was supported by Grant-in-Aid for Scientific Research (Grants No.15H05854, No.26107505, and No.26400308) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

  3. Three dimensional Dirac point at k=0 in photonic and phononic systems

    OpenAIRE

    Huang, Xueqin; Liu, Fengming; Chan, C. T.

    2012-01-01

    While "Dirac cone" dispersions can only be meaningfully defined in two dimensional (2D) systems, the notion of a Dirac point can be extended to three dimensional (3D) classical wave systems. We show that a simple cubic photonic crystal composing of core-shell spheres exhibits a 3D Dirac point at the center of the Brillouin zone at a finite frequency. Using effective medium theory, we can map our structure to a zero refractive index material in which the effective permittivity and permeability...

  4. General solution of the Dirac equation for quasi-two-dimensional electrons

    Energy Technology Data Exchange (ETDEWEB)

    Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)

    2016-06-15

    The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.

  5. Einstein-Cartan-Dirac theory in (1+2)-dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Dereli, Tekin [Koc University, Department of Physics, Istanbul (Turkey); Oezdemir, Nese [Istanbul Technical University, Department of Physics Engineering, Istanbul (Turkey); Sert, Oezcan [Pamukkale University, Department of Physics, Denizli (Turkey)

    2013-01-15

    Einstein-Cartan theory is formulated in (1+2) dimensions using the algebra of exterior differential forms. A Dirac spinor is coupled to gravity and the field equations are obtained by a variational principle. The space-time torsion is found to be given algebraically in terms of a quadratic spinor condensate field. Circularly symmetric, exact solutions that collapse to AdS{sub 3} geometry in the absence of the Dirac condensate are found. (orig.)

  6. Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates

    Science.gov (United States)

    Cheng, Ralph T.; Casulli, Vincenzo; Milford, S. Nevil

    1984-01-01

    The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system. The values of the dependent variable off the grid are calculated by interpolation. When a linear interpolation is used, the method is a slight improvement over the upwind difference method. At this level of approximation both the ELM and the upwind difference method suffer from large numerical dispersion. However, if second-order Lagrangian polynomials are used in the interpolation, the ELM is proven to be free of artificial numerical dispersion for the convection-dispersion equation. The concept of the ELM is extended for treatment of anisotropic dispersion in natural coordinates. In this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field. Several numerical examples are given to further substantiate the results of the present analysis.

  7. Bosonic Analogue of Dirac Composite Fermi Liquid

    Science.gov (United States)

    Mross, David; Alicea, Jason; Motrunich, Olexei

    The status of particle-hole symmetry has long posed a challenge to the theory of the quantum Hall effect. It is expected to be present in the half-filled Landau level, but is absent in the conventional field theory, i.e., the composite Fermi liquid. Recently, Son proposed an alternative, explicitly particle-hole symmetric theory which features composite fermions that exhibit a Dirac dispersion. In my talk, I will introduce an analogous particle-hole-symmetric metallic state of bosons at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding 2 Ï Berry flux, protected by particle-hole and discrete rotation symmetries. As in the Dirac composite Fermi liquid introduced by Son, breaking particle-hole symmetry recovers the familiar Chern-Simons theory. I will discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as its signatures in experiments and simulations.

  8. Travelling wave solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations

    Directory of Open Access Journals (Sweden)

    M. Arshad

    Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method

  9. Three-dimensional periodic dielectric structures having photonic Dirac points

    Science.gov (United States)

    Bravo-Abad, Jorge; Joannopoulos, John D.; Soljacic, Marin

    2015-06-02

    The dielectric, three-dimensional photonic materials disclosed herein feature Dirac-like dispersion in quasi-two-dimensional systems. Embodiments include a face-centered cubic (fcc) structure formed by alternating layers of dielectric rods and dielectric slabs patterned with holes on respective triangular lattices. This fcc structure also includes a defect layer, which may comprise either dielectric rods or a dielectric slab with patterned with holes. This defect layer introduces Dirac cone dispersion into the fcc structure's photonic band structure. Examples of these fcc structures enable enhancement of the spontaneous emission coupling efficiency (the .beta.-factor) over large areas, contrary to the conventional wisdom that the .beta.-factor degrades as the system's size increases. These results enable large-area, low-threshold lasers; single-photon sources; quantum information processing devices; and energy harvesting systems.

  10. Three-dimensional periodic dielectric structures having photonic Dirac points

    Energy Technology Data Exchange (ETDEWEB)

    Bravo-Abad, Jorge; Joannopoulos, John D.; Soljacic, Marin

    2015-06-02

    The dielectric, three-dimensional photonic materials disclosed herein feature Dirac-like dispersion in quasi-two-dimensional systems. Embodiments include a face-centered cubic (fcc) structure formed by alternating layers of dielectric rods and dielectric slabs patterned with holes on respective triangular lattices. This fcc structure also includes a defect layer, which may comprise either dielectric rods or a dielectric slab with patterned with holes. This defect layer introduces Dirac cone dispersion into the fcc structure's photonic band structure. Examples of these fcc structures enable enhancement of the spontaneous emission coupling efficiency (the .beta.-factor) over large areas, contrary to the conventional wisdom that the .beta.-factor degrades as the system's size increases. These results enable large-area, low-threshold lasers; single-photon sources; quantum information processing devices; and energy harvesting systems.

  11. The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

    Energy Technology Data Exchange (ETDEWEB)

    Finster, Felix E-mail: felix.finster@mis.mpg.de; Smoller, Joel E-mail: smoller@umich.edu; Yau, S.-T. E-mail: yau@math.harvard.edu

    2000-09-18

    We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

  12. The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

    Science.gov (United States)

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    2000-09-01

    We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

  13. The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

    International Nuclear Information System (INIS)

    Finster, Felix; Smoller, Joel; Yau, S.-T.

    2000-01-01

    We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling

  14. Symmetry and exact solutions of nonlinear spinor equations

    International Nuclear Information System (INIS)

    Fushchich, W.I.; Zhdanov, R.Z.

    1989-01-01

    This review is devoted to the application of algebraic-theoretical methods to the problem of constructing exact solutions of the many-dimensional nonlinear systems of partial differential equations for spinor, vector and scalar fields widely used in quantum field theory. Large classes of nonlinear spinor equations invariant under the Poincare group P(1, 3), Weyl group (i.e. Poincare group supplemented by a group of scale transformations), and the conformal group C(1, 3) are described. Ansaetze invariant under the Poincare and the Weyl groups are constructed. Using these we reduce the Poincare-invariant nonlinear Dirac equations to systems of ordinary differential equations and construct large families of exact solutions of the nonlinear Dirac-Heisenberg equation depending on arbitrary parameters and functions. In a similar way we have obtained new families of exact solutions of the nonlinear Maxwell-Dirac and Klein-Gordon-Dirac equations. The obtained solutions can be used for quantization of nonlinear equations. (orig.)

  15. Derivation of simplified basic equations of gas-liquid two-phase dispersed flow based on two-fluid model

    International Nuclear Information System (INIS)

    Kataoka, Isao; Tomiyama, Akio

    2004-01-01

    The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill

  16. A semi-Dirac point and an electromagnetic topological transition in a dielectric photonic crystal

    KAUST Repository

    Wu, Ying

    2014-01-01

    Accidental degeneracy in a photonic crystal consisting of a square array of elliptical dielectric cylinders leads to both a semi-Dirac point at the center of the Brillouin zone and an electromagnetic topological transition (ETT). A perturbation method is deduced to affirm the peculiar linear-parabolic dispersion near the semi-Dirac point. An effective medium theory is developed to explain the simultaneous semi-Dirac point and ETT and to show that the photonic crystal is either a zero-refractive-index material or an epsilon-near-zero material at the semi-Dirac point. Drastic changes in the wave manipulation properties at the semi-Dirac point, resulting from ETT, are described.©2014 Optical Society of America.

  17. New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method

    International Nuclear Information System (INIS)

    Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing

    2009-01-01

    In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.

  18. Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

    KAUST Repository

    Zhang, Zhendong; Schuster, Gerard T.; Liu, Yike; Hanafy, Sherif M.; Li, Jing

    2016-01-01

    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized

  19. The Dirac Equation in the algebraic approximation. VII. A comparison of molecular finite difference and finite basis set calculations using distributed Gaussian basis sets

    NARCIS (Netherlands)

    Quiney, H. M.; Glushkov, V. N.; Wilson, S.; Sabin,; Brandas, E

    2001-01-01

    A comparison is made of the accuracy achieved in finite difference and finite basis set approximations to the Dirac equation for the ground state of the hydrogen molecular ion. The finite basis set calculations are carried out using a distributed basis set of Gaussian functions the exponents and

  20. Dirac's aether in relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Petroni, N.C.; Bari Univ.; Vigier, J.P.

    1984-01-01

    The paper concerns Dirac's aether model, based on a stochastic covariant distribution of subquantum motions. Stochastic derivation of the relativistic quantum equations; deterministic nonlocal interpretation of the Aspect-Rapisarda experiments on the EPR paradox; and photon interference with itself; are all discussed. (U.K.)

  1. On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk

    International Nuclear Information System (INIS)

    Lisovyy, O.

    2008-01-01

    Dirac Hamiltonian on the Poincare disk in the presence of an Aharonov-Bohm flux and a uniform magnetic field admits a one-parameter family of self-adjoint extensions. We determine the spectrum and calculate the resolvent for each element of this family. Explicit expressions for Green's functions are then used to find Fredholm determinant representations for the tau function of the Dirac operator with two branch points on the Poincare disk. Isomonodromic deformation theory for the Dirac equation relates this tau function to a one-parameter class of solutions of the Painleve VI equation with γ=0. We analyze long-distance behavior of the tau function, as well as the asymptotics of the corresponding Painleve VI transcendents as s→1. Considering the limit of flat space, we also obtain a class of solutions of the Painleve V equation with β=0

  2. Out-of-Bounds Hydrodynamics in Anisotropic Dirac Fluids

    Science.gov (United States)

    Link, Julia M.; Narozhny, Boris N.; Kiselev, Egor I.; Schmalian, Jörg

    2018-05-01

    We study hydrodynamic transport in two-dimensional, interacting electronic systems with merging Dirac points at charge neutrality. The dispersion along one crystallographic direction is Dirac-like, while it is Newtonian-like in the orthogonal direction. As a result, the electrical conductivity is metallic in one and insulating in the other direction. The shear viscosity tensor contains six independent components, which can be probed by measuring an anisotropic thermal flow. One of the viscosity components vanishes at zero temperature leading to a generalization of the previously conjectured lower bound for the shear viscosity to entropy density ratio.

  3. Levinson theorem for Dirac particles in n dimensions

    International Nuclear Information System (INIS)

    Jiang Yu

    2005-01-01

    We study the Levinson theorem for a Dirac particle in an n-dimensional central field by use of the Green function approach, based on an analysis of the n-dimensional radial Dirac equation obtained through a simple algebraic derivation. We show that the zero-momentum phase shifts are related to the number of bound states with |E|< m plus the number of half-bound states of zero momenta--i.e., |E|=m--which are denoted by finite, but not square-integrable, wave functions

  4. Heun Polynomials and Exact Solutions for the Massless Dirac Particle in the C-Metric

    Science.gov (United States)

    Kar, Priyasri; Singh, Ritesh K.; Dasgupta, Ananda; Panigrahi, Prasanta K.

    2018-03-01

    The equation of motion of a massless Dirac particle in the C-metric leads to the general Heun equation (GHE) for the radial and the polar variables. The GHE, under certain parametric conditions, is cast in terms of a new set of su(1, 1) generators involving differential operators of degrees ±1/2 and 0. Additional Heun polynomials are obtained using this new algebraic structure and are used to construct some exact solutions for the radial and the polar parts of the Dirac equation.

  5. The motion of a Dirac wave packet in a gravitational field

    International Nuclear Information System (INIS)

    Pietropaolo, F.; Toller, M.

    1983-01-01

    It is studied the motion of a test particle provided with spin in a gravitational field with a nonvanishing torsion with the aim of clarifying the relationship between the approach based on the balance equations for energy, momentum and angular momentum and the approach based directly on a semiclassical approximation of the Dirac equation. The balance equations in the pole-dipole approximation are applied to a Dirac wave packet minimally coupled to the gravitational field and it is shown that, in this particular case, it is possible to compute the dipole moments of energy current, which are essential for a correct calculation of the motion of the centre of the particle and of the precession of its spin

  6. PREFACE: International Workshop on Dirac Electrons in Solids 2015

    Science.gov (United States)

    Ogata, M.; Suzumura, Y.; Fuseya, Y.; Matsuura, H.

    2015-04-01

    It is our pleasure to publish the Proceedings of the International Workshop on Dirac Electrons in Solids held in University of Tokyo, Japan, for January 14-15, 2015. The workshop was organized by the entitled project which lasted from April 2012 to March 2015 with 10 theorists. It has been supported by a Grand-in-Aid for Scientific Research (A) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. The subjects discussed in the workshop include bismuth, organic conductors, graphene, topological insulators, new materials including Ca3PbO, and new directions in theory (superconductivity, orbital susceptibility, etc). The number of participants was about 70 and the papers presented in the workshop include four invited talks, 16 oral presentations, and 23 poster presentations. Dirac electron systems appear in various systems, such as graphene, quasi-two-dimensional organic conductors, bismuth, surface states in topological insulators, new materials like Ca3PbO. In these systems, characteristic transport properties caused by the linear dispersion of Dirac electrons and topological properties, have been extensively discussed. In addition to these, there are many interesting research fields such as Spin-Hall effect, orbital diamagnetism due to interband effects, Landau levels characteristic to Dirac dispersion, anomalous interlayer transport phenomena and magnetoresistance, the effects of spin-orbit interaction, and electron correlation. The workshop focused on recent developments of theory and experiment of Dirac electron systems in the above materials. We note that all papers published in this volume of Journal of Physics: Conference Series were peer reviewed. Reviews were performed by expert referees with professional knowledge and high scientific standards in this field. Editors made efforts so that the papers may satisfy the criterion of a proceedings journal published by IOP Publishing. We hope that all the participants of the workshop

  7. A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

    KAUST Repository

    Wu, Zedong

    2018-04-05

    Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is is highly accurate and efficient.

  8. Topological Crystalline Insulators and Dirac Octets in Anti-perovskites

    OpenAIRE

    Hsieh, Timothy H.; Liu, Junwei; Fu, Liang

    2014-01-01

    We predict a new class of topological crystalline insulators (TCI) in the anti-perovskite material family with the chemical formula A$_3$BX. Here the nontrivial topology arises from band inversion between two $J=3/2$ quartets, which is described by a generalized Dirac equation for a "Dirac octet". Our work suggests that anti-perovskites are a promising new venue for exploring the cooperative interplay between band topology, crystal symmetry and electron correlation.

  9. Point Coulomb solutions of the Dirac equation: analytical results required for the evaluation of the bound electron propagator in quantum electrodynamics

    International Nuclear Information System (INIS)

    Whittingham, I.B.

    1977-12-01

    The bound electron propagator in quantum electrodynamics is reviewed and the Brown and Schaefer angular momentum representation of the propagator discussed. Regular and irregular solutions of the radial Dirac equations for both /E/ 2 and /E/ >or= mc 2 are required for the computation of the propagator. Analytical expressions for these solutions, and their corresponding Wronskians, are obtained for a point Coulomb potential. Some computational aspects are discussed in an appendix

  10. Local energy decay of massive Dirac fields in the 5D Myers-Perry metric

    International Nuclear Information System (INIS)

    Daudé, Thierry; Kamran, Niky

    2012-01-01

    We consider massive Dirac fields evolving in the exterior region of a five-dimensional Myers-Perry black hole and study their propagation properties. Our main result states that the local energy of such fields decays in a weak sense at late times. We obtain this result in two steps: first, using the separability of the Dirac equation, we prove the absence of a pure point spectrum for the corresponding Dirac operator; second, using a new form of the equation adapted to the local rotations of the black hole, we show by a Mourre theory argument that the spectrum is absolutely continuous. This leads directly to our main result. (paper)

  11. Modification of the quantum-mechanical equations for the system of charged Dirac particles by including additional tensor terms of the Pauli type. Pt. 1. [Amplified Bethe-Salpeter, radiative corrections, fine structure

    Energy Technology Data Exchange (ETDEWEB)

    Janyszek, H [Uniwersytet Mikolaja Kopernika, Torun (Poland). Instytut Fizyki

    1974-01-01

    A new modified quasirelativistic equation (different from that of Breit) for N charged Dirac particles in the external stationary electromagnetic field is proposed. This equation is an amplified quantum-mechanical Bethe-Salpeter equation obtained by adding (in a semi-phenomenological manner) terms which take into account radiative corrections. The application of this approximate equations is limited to third order terms in the fine structure constant ..cap alpha...

  12. Separation Transformation and New Exact Solutions of the (N + 1)-dimensional Dispersive Double sine-Gordon Equation

    International Nuclear Information System (INIS)

    Tian Ye; Chen Jing; Zhang Zhifei

    2012-01-01

    In this paper, the separation transformation approach is extended to the (N + 1)-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of 3 He superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obtained and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the (N + 1)-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N > 2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.

  13. Relativistic wave equations and compton scattering

    International Nuclear Information System (INIS)

    Sutanto, S.H.; Robson, B.A.

    1998-01-01

    Full text: Recently an eight-component relativistic wave equation for spin-1/2 particles was proposed.This equation was obtained from a four-component spin-1/2 wave equation (the KG1/2 equation), which contains second-order derivatives in both space and time, by a procedure involving a linearisation of the time derivative analogous to that introduced by Feshbach and Villars for the Klein-Gordon equation. This new eight-component equation gives the same bound-state energy eigenvalue spectra for hydrogenic atoms as the Dirac equation but has been shown to predict different radiative transition probabilities for the fine structure of both the Balmer and Lyman a-lines. Since it has been shown that the new theory does not always give the same results as the Dirac theory, it is important to consider the validity of the new equation in the case of other physical problems. One of the early crucial tests of the Dirac theory was its application to the scattering of a photon by a free electron: the so-called Compton scattering problem. In this paper we apply the new theory to the calculation of Compton scattering to order e 2 . It will be shown that in spite of the considerable difference in the structure of the new theory and that of Dirac the cross section is given by the Klein-Nishina formula

  14. On Kaehler's geometric description of dirac fields

    International Nuclear Information System (INIS)

    Goeckeler, M.; Joos, H.

    1983-12-01

    A differential geometric generalization of the Dirac equation due to E. Kaehler seems to be an appropriate starting point for the lattice approximation of matter fields. It is the purpose of this lecture to illustrate several aspects of this approach. (orig./HSI)

  15. First-Principles Prediction of Spin-Polarized Multiple Dirac Rings in Manganese Fluoride

    Science.gov (United States)

    Jiao, Yalong; Ma, Fengxian; Zhang, Chunmei; Bell, John; Sanvito, Stefano; Du, Aijun

    2017-07-01

    Spin-polarized materials with Dirac features have sparked great scientific interest due to their potential applications in spintronics. But such a type of structure is very rare and none has been fabricated. Here, we investigate the already experimentally synthesized manganese fluoride (MnF3 ) as a novel spin-polarized Dirac material by using first-principles calculations. MnF3 exhibits multiple Dirac cones in one spin orientation, while it behaves like a large gap semiconductor in the other spin channel. The estimated Fermi velocity for each cone is of the same order of magnitude as that in graphene. The 3D band structure further reveals that MnF3 possesses rings of Dirac nodes in the Brillouin zone. Such a spin-polarized multiple Dirac ring feature is reported for the first time in an experimentally realized material. Moreover, similar band dispersions can be also found in other transition metal fluorides (e.g., CoF3 , CrF3 , and FeF3 ). Our results highlight a new interesting single-spin Dirac material with promising applications in spintronics and information technologies.

  16. First-Principles Prediction of Spin-Polarized Multiple Dirac Rings in Manganese Fluoride.

    Science.gov (United States)

    Jiao, Yalong; Ma, Fengxian; Zhang, Chunmei; Bell, John; Sanvito, Stefano; Du, Aijun

    2017-07-07

    Spin-polarized materials with Dirac features have sparked great scientific interest due to their potential applications in spintronics. But such a type of structure is very rare and none has been fabricated. Here, we investigate the already experimentally synthesized manganese fluoride (MnF_{3}) as a novel spin-polarized Dirac material by using first-principles calculations. MnF_{3} exhibits multiple Dirac cones in one spin orientation, while it behaves like a large gap semiconductor in the other spin channel. The estimated Fermi velocity for each cone is of the same order of magnitude as that in graphene. The 3D band structure further reveals that MnF_{3} possesses rings of Dirac nodes in the Brillouin zone. Such a spin-polarized multiple Dirac ring feature is reported for the first time in an experimentally realized material. Moreover, similar band dispersions can be also found in other transition metal fluorides (e.g., CoF_{3}, CrF_{3}, and FeF_{3}). Our results highlight a new interesting single-spin Dirac material with promising applications in spintronics and information technologies.

  17. Electronic structure, Dirac points and Fermi arc surface states in three-dimensional Dirac semimetal Na3Bi from angle-resolved photoemission spectroscopy

    International Nuclear Information System (INIS)

    Liang Aiji; Chen Chaoyu; Wang Zhijun; Shi Youguo; Feng Ya; Yi Hemian; Xie Zhuojin; He Shaolong; He Junfeng; Peng Yingying; Liu Yan; Liu Defa; Hu Cheng; Zhao Lin; Liu Guodong; Dong Xiaoli; Zhang Jun; Nakatake, M; Iwasawa, H; Shimada, K

    2016-01-01

    The three-dimensional (3D) Dirac semimetals have linearly dispersive 3D Dirac nodes where the conduction band and valence band are connected. They have isolated 3D Dirac nodes in the whole Brillouin zone and can be viewed as a 3D counterpart of graphene. Recent theoretical calculations and experimental results indicate that the 3D Dirac semimetal state can be realized in a simple stoichiometric compound A 3 Bi ( A = Na, K, Rb). Here we report comprehensive high-resolution angle-resolved photoemission (ARPES) measurements on the two cleaved surfaces, (001) and (100), of Na 3 Bi. On the (001) surface, by comparison with theoretical calculations, we provide a proper assignment of the observed bands, and in particular, pinpoint the band that is responsible for the formation of the three-dimensional Dirac cones. We observe clear evidence of 3D Dirac cones in the three-dimensional momentum space by directly measuring on the k x – k y plane and by varying the photon energy to get access to different out-of-plane k z s. In addition, we reveal new features around the Brillouin zone corners that may be related with surface reconstruction. On the (100) surface, our ARPES measurements over a large momentum space raise an issue on the selection of the basic Brillouin zone in the (100) plane. We directly observe two isolated 3D Dirac nodes on the (100) surface. We observe the signature of the Fermi-arc surface states connecting the two 3D Dirac nodes that extend to a binding energy of ∼150 meV before merging into the bulk band. Our observations constitute strong evidence on the existence of the Dirac semimetal state in Na 3 Bi that are consistent with previous theoretical and experimental work. In addition, our results provide new information to clarify on the nature of the band that forms the 3D Dirac cones, on the possible formation of surface reconstruction of the (001) surface, and on the issue of basic Brillouin zone selection for the (100) surface. (rapid communication)

  18. Generalization of the Dirac’s Equation and Sea

    DEFF Research Database (Denmark)

    Javadi, Hossein; Forouzbakhsh, Farshid; Daei Kasmaei, Hamed

    2016-01-01

    Newton's second law is motion equation in classic mechanics that does not say anything about the nature of force. The equivalent formulations and their extensions such as Lagrangian and Hamiltonian do not explain about mechanism of converting Potential energy to Kinetic energy and Vice versa....... In quantum mechanics, Schrodinger equation is similar to Newton's second law in classic mechanics. Quantum mechanics is also extension of Newtonian mechanics to atomic and subatomic scales and relativistic mechanics is extension of Newtonian mechanics to high velocities near to velocity of light too....... Schrodinger equation is not a relativistic equation, because it is not invariant under Lorentz transformations. Dirac expanded The Schrodinger equation by presenting Dirac Sea and founded relativistic quantum mechanics. In this paper by reconsidering the Dirac Sea and his equation, the structure of photon...

  19. Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material

    Science.gov (United States)

    Banerjee, S.; Fransson, J.; Black-Schaffer, A. M.; Ågren, H.; Balatsky, A. V.

    2016-04-01

    We examine the low-energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in a honeycomb lattice structure. Using the example of graphene, we present evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K' points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. We show that the Dirac node is preserved in the presence of an intergrain interaction, despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sublattice symmetry by choosing different on-site potentials for the two sublattices leads to a gap opening near the Dirac node, in analogy with fermionic Dirac materials. The Dirac node dispersion of bosonic excitations is thus expanding the discussion of the conventional Dirac cone excitations to the case of bosons. We call this case as a representative of bosonic Dirac materials (BDM), similar to the case of Fermionic Dirac materials extensively discussed in the literature.

  20. Dirac materials

    OpenAIRE

    Wehling, T. O.; Black-Schaffer, A. M.; Balatsky, A. V.

    2014-01-01

    A wide range of materials, like d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles rather than fermions obeying the usual Schrodinger Hamiltonian. This emergent behavior of Dirac fermions in condensed matter systems defines the unifying framework for a class of materials we call "Dirac materials''. In order to establish this class of materials, we illustrate how Dirac fermions ...

  1. On the equation of motion in electrodynamics

    International Nuclear Information System (INIS)

    Papas, C.H.

    1975-01-01

    A new vector equation of motion in electrodynamics is proposed by replacing the Schott term in the Lorentz-Dirac equation by an expression depending on the electro-magnetic field vectors E and B and the velocity vector V. It is argued that several conceptual difficulties in the Lorentz-Dirac equation disappear while the results remain the same except for extreme high fields and velocities as could be encountered in astrophysics

  2. Radiationless Zitterbewegung of Dirac particles and mass formula

    International Nuclear Information System (INIS)

    Noboru Hokkyo.

    1987-06-01

    The Zitterbewegung of the Dirac particle is given a visual representation by solving the two-component difference form of the Dirac equation. It is seen that the space-time trajectory of a Dirac particle can be pictured as a correlated whole of a network of zigzags of left- and right-handed chiral neutrino-like line elements. These zigzags can feel the curl of the external electromagnetic vector potential and give rise to the spin magnetic interaction, confirming Schroedinger's earlier intuitive picture of the spin as the orbital angular momentum of the Zitterbewegung. The network of zigzags associated with an electron splits and reunites in passing through the slits in the electron beam interference experiment. It is proposed to interpret Nambu's empirical mass formula m n =(n/2)137m e =(n/2)((h/2π)/cL), n=integer, as a radiationless condition for the Zitterbewegung of the hadronic Dirac particle of the linear spatial extension of the order of the classical electron radius L=e 2 /m e c 2 . (author). 20 refs, 4 figs

  3. LHCb: LHCbDirac is a DIRAC extension to support LHCb specific workflows

    CERN Multimedia

    Stagni, Federico

    2012-01-01

    We present LHCbDIRAC, an extension of the DIRAC community Grid solution to handle the LHCb specificities. The DIRAC software has been developed for many years within LHCb only. Nowadays it is a generic software, used by many scientific communities worldwide. Each community wanting to take advantage of DIRAC has to develop an extension, containing all the necessary code for handling their specific cases. LHCbDIRAC is an actively developed extension, implementing the LHCb computing model and workflows. LHCbDIRAC extends DIRAC to handle all the distributed computing activities of LHCb. Such activities include real data processing (reconstruction, stripping and streaming), Monte-Carlo simulation and data replication. Other activities are groups and user analysis, data management, resources management and monitoring, data provenance, accounting for user and production jobs. LHCbDIRAC also provides extensions of the DIRAC interfaces, including a secure web client, python APIs and CLIs. While DIRAC and LHCbDIRAC f...

  4. Large nonsaturating magnetoresistance and signature of nondegenerate Dirac nodes in ZrSiS.

    Science.gov (United States)

    Singha, Ratnadwip; Pariari, Arnab Kumar; Satpati, Biswarup; Mandal, Prabhat

    2017-03-07

    Whereas the discovery of Dirac- and Weyl-type excitations in electronic systems is a major breakthrough in recent condensed matter physics, finding appropriate materials for fundamental physics and technological applications is an experimental challenge. In all of the reported materials, linear dispersion survives only up to a few hundred millielectronvolts from the Dirac or Weyl nodes. On the other hand, real materials are subject to uncontrolled doping during preparation and thermal effect near room temperature can hinder the rich physics. In ZrSiS, angle-resolved photoemission spectroscopy measurements have shown an unusually robust linear dispersion (up to [Formula: see text]2 eV) with multiple nondegenerate Dirac nodes. In this context, we present the magnetotransport study on ZrSiS crystal, which represents a large family of materials ( WHM with W = Zr, Hf; H = Si, Ge, Sn; M = O, S, Se, Te) with identical band topology. Along with extremely large and nonsaturating magnetoresistance (MR), [Formula: see text]1.4 [Formula: see text] 10 5 % at 2 K and 9 T, it shows strong anisotropy, depending on the direction of the magnetic field. Quantum oscillation and Hall effect measurements have revealed large hole and small electron Fermi pockets. A nontrivial [Formula: see text] Berry phase confirms the Dirac fermionic nature for both types of charge carriers. The long-sought relativistic phenomenon of massless Dirac fermions, known as the Adler-Bell-Jackiw chiral anomaly, has also been observed.

  5. The dispersion-managed Ginzburg–Landau equation and its application to femtosecond lasers

    International Nuclear Information System (INIS)

    Biondini, Gino

    2008-01-01

    The complex Ginzburg–Landau equation has been used extensively to describe various nonequilibrium phenomena. In the context of lasers, it models the dynamics by averaging over the effects that take place inside the cavity. Pulses produced by Ti : sapphire femtosecond lasers, however, undergo significant changes in different parts of the cavity during each round-trip. The dynamics of such pulses is therefore not adequately described by an average model that does not take such changes into account. The purpose of this work is severalfold. We introduce the dispersion-managed Ginzburg–Landau equation (DMGLE) as an average model that describes the long-term dynamics of systems characterized by rapid variations of dispersion, nonlinearity and gain in a general setting, and we study the properties of the equation. We then explain how in particular the DMGLE arises for Ti : sapphire femtosecond lasers and we characterize its solutions. In particular, we show that, for moderate values of the gain/loss parameters, the solutions of the DMGLE are well approximated by those of the dispersion-managed nonlinear Schrödinger equation (DMNLSE), and the main effect of gain and loss dynamics is simply to select one among the one-parameter family of solutions of the DMNLSE

  6. The modified extended Fan's sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation

    International Nuclear Information System (INIS)

    Yomba, Emmanuel

    2005-01-01

    By using a modified extended Fan's sub-equation method, we have obtained new and more general solutions including a series of non-travelling wave and coefficient function solutions namely: soliton-like solutions, triangular-like solutions, single and combined non-degenerative Jacobi elliptic wave function-like solutions for the (2 + 1)-dimensional dispersive long wave equation. The most important achievement of this method lies on the fact that, we have succeeded in one move to give all the solutions which can be previously obtained by application of at least four methods (method using Riccati equation, or first kind elliptic equation, or auxiliary ordinary equation, or generalized Riccati equation as mapping equation)

  7. Higher dimensional supersymmetric quantum mechanics and Dirac ...

    Indian Academy of Sciences (India)

    We exhibit the supersymmetric quantum mechanical structure of the full 3+1 dimensional Dirac equation considering `mass' as a function of coordinates. Its usefulness in solving potential problems is discussed with specific examples. We also discuss the `physical' significance of the supersymmetric states in this formalism.

  8. Dispersionless wave packets in Dirac materials

    Czech Academy of Sciences Publication Activity Database

    Jakubský, Vít; Tušek, M.

    2017-01-01

    Roč. 378, MAR (2017), s. 171-182 ISSN 0003-4916 R&D Projects: GA ČR(CZ) GJ15-07674Y; GA ČR GA17-01706S Institutional support: RVO:61389005 Keywords : quantum systems * wave packets * dispersion * dirac materials Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 2.465, year: 2016

  9. A sequence of Clifford algebras and three replicas of Dirac particle

    International Nuclear Information System (INIS)

    Krolikowski, W.; Warsaw Univ.

    1990-01-01

    The embedding of Dirac algebra into a sequence N=1, 2, 3,... of Clifford algebras is discussed, leading to Dirac equations with N=1 additional, electromagnetically ''hidden'' spins 1/2. It is shown that there are three and only three replicas N=1, 3, 5 of Dirac particle if the theory of relativity together with the probability interpretation of wave function is applied both to the ''visible'' spin and ''hidden'' spins, and a new ''hidden exclusion principle''is imposed on the wave function (then ''hidden'' spins add up to zero). It is appealing to explore this idea in order to explain the puzzle of three generations of lepton and quarks. (author)

  10. Relativistic Dirac-Fock and many-body perturbation calculations on He, He-like ions, Ne, and Ar

    International Nuclear Information System (INIS)

    Ishikawa, Y.

    1990-01-01

    Relativistic Dirac-Fock and diagrammatic many-body perturbation-theory calculations have been performed on He, several He-like ions, Ne, and Ar. The no-pair Dirac-Coulomb Hamiltonian is taken as the starting point. A solution of the Dirac-Fock equations is obtained by analytic expansion in basis sets of Gaussian-type functions. Many-body perturbation improvements of Coulomb correlation are done to third order

  11. Model Equation for Acoustic Nonlinear Measurement of Dispersive Specimens at High Frequency

    Science.gov (United States)

    Zhang, Dong; Kushibiki, Junichi; Zou, Wei

    2006-10-01

    We present a theoretical model for acoustic nonlinearity measurement of dispersive specimens at high frequency. The nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation governs the nonlinear propagation in the SiO2/specimen/SiO2 multi-layer medium. The dispersion effect is considered in a special manner by introducing the frequency-dependant sound velocity in the KZK equation. Simple analytic solutions are derived by applying the superposition technique of Gaussian beams. The solutions are used to correct the diffraction and dispersion effects in the measurement of acoustic nonlinearity of cottonseed oil in the frequency range of 33-96 MHz. Regarding two different ultrasonic devices, the accuracies of the measurements are improved to ±2.0% and ±1.3% in comparison with ±9.8% and ±2.9% obtained from the previous plane wave model.

  12. The Dirac-Kaehler equation and fermions on the lattice

    International Nuclear Information System (INIS)

    Becher, P.

    1982-05-01

    The geometrical description of spinor fields by E. Kaehler is used to formulate a consistent lattice approximation of fermions. The relation to free simple Dirac fields as well as to Susskind's description of lattice fermions is clarified. The first steps towards a quantized interacting theory are given. The correspondence between the calculus of differential forms and concepts of algebraic topology is shown to be a useful method for a completely analogous treatment of the problems in the continuum and on the lattice. (orig.)

  13. DIRAC RESTful API

    International Nuclear Information System (INIS)

    Casajus Ramo, A; Graciani Diaz, R; Tsaregorodtsev, A

    2012-01-01

    The DIRAC framework for distributed computing has been designed as a flexible and modular solution that can be adapted to the requirements of any community. Users interact with DIRAC via command line, using the web portal or accessing resources via the DIRAC python API. The current DIRAC API requires users to use a python version valid for DIRAC. Some communities have developed their own software solutions for handling their specific workload, and would like to use DIRAC as their back-end to access distributed computing resources easily. Many of these solutions are not coded in python or depend on a specific python version. To solve this gap DIRAC provides a new language agnostic API that any software solution can use. This new API has been designed following the RESTful principles. Any language with libraries to issue standard HTTP queries may use it. GSI proxies can still be used to authenticate against the API services. However GSI proxies are not a widely adopted standard. The new DIRAC API also allows clients to use OAuth for delegating the user credentials to a third party solution. These delegated credentials allow the third party software to query to DIRAC on behalf of the users. This new API will further expand the possibilities communities have to integrate DIRAC into their distributed computing models.

  14. Dirac relaxation of the Israel junction conditions: Unified Randall-Sundrum brane theory

    International Nuclear Information System (INIS)

    Davidson, Aharon; Gurwich, Ilya

    2006-01-01

    Following Dirac's brane variation prescription, the brane must not be deformed during the variation process, or else the linearity of the variation may be lost. Alternatively, the variation of the brane is done, in a special Dirac frame, by varying the bulk coordinate system itself. Imposing appropriate Dirac-style boundary conditions on the constrained 'sandwiched' gravitational action, we show how Israel junction conditions get relaxed, but remarkably, all solutions of the original Israel equations are still respected. The Israel junction conditions are traded, in the Z 2 -symmetric case, for a generalized Regge-Teitelboim type equation (plus a local conservation law), and in the generic Z 2 -asymmetric case, for a pair of coupled Regge-Teitelboim equations. The Randall-Sundrum model and its derivatives, such as the Dvali-Gabadadze-Porrati and the Collins-Holdom models, get generalized accordingly. Furthermore, Randall-Sundrum and Regge-Teitelboim brane theories appear now to be two different faces of the one and the same unified brane theory. Within the framework of unified brane cosmology, we examine the dark matter/energy interpretation of the effective energy/momentum deviations from general relativity

  15. Fractional quantum Hall systems near nematicity: Bimetric theory, composite fermions, and Dirac brackets

    Science.gov (United States)

    Nguyen, Dung Xuan; Gromov, Andrey; Son, Dam Thanh

    2018-05-01

    We perform a detailed comparison of the Dirac composite fermion and the recently proposed bimetric theory for a quantum Hall Jain states near half filling. By tuning the composite Fermi liquid to the vicinity of a nematic phase transition, we find that the two theories are equivalent to each other. We verify that the single mode approximation for the response functions and the static structure factor becomes reliable near the phase transition. We show that the dispersion relation of the nematic mode near the phase transition can be obtained from the Dirac brackets between the components of the nematic order parameter. The dispersion is quadratic at low momenta and has a magnetoroton minimum at a finite momentum, which is not related to any nearby inhomogeneous phase.

  16. Manipulation of Dirac cones in metal-intercalated epitaxial graphene

    Science.gov (United States)

    Wang, Cai-Zhuang; Kim, Minsung; Tringides, Michael; Ho, Kai-Ming

    Graphene is one of the most attractive materials from both fundamental and practical points of view due to its characteristic Dirac cones. The electronic property of graphene can be modified through the interaction with substrate or another graphene layer as illustrated in few-layer epitaxial graphene. Recently, metal intercalation became an effective method to manipulate the electronic structure of graphene by modifying the coupling between the constituent layers. In this work, we show that the Dirac cones of epitaxial graphene can be manipulated by intercalating rare-earth metals. We demonstrate that rare-earth metal intercalated epitaxial graphene has tunable band structures and the energy levels of Dirac cones as well as the linear or quadratic band dispersion can be controlled depending on the location of the intercalation layer and density. Our results could be important for applications and characterizations of the intercalated epitaxial graphene. Supported by the U.S. DOE-BES under Contract No. DE-AC02-07CH11358.

  17. Decay Rates and Probability Estimatesfor Massive Dirac Particlesin the Kerr-Newman Black Hole Geometry

    Science.gov (United States)

    Finster, F.; Kamran, N.; Smoller, J.; Yau, S.-T.

    The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr-Newman geometry, for smooth initial data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays in L∞ {loc} at least at the rate t-5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p = 0, 1 or 0 < p < 1. The proofs are based on a refined analysis of the Dirac propagator constructed in [4].

  18. Two-dimensional spin-orbit Dirac point in monolayer HfGeTe

    Science.gov (United States)

    Guan, Shan; Liu, Ying; Yu, Zhi-Ming; Wang, Shan-Shan; Yao, Yugui; Yang, Shengyuan A.

    2017-10-01

    Dirac points in two-dimensional (2D) materials have been a fascinating subject of research, with graphene as the most prominent example. However, the Dirac points in existing 2D materials, including graphene, are vulnerable against spin-orbit coupling (SOC). Here, based on first-principles calculations and theoretical analysis, we propose a new family of stable 2D materials, the HfGeTe-family monolayers, which host so-called spin-orbit Dirac points (SDPs) close to the Fermi level. These Dirac points are special in that they are formed only under significant SOC, hence they are intrinsically robust against SOC. We show that the existence of a pair of SDPs are dictated by the nonsymmorphic space group symmetry of the system, which are very robust under various types of lattice strains. The energy, the dispersion, and the valley occupation around the Dirac points can be effectively tuned by strain. We construct a low-energy effective model to characterize the Dirac fermions around the SDPs. Furthermore, we find that the material is simultaneously a 2D Z2 topological metal, which possesses nontrivial Z2 invariant in the bulk and spin-helical edge states on the boundary. From the calculated exfoliation energies and mechanical properties, we show that these materials can be readily obtained in experiment from the existing bulk materials. Our result reveals HfGeTe-family monolayers as a promising platform for exploring spin-orbit Dirac fermions and topological phases in two-dimensions.

  19. Continuity relations and quantum wave equations

    International Nuclear Information System (INIS)

    Goedecke, G.H.; Davis, B.T.

    2010-01-01

    We investigate the mathematical synthesis of the Schroedinger, Klein-Gordon, Pauli-Schroedinger, and Dirac equations starting from probability continuity relations. We utilize methods similar to those employed by R. E. Collins (Lett. Nuovo Cimento, 18 (1977) 581) in his construction of the Schroedinger equation from the position probability continuity relation for a single particle. Our new results include the mathematical construction of the Pauli-Schroedinger and Dirac equations from the position probability continuity relations for a particle that can transition between two states or among four states, respectively.

  20. Solution of the Dirac Coulomb equation for helium-like ions in the Poet-Temkin model.

    Science.gov (United States)

    Tang, Li-Yan; Tang, Yong-Bo; Shi, Ting-Yun; Mitroy, J

    2013-10-07

    The Dirac-Coulomb equation for the helium atom is studied under the restrictions of the Poet-Temkin model which replaces the 1/r12 interaction by the simplified 1/r> form. The effective reduction in the dimensionality made it possible to obtain binding energies for the singlet and triplet states in this model problem with a relative precision from 10(-8) to 10(-10). The energies for the singlet state were consistent with a previous configuration interaction calculation [H. Tatewaki and Y. Watanabe, Chem. Phys. 389, 58 (2011)]. Manifestations of Brown-Ravenhall disease were noted at higher values of nuclear charge and ultimately limited the accuracy of the Poet-Temkin model energy. The energies from a no-pair configuration interaction (CI) calculation (the negative-energy states for the appropriate hydrogen-like ion were excluded from the CI expansion) were found to be different from the unrestricted B-spline calculation.

  1. Solution of the Dirac Coulomb equation for helium-like ions in the Poet-Temkin model

    Science.gov (United States)

    Tang, Li-Yan; Tang, Yong-Bo; Shi, Ting-Yun; Mitroy, J.

    2013-10-01

    The Dirac-Coulomb equation for the helium atom is studied under the restrictions of the Poet-Temkin model which replaces the 1/r12 interaction by the simplified 1/r> form. The effective reduction in the dimensionality made it possible to obtain binding energies for the singlet and triplet states in this model problem with a relative precision from 10-8 to 10-10. The energies for the singlet state were consistent with a previous configuration interaction calculation [H. Tatewaki and Y. Watanabe, Chem. Phys. 389, 58 (2011)]. Manifestations of Brown-Ravenhall disease were noted at higher values of nuclear charge and ultimately limited the accuracy of the Poet-Temkin model energy. The energies from a no-pair configuration interaction (CI) calculation (the negative-energy states for the appropriate hydrogen-like ion were excluded from the CI expansion) were found to be different from the unrestricted B-spline calculation.

  2. Approaching the Type-II Dirac Point and Concomitant Superconductivity in Pt-doping Stabilized Metastable 1T-phase IrTe2

    OpenAIRE

    Fei, Fucong; Bo, Xiangyan; Wang, Pengdong; Ying, Jianghua; Chen, Bo; Liu, Qianqian; Zhang, Yong; Sun, Zhe; Qu, Fanming; Zhang, Yi; Li, Jian; Song, Fengqi; Wan, Xiangang; Wang, Baigeng; Wang, Guanghou

    2017-01-01

    Topological semimetal is a topic of general interest in material science. Recently, a new kind of topological semimetal called type-II Dirac semimetal with tilted Dirac cones is discovered in PtSe2 family. However, the further investigation is hindered due to the huge energy difference from Dirac points to Fermi level and the irrelevant conducting pockets at Fermi surface. Here we characterize the optimized type-II Dirac dispersions in a metastable 1T phase of IrTe2. Our strategy of Pt doping...

  3. Developing A New Predictive Dispersion Equation Based on Tidal Average (TA) Condition in Alluvial Estuaries

    Science.gov (United States)

    Anak Gisen, Jacqueline Isabella; Nijzink, Remko C.; Savenije, Hubert H. G.

    2014-05-01

    Dispersion mathematical representation of tidal mixing between sea water and fresh water in The definition of dispersion somehow remains unclear as it is not directly measurable. The role of dispersion is only meaningful if it is related to the appropriate temporal and spatial scale of mixing, which are identified as the tidal period, tidal excursion (longitudinal), width of estuary (lateral) and mixing depth (vertical). Moreover, the mixing pattern determines the salt intrusion length in an estuary. If a physically based description of the dispersion is defined, this would allow the analytical solution of the salt intrusion problem. The objective of this study is to develop a predictive equation for estimating the dispersion coefficient at tidal average (TA) condition, which can be applied in the salt intrusion model to predict the salinity profile for any estuary during different events. Utilizing available data of 72 measurements in 27 estuaries (including 6 recently studied estuaries in Malaysia), regressions analysis has been performed with various combinations of dimensionless parameters . The predictive dispersion equations have been developed for two different locations, at the mouth D0TA and at the inflection point D1TA (where the convergence length changes). Regressions have been carried out with two separated datasets: 1) more reliable data for calibration; and 2) less reliable data for validation. The combination of dimensionless ratios that give the best performance is selected as the final outcome which indicates that the dispersion coefficient is depending on the tidal excursion, tidal range, tidal velocity amplitude, friction and the Richardson Number. A limitation of the newly developed equation is that the friction is generally unknown. In order to compensate this problem, further analysis has been performed adopting the hydraulic model of Cai et. al. (2012) to estimate the friction and depth. Keywords: dispersion, alluvial estuaries, mixing, salt

  4. Collective modes of massive Dirac fermions in armchair graphene nanoribbons

    International Nuclear Information System (INIS)

    Andersen, David R; Raza, Hassan

    2013-01-01

    We report the plasmon dispersion characteristics of intrinsic and extrinsic armchair graphene nanoribbons of atomic width N = 5 using a p z -orbital tight binding model with third-nearest-neighbor (3nn) coupling. The hopping parameters are obtained by fitting the 3nn dispersions to those of an extended Hückel theory. The resultant massive Dirac fermion system has a band gap E g ≈ 64 meV. The extrinsic plasmon dispersion relation is found to asymptotically approach a universal dispersion curve as the chemical potential μ increases, whereas the intrinsic plasmon dispersion relation is found to have both energy and momentum thresholds. We also report an analytical model for the extrinsic plasmon group velocity in the q → 0 limit.

  5. General-Covariant Quantum Mechanics of Dirac Particle in Curved Space-Times

    International Nuclear Information System (INIS)

    Tagirov, Eh.A.

    1994-01-01

    A general covariant analog of the standard non-relativistic Quantum Mechanics with relativistic corrections in normal geodesic frames in the general Riemannian space-time is constructed for the Dirac particle. Not only the Pauli equation with hermitian Hamiltonian and the pre-Hilbert structure of space of its solutions but also the matrix elements of hermitian operators of momentum, (curvilinear) spatial coordinates and spin of the particle are deduced as general-covariant asymptotic approximation in c -2 , c being the velocity of light, to their naturally determined general-relativistic pre images. It is shown that the Hamiltonian in the Pauli equation originated by the Dirac equation is unitary equivalent to the operator of energy, originated by the metric energy-momentum tensor of the spinor field. Commutation and other properties of the observables connected with the considered change of geometrical background of Quantum Mechanics are briefly discussed. 7 refs

  6. Supersymmetric Dirac particles in Riemann-Cartan space-time

    International Nuclear Information System (INIS)

    Rumpf, H.

    1981-01-01

    A natural extension of the supersymmetric model of Di Vecchia and Ravndal yields a nontrivial coupling of classical spinning particles to torsion in a Riemann-Cartan geometry. The equations of motion implied by this model coincide with a consistent classical limit of the Heisenberg equations derived from the minimally coupled Dirac equation. Conversely, the latter equation is shown to arise from canonical quantization of the classical system. The Heisenberg equations are obtained exact in all powers of h/2π and thus complete the partial results of previous WKB calculations. The author also considers such matters of principle as the mathematical realization of anticommuting variables, the physical interpretation of supersymmetry transformations, and the effective variability of rest mass. (Auth.)

  7. On the dispersion characteristics of extraordinary mode in a relativistic fully degenerate electron plasma

    Science.gov (United States)

    Noureen, S.; Abbas, G.; Sarfraz, M.

    2018-01-01

    The study of relativistic degenerate plasmas is important in many astrophysical and laboratory environments. Using linearized relativistic Vlasov-Maxwell equations, a generalized expression for the plasma conductivity tensor is derived. Employing Fermi-Dirac distribution at zero temperature, the dispersion relation of the extraordinary mode in a relativistic degenerate electron plasma is investigated. The propagation characteristics are examined in different relativistic density ranges. The shifting of cutoff points due to relativistic effects is observed analytically and graphically. Non-relativistic and ultra-relativistic limiting cases are also presented.

  8. DIRAC Security

    CERN Document Server

    Casajús Ramo, A

    2006-01-01

    DIRAC is the LHCb Workload and Data Management System. Based on a service-oriented architecture, it enables generic distributed computing with lightweight Agents and Clients for job execution and data transfers. DIRAC implements a client-server architecture exposing server methods through XML Remote Procedure Call (XML-RPC) protocol. DIRAC is mostly coded in python. DIRAC security infrastructure has been designed to be a completely generic XML-RPC transport over a SSL tunnel. This new security layer is able to handle standard X509 certificates as well as grid-proxies to authenticate both sides of the connection. Serve and client authentication relies over OpenSSL and py-Open SSL, but to be able to handle grid proxies some modifications have been added to those libraries. DIRAC security infrastructure handles authorization and authorization as well as provides extended capabilities like secure connection tunneling and file transfer. Using this new security infrastructure all LHCb users can safely make use o...

  9. A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene

    KAUST Repository

    Brinkman, Daniel; Heitzinger, Clemens Heitzinger; Markowich, Peter A.

    2014-01-01

    We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac-Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac-Poisson system where potentials act as beam splitters or Veselago lenses. © 2013 Elsevier Inc.

  10. Quantum confinement and heavy surface states of Dirac fermions in bismuth (111) films: An analytical approach

    Science.gov (United States)

    Enaldiev, V. V.; Volkov, V. A.

    2018-03-01

    Recent high-resolution angle-resolved photoemission spectroscopy experiments have given a reason to believe that pure bismuth is a topologically nontrivial semimetal. We derive an analytic theory of surface and size-quantized states of Dirac fermions in Bi(111) films taking into account the new data. The theory relies on a new phenomenological momentum-dependent boundary condition for the effective Dirac equation. The boundary condition is described by two real parameters that are expressed by a linear combination of the Dresselhaus and Rashba interface spin-orbit interaction parameters. In semi-infinite Bi(111), near the M ¯ point the surface states possess anisotropical parabolic dispersion with very heavy effective mass in the Γ ¯-M ¯ direction order of ten free electron masses and light effective mass in the M ¯-K ¯ direction order of one hundredth of free electron mass. In Bi(111) films with equivalent surfaces, the surface states from top and bottom surfaces are not split. In such a symmetric film with arbitrary thickness, the bottom of the lowest quantum confinement subband in the conduction band coincides with the bottom of the bulk conduction band in the M ¯ point.

  11. Wave-equation dispersion inversion of surface waves recorded on irregular topography

    KAUST Repository

    Li, Jing; Schuster, Gerard T.; Lin, Fan-Chi; Alam, Amir

    2017-01-01

    Significant topographic variations will strongly influence the amplitudes and phases of propagating surface waves. Such effects should be taken into account, otherwise the S-velocity model inverted from the Rayleigh dispersion curves will contain significant inaccuracies. We now show that the recently developed wave-equation dispersion inversion (WD) method naturally takes into account the effects of topography to give accurate S-velocity tomograms. Application of topographic WD to demonstrates that WD can accurately invert dispersion curves from seismic data recorded over variable topography. We also apply this method to field data recorded on the crest of mountainous terrain and find with higher resolution than the standard WD tomogram.

  12. Wave-equation dispersion inversion of surface waves recorded on irregular topography

    KAUST Repository

    Li, Jing

    2017-08-17

    Significant topographic variations will strongly influence the amplitudes and phases of propagating surface waves. Such effects should be taken into account, otherwise the S-velocity model inverted from the Rayleigh dispersion curves will contain significant inaccuracies. We now show that the recently developed wave-equation dispersion inversion (WD) method naturally takes into account the effects of topography to give accurate S-velocity tomograms. Application of topographic WD to demonstrates that WD can accurately invert dispersion curves from seismic data recorded over variable topography. We also apply this method to field data recorded on the crest of mountainous terrain and find with higher resolution than the standard WD tomogram.

  13. DIRAC distributed secure framework

    International Nuclear Information System (INIS)

    Casajus, A; Graciani, R

    2010-01-01

    DIRAC, the LHCb community Grid solution, provides access to a vast amount of computing and storage resources to a large number of users. In DIRAC users are organized in groups with different needs and permissions. In order to ensure that only allowed users can access the resources and to enforce that there are no abuses, security is mandatory. All DIRAC services and clients use secure connections that are authenticated using certificates and grid proxies. Once a client has been authenticated, authorization rules are applied to the requested action based on the presented credentials. These authorization rules and the list of users and groups are centrally managed in the DIRAC Configuration Service. Users submit jobs to DIRAC using their local credentials. From then on, DIRAC has to interact with different Grid services on behalf of this user. DIRAC has a proxy management service where users upload short-lived proxies to be used when DIRAC needs to act on behalf of them. Long duration proxies are uploaded by users to a MyProxy service, and DIRAC retrieves new short delegated proxies when necessary. This contribution discusses the details of the implementation of this security infrastructure in DIRAC.

  14. Dirac electron in a chiral space-time crystal created by counterpropagating circularly polarized plane electromagnetic waves

    Science.gov (United States)

    Borzdov, G. N.

    2017-10-01

    The family of solutions to the Dirac equation for an electron moving in an electromagnetic lattice with the chiral structure created by counterpropagating circularly polarized plane electromagnetic waves is obtained. At any nonzero quasimomentum, the dispersion equation has two solutions which specify bispinor wave functions describing electron states with different energies and mean values of momentum and spin operators. The inversion of the quasimomentum results in two other linearly independent solutions. These four basic wave functions are uniquely defined by eight complex scalar functions (structural functions), which serve as convenient building blocks of the relations describing the electron properties. These properties are illustrated in graphical form over a wide range of quasimomenta. The superpositions of two basic wave functions describing different spin states and corresponding to (i) the same quasimomentum (unidirectional electron states with the spin precession) and (ii) the two equal-in-magnitude but oppositely directed quasimomenta (bidirectional electron states) are also treated.

  15. Nonsymmorphic cubic Dirac point and crossed nodal rings across the ferroelectric phase transition in LiOsO3

    Science.gov (United States)

    Yu, Wing Chi; Zhou, Xiaoting; Chuang, Feng-Chuan; Yang, Shengyuan A.; Lin, Hsin; Bansil, Arun

    2018-05-01

    Crystalline symmetries can generate exotic band-crossing features, which can lead to unconventional fermionic excitations with interesting physical properties. We show how a cubic Dirac point—a fourfold-degenerate band-crossing point with cubic dispersion in a plane and a linear dispersion in the third direction—can be stabilized through the presence of a nonsymmorphic glide mirror symmetry in the space group of the crystal. Notably, the cubic Dirac point in our case appears on a threefold axis, even though it has been believed previously that such a point can only appear on a sixfold axis. We show that a cubic Dirac point involving a threefold axis can be realized close to the Fermi level in the nonferroelectric phase of LiOsO3. Upon lowering temperature, LiOsO3 has been shown experimentally to undergo a structural phase transition from the nonferroelectric phase to the ferroelectric phase with spontaneously broken inversion symmetry. Remarkably, we find that the broken symmetry transforms the cubic Dirac point into three mutually crossed nodal rings. There also exist several linear Dirac points in the low-energy band structure of LiOsO3, each of which is transformed into a single nodal ring across the phase transition.

  16. A maximally particle-hole asymmetric spectrum emanating from a semi-Dirac point

    Science.gov (United States)

    Quan, Yundi; Pickett, Warren E.

    2018-02-01

    Tight binding models have proven an effective means of revealing Dirac (massless) dispersion, flat bands (infinite mass), and intermediate cases such as the semi-Dirac (sD) dispersion. This approach is extended to a three band model that yields, with chosen parameters in a two-band limit, a closed line with maximally asymmetric particle-hole dispersion: infinite mass holes, zero mass particles. The model retains the sD points for a general set of parameters. Adjacent to this limiting case, hole Fermi surfaces are tiny and needle-like. A pair of large electron Fermi surfaces at low doping merge and collapse at half filling to a flat (zero energy) closed contour with infinite mass along the contour and enclosing no carriers on either side, while the hole Fermi surface has shrunk to a point at zero energy, also containing no carriers. The tight binding model is used to study several characteristics of the dispersion and density of states. The model inspired generalization of sD dispersion to a general  ± \\sqrt{k_x2n +k_y2m} form, for which analysis reveals that both n and m must be odd to provide a diabolical point with topological character. Evolution of the Hofstadter spectrum of this three band system with interband coupling strength is presented and discussed.

  17. Rare-Region-Induced Avoided Quantum Criticality in Disordered Three-Dimensional Dirac and Weyl Semimetals

    Directory of Open Access Journals (Sweden)

    J. H. Pixley

    2016-06-01

    Full Text Available We numerically study the effect of short-ranged potential disorder on massless noninteracting three-dimensional Dirac and Weyl fermions, with a focus on the question of the proposed (and extensively theoretically studied quantum critical point separating semimetal and diffusive-metal phases. We determine the properties of the eigenstates of the disordered Dirac Hamiltonian (H and exactly calculate the density of states (DOS near zero energy, using a combination of Lanczos on H^{2} and the kernel polynomial method on H. We establish the existence of two distinct types of low-energy eigenstates contributing to the disordered density of states in the weak-disorder semimetal regime. These are (i typical eigenstates that are well described by linearly dispersing perturbatively dressed Dirac states and (ii nonperturbative rare eigenstates that are weakly dispersive and quasilocalized in the real-space regions with the largest (and rarest local random potential. Using twisted boundary conditions, we are able to systematically find and study these two (essentially independent types of eigenstates. We find that the Dirac states contribute low-energy peaks in the finite-size DOS that arise from the clean eigenstates which shift and broaden in the presence of disorder. On the other hand, we establish that the rare quasilocalized eigenstates contribute a nonzero background DOS which is only weakly energy dependent near zero energy and is exponentially small at weak disorder. We also find that the expected semimetal to diffusive-metal quantum critical point is converted to an avoided quantum criticality that is “rounded out” by nonperturbative effects, with no signs of any singular behavior in the DOS at the energy of the clean Dirac point. However, the crossover effects of the avoided (or hidden criticality manifest themselves in a so-called quantum critical fan region away from the Dirac energy. We discuss the implications of our results for

  18. The GridPP DIRAC project - DIRAC for non-LHC communities

    CERN Document Server

    Bauer, D; Currie, R; Fayer, S; Huffman, A; Martyniak, J; Rand, D; Richards, A

    2015-01-01

    The GridPP consortium in the UK is currently testing a multi-VO DIRAC service aimed at non-LHC VOs. These VOs (Virtual Organisations) are typically small and generally do not have a dedicated computing support post. The majority of these represent particle physics experiments (e.g. NA62 and COMET), although the scope of the DIRAC service is not limited to this field. A few VOs have designed bespoke tools around the EMI-WMS & LFC, while others have so far eschewed distributed resources as they perceive the overhead for accessing them to be too high. The aim of the GridPP DIRAC project is to provide an easily adaptable toolkit for such VOs in order to lower the threshold for access to distributed resources such as Grid and cloud computing. As well as hosting a centrally run DIRAC service, we will also publish our changes and additions to the upstream DIRAC codebase under an open-source license. We report on the current status of this project and show increasing adoption of DIRAC within the non-LHC communiti...

  19. The GridPP DIRAC project - DIRAC for non-LHC communities

    Science.gov (United States)

    Bauer, D.; Colling, D.; Currie, R.; Fayer, S.; Huffman, A.; Martyniak, J.; Rand, D.; Richards, A.

    2015-12-01

    The GridPP consortium in the UK is currently testing a multi-VO DIRAC service aimed at non-LHC VOs. These VOs (Virtual Organisations) are typically small and generally do not have a dedicated computing support post. The majority of these represent particle physics experiments (e.g. NA62 and COMET), although the scope of the DIRAC service is not limited to this field. A few VOs have designed bespoke tools around the EMI-WMS & LFC, while others have so far eschewed distributed resources as they perceive the overhead for accessing them to be too high. The aim of the GridPP DIRAC project is to provide an easily adaptable toolkit for such VOs in order to lower the threshold for access to distributed resources such as Grid and cloud computing. As well as hosting a centrally run DIRAC service, we will also publish our changes and additions to the upstream DIRAC codebase under an open-source license. We report on the current status of this project and show increasing adoption of DIRAC within the non-LHC communities.

  20. A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Taohua Liu

    2017-01-01

    Full Text Available Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K and computational cost of O(Klog⁡K. Traditionally, the Gaussian elimination method requires storage of O(K2 and computational cost of O(K3. Finally, the accuracy and efficiency of the method are checked with a numerical example.

  1. Quantum tunneling effect of Dirac particles in a Schwarzschild-Godel space-time

    Energy Technology Data Exchange (ETDEWEB)

    Qi, D.-J.; Li, S.-M., E-mail: qidejiang0504@126.com [Shenyang Inst. of Engineering, Shenyang (China); Ru, H.-Q. [Northeastern Univ., Shenyang (China)

    2010-11-15

    In this paper, motivated by the Kerner and Man fermion tunneling method of 4-dimensional black holes, we further improve the analysis to investigate the quantum tunneling effect of Dirac particles from the five-dimensional Schwarzschild-Godel black hole. We successfully construct a set of appropriate matrices γ{sup μ} for the general covariant Dirac equation and derive the tunneling probability and Hawking temperature, which is exactly the same as that obtained by other methods. (author)

  2. Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones

    OpenAIRE

    Assili, Mohamed; Haddad, Sonia

    2013-01-01

    We theoretically study the effect of the motion and the merging of Dirac cone on the interlayer magnetoresistance in multilayer graphene like systems. This merging, which could be induced by a uniaxial strain, gives rise in monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase where Dirac points disappear. Based on a universal Hamiltonian proposed to describe the motion and the merging of Dirac points in two dimensional Dirac electron cr...

  3. A new approach to obtaining the roots of the dispersion equation for slab geometry multiplying media

    International Nuclear Information System (INIS)

    Silva, Davi J.M.; Barros, Ricardo C.; Alves Filho, Hermes

    2013-01-01

    In this work we describe an alternative approach for obtaining the roots of the dispersion equation. For the mathematical model, we used the slab-geometry neutron transport equation in the discrete ordinates (S N ), formulation, considering isotropic scattering and monoenergetic model. The basic idea is to find a basis for the kernel of the S N differential operator, whose elements are exponential eigenfunctions corresponding to distinct eigenvalues which are the roots of the dispersion equation. That strategy yields a gain in programming computational codes, including the strategy used to obtain the purely imaginary eigenvalues and their associated complex eigenfunctions, that appear in the spectral analysis of the S N equations in multiplying media. These eigenvalues and corresponding eigenfunctions are used to obtain the parameters of the auxiliary equations of the spectral nodal methods, e.g., the spectral diamond (SD) auxiliary equation. (author)

  4. Photon-Assisted Spectroscopy of Dirac Electrons in Graphene

    Directory of Open Access Journals (Sweden)

    Abdelrazek A. S.

    2012-01-01

    Full Text Available The quantum Goos-Hanchen effect in graphene is investigated. The Goos-Hanchen phase shift is derived by solving the Dirac eigenvalue differential equation. This phase shift varies with the angle of incidence of the quasiparticle Dirac fermions on the bar- rier. Calculations show that the dependence of the phase shift on the angle of incidence is sensitive to the variation of the energy gap of graphene, the applied magnetic field and the frequency of the electromagnetic waves. The present results show that the con- ducting states in the sidebands is very effective in the phase shift for frequencies of the applied electromagnetic field. This investigation is very important for the application of graphene in nanoelectronics and nanophotonics.

  5. Interplay between topology and disorder in a two-dimensional semi-Dirac material

    OpenAIRE

    Sriluckshmy, P. V.; Saha, Kush; Moessner, Roderich

    2017-01-01

    We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one, and a parabolic dispersion in the orthogonal, direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semi-metal, as it generates a momentum independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three dist...

  6. Positive solutions for nonlocal dispersal equation with spatial degeneracy

    Science.gov (United States)

    Sun, Jian-Wen

    2018-02-01

    In this paper, we consider the positive solutions of the nonlocal dispersal equation \\int \\limits _{Ω }J(x,y)[u(y)-u(x)]dy=-λ m(x)u(x)+[c(x)+ɛ ]u^p(x) \\quad { in }\\bar{Ω }, where Ω \\subset R^N is a bounded domain, λ ,ɛ and p>1 are positive constants. The dispersal kernel J and the coefficient c( x) are nonnegative, but c( x) has a degeneracy in some subdomain of Ω . In order to study the influence of heterogeneous environment on the nonlocal system, we study the sharp spatial patterns of positive solutions as ɛ → 0. We obtain that the positive solutions always have blow-up asymptotic profiles in \\bar{Ω }. Meanwhile, we find that the profiles in degeneracy domain are different from the domain without degeneracy.

  7. Exact solutions with solitary patterns for the Zakharov-Kuznetsov equations with fully nonlinear dispersion

    International Nuclear Information System (INIS)

    Inc, Mustafa

    2007-01-01

    In this paper, the nonlinear dispersive Zakharov-Kuznetsov ZK(m, n, k) equations are solved exactly by using the Adomian decomposition method. The two special cases, ZK(2, 2, 2) and ZK(3, 3, 3), are chosen to illustrate the concrete scheme of the decomposition method in ZK(m, n, k) equations. General formulas for the solutions of ZK(m, n, k) equations are established

  8. Dirac gap-induced graphene quantum dot in an electrostatic potential

    Science.gov (United States)

    Giavaras, G.; Nori, Franco

    2011-04-01

    A spatially modulated Dirac gap in a graphene sheet leads to charge confinement, thus enabling a graphene quantum dot to be formed without the application of external electric and magnetic fields [G. Giavaras and F. Nori, Appl. Phys. Lett. 97, 243106 (2010)]. This can be achieved provided the Dirac gap has a local minimum in which the states become localized. In this work, the physics of such a gap-induced dot is investigated in the continuum limit by solving the Dirac equation. It is shown that gap-induced confined states couple to the states introduced by an electrostatic quantum well potential. Hence the region in which the resulting hybridized states are localized can be tuned with the potential strength, an effect which involves Klein tunneling. The proposed quantum dot may be used to probe quasirelativistic effects in graphene, while the induced confined states may be useful for graphene-based nanostructures.

  9. Electronic structure of a graphene superlattice with massive Dirac fermions

    International Nuclear Information System (INIS)

    Lima, Jonas R. F.

    2015-01-01

    We study the electronic and transport properties of a graphene-based superlattice theoretically by using an effective Dirac equation. The superlattice consists of a periodic potential applied on a single-layer graphene deposited on a substrate that opens an energy gap of 2Δ in its electronic structure. We find that extra Dirac points appear in the electronic band structure under certain conditions, so it is possible to close the gap between the conduction and valence minibands. We show that the energy gap E g can be tuned in the range 0 ≤ E g  ≤ 2Δ by changing the periodic potential. We analyze the low energy electronic structure around the contact points and find that the effective Fermi velocity in very anisotropic and depends on the energy gap. We show that the extra Dirac points obtained here behave differently compared to previously studied systems

  10. DIRAC MATRICES IN CHIRAL REPRESENTATION AND THE CONNECTION WITH THE ELECTRIC FIELD PARALLEL TO THE MAGNETIC FIELD MATRICES DE DIRAC EN REPRESENTACIÓN QUIRAL Y LA CONEXIÓN CON EL CAMPO ELÉCTRICO PARALELO AL CAMPO MAGNÉTICO

    Directory of Open Access Journals (Sweden)

    Héctor Torres-Silva

    2008-11-01

    Full Text Available In this paper we offer an expression of the general Foldy-Wouthuysen transformation in the chiral representation of Dirac matrices interacting with fermion field. Our hypothesis is that through the multiplication of the Pauli matrix and Maxwell's chiral equations in the case of ,one obtains the Dirac's chiral equation. This is the proof of the theorem that the wave mechanics of quantum particles represent a specialized electrodynamic.En este trabajo se presenta una expresión de la transformación general de Foldy-Wouthuysen a la representación quiral de las matrices de Dirac interactuando con un campo de fermión. La hipótesis es que a través de la multiplicación de la matriz de Pauli por las ecuaciones quirales de Maxwell en el caso de , se obtiene la ecuación quiral de Dirac. Esta es la prueba del teorema de que la mecánica de ondas de partícula cuántica representa una electrodinámica especializada.

  11. Direct and inverse source problems for a space fractional advection dispersion equation

    KAUST Repository

    Aldoghaither, Abeer; Laleg-Kirati, Taous-Meriem; Liu, Da Yan

    2016-01-01

    In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from final observations. We first derive the analytic

  12. Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method

    International Nuclear Information System (INIS)

    Lewandowski, Jerome L.V.

    2005-01-01

    A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details

  13. Dirac-Screening Stabilized Surface-State Transport in a Topological Insulator

    Directory of Open Access Journals (Sweden)

    Christoph Brüne

    2014-12-01

    Full Text Available We report magnetotransport studies on a gated strained HgTe device. This material is a three-dimensional topological insulator and exclusively shows surface-state transport. Remarkably, the Landau-level dispersion and the accuracy of the Hall quantization remain unchanged over a wide density range (3×10^{11}  cm^{−2}Dirac-type quantum Hall effect allows us to identify the contributions from the individual surfaces. A k·p model can describe the experiments but only when assuming a steep band bending across the regions where the topological surface states are contained. This steep potential originates from the specific screening properties of Dirac systems and causes the gate voltage to influence the position of the Dirac points rather than that of the Fermi level.

  14. Connection between Dirac and matrix Schroedinger inverse-scattering transforms

    International Nuclear Information System (INIS)

    Jaulent, M.; Leon, J.J.P.

    1978-01-01

    The connection between two applications of the inverse scattering method for solving nonlinear equations is established. The inverse method associated with the massive Dirac system (D) : (iσ 3 d/dx - i q 3 σ 1 - q 1 σ 2 + mσ 2 )Y = epsilonY is rediscovered from the inverse method associated with the 2 x 2 matrix Schroedinger equation (S) : Ysub(xx) + (k 2 -Q)Y = 0. Here Q obeys a nonlinear constraint equivalent to a linear constraint on the reflection coefficient for (S). (author)

  15. LHCb: DIRAC Secure Distributed Platform

    CERN Multimedia

    Casajus, A

    2009-01-01

    DIRAC, the LHCb community grid solution, provides access to a vast amount of computing and storage resources to a large number of users. In DIRAC users are organized in groups with different needs and permissions. In order to ensure that only allowed users can access the resources and to enforce that there are no abuses, security is mandatory. All DIRAC services and clients use secure connections that are authenticated using certificates and grid proxies. Once a client has been authenticated, authorization rules are applied to the requested action based on the presented credentials. These authorization rules and the list of users and groups are centrally managed in the DIRAC Configuration Service. Users submit jobs to DIRAC using their local credentials. From then on, DIRAC has to interact with different Grid services on behalf of this user. DIRAC has a proxy management service where users upload short-lived proxies to be used when DIRAC needs to act on behalf of them. Long duration proxies are uploaded by us...

  16. Direct and inverse scattering at fixed energy for massless charged Dirac fields by Kerr-Newman-de Sitter black holes

    CERN Document Server

    Daudé, Thierry

    2017-01-01

    In this paper, the authors study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, they establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields. This leads to the definition of the time-dependent scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons. The authors also use the miraculous property (quoting Chandrasekhar)-that the Dirac equation can be separated into radial and angular ordinary differential equations-to make the link between the time-dependent scattering operator and its stationary counterpart. This leads to a nice expression of the scattering matrix at fixed energy in terms of stationary solutions of the system of separated equations. In a second part, the authors use this expression of ...

  17. Angular Magnetoresistance and Hall Measurements in New Dirac Material, ZrSiS

    Science.gov (United States)

    Ali, Mazhar; Schoop, Leslie; Lotsch, Bettina; Parkin, Stuart

    Dirac and Weyl materials have shot to the forefront of condensed matter research in the last few years. Recently, the square-net material, ZrSiS, was theorized and experimentally shown (via ARPES) to host several highly dispersive Dirac cones, including the first Dirac cone demanded by non-symmorphic symmetry in a Si square net. Here we report the magnetoresistance and Hall Effect measurements in this compound. ZrSiS samples with RRR = 40 were found to have MR values up to 6000% at 2 K, be predominantly p-type with a carrier concentration of ~8 x 1019 cm-3 and mobility ~8500 cm2/Vs. Angular magnetoresistance measurements reveal a peculiar behavior with multiple local maxima, depending on field strength, indicating of a sensitive and sensitive Fermi surface. SdH oscillations analysis confirms Hall and angular magnetoresistance measurements. These results, in the context of the theoretical and ARPES results, will be discussed.

  18. STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS

    KAUST Repository

    FELLNER, KLEMENS

    2010-12-01

    In this paper, we are interested in the large-time behaviour of a solution to a non-local interaction equation, where a density of particles/individuals evolves subject to an interaction potential and an external potential. It is known that for regular interaction potentials, stable stationary states of these equations are generically finite sums of Dirac masses. For a finite sum of Dirac masses, we give (i) a condition to be a stationary state, (ii) two necessary conditions of linear stability w.r.t. shifts and reallocations of individual Dirac masses, and (iii) show that these linear stability conditions imply local non-linear stability. Finally, we show that for regular repulsive interaction potential Wε converging to a singular repulsive interaction potential W, the Dirac-type stationary states ρ̄ ε approximate weakly a unique stationary state ρ̄ ∈ L∞. We illustrate our results with numerical examples. © 2010 World Scientific Publishing Company.

  19. Blow up of solutions to ordinary differential equations arising in nonlinear dispersive problems

    Directory of Open Access Journals (Sweden)

    Milena Dimova

    2018-03-01

    Full Text Available We study a new class of ordinary differential equations with blow up solutions. Necessary and sufficient conditions for finite blow up time are proved. Based on the new differential equation, a revised version of the concavity method of Levine is proposed. As an application we investigate the non-existence of global solutions to the Cauchy problem of Klein-Gordon, and to the double dispersive equations. We obtain necessary and sufficient condition for finite time blow up with arbitrary positive energy. A very general sufficient condition for blow up is also given.

  20. A toy model for higher spin Dirac operators

    International Nuclear Information System (INIS)

    Eelbode, D.; Van de Voorde, L.

    2010-01-01

    This paper deals with the higher spin Dirac operator Q 2,1 acting on functions taking values in an irreducible representation space for so(m) with highest weight (5/2, 3/2, 1/2,..., 1/2). . This operator acts as a toy model for generalizations of the classical Rarita-Schwinger equations in Clifford analysis. Polynomial null solutions for this operator are studied in particular.

  1. Surface regulated arsenenes as Dirac materials: From density functional calculations

    International Nuclear Information System (INIS)

    Yuan, Junhui; Xie, Qingxing; Yu, Niannian; Wang, Jiafu

    2017-01-01

    Highlights: • The presence of Dirac cones in chemically decorated buckled arsenene AsX (X = CN, NC, NCO, NCS, and NCSe) has been revealed. • First-principles calculations show that all these chemically decorated arsenenes are kinetically stable in defending thermal fluctuations in room temperature. - Abstract: Using first principle calculations based on density functional theory (DFT), we have systematically investigated the structure stability and electronic properties of chemically decorated arsenenes, AsX (X = CN, NC, NCO, NCS and NCSe). Phonon dispersion and formation energy analysis reveal that all the five chemically decorated buckled arsenenes are energetically favorable and could be synthesized. Our study shows that wide-bandgap arsenene would turn into Dirac materials when functionalized by -X (X = CN, NC, NCO, NCS and NCSe) groups, rendering new promises in next generation high-performance electronic devices.

  2. The many faces of Maxwell, Dirac and Einstein equations a Clifford bundle approach

    CERN Document Server

    Rodrigues, Jr, Waldyr A

    2016-01-01

    This book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research. This thoroughly revised second edition also adds three new chapters: on the Clifford bundle approach to the Riemannian or semi-Riemannian differential geometry of branes; on Komar currents in the context of the General Relativity theory; and an analysis of the similarities and main differences between Dirac, Majorana and ELKO spinor fields. The exercises with solut...

  3. The bundles of algebraic and Dirac-Hestenes spinor fields

    International Nuclear Information System (INIS)

    Mosna, Ricardo A.; Rodrigues, Waldyr A. Jr.

    2004-01-01

    Our main objective in this paper is to clarify the ontology of Dirac-Hestenes spinor fields (DHSF) and its relationship with even multivector fields, on a Riemann-Cartan spacetime (RCST) M=(M,g,∇,τ g ,↑) admitting a spin structure, and to give a mathematically rigorous derivation of the so-called Dirac-Hestenes equation (DHE) in the case where M is a Lorentzian spacetime (the general case when M is a RCST will be discussed in another publication). To this aim we introduce the Clifford bundle of multivector fields (Cl(M,g)) and the left (Cl Spin 1,3 e l (M)) and right (Cl Spin 1,3 e r (M)) spin-Clifford bundles on the spin manifold (M,g). The relation between left ideal algebraic spinor fields (LIASF) and Dirac-Hestenes spinor fields (both fields are sections of Cl Spin 1,3 e l (M)) is clarified. We study in detail the theory of covariant derivatives of Clifford fields as well as that of left and right spin-Clifford fields. A consistent Dirac equation for a DHSF Ψ is a member of sec Cl Spin 1,3 e l (M) (denoted DECl l ) on a Lorentzian spacetime is found. We also obtain a representation of the DECl l in the Clifford bundle Cl(M,g). It is such equation that we call the DHE and it is satisfied by Clifford fields ψ Ξ is a member of sec Cl(M,g). This means that to each DHSF Ψ is a member of sec Cl Spin 1,3 e l (M) and spin frame Ξ is a member of sec P Spin 1,3 e (M), there is a well-defined sum of even multivector fields ψ Ξ isa member of sec Cl(M,g) (EMFS) associated with Ψ. Such an EMFS is called a representative of the DHSF on the given spin frame. And, of course, such a EMFS (the representative of the DHSF) is not a spinor field. With this crucial distinction between a DHSF and its representatives on the Clifford bundle, we provide a consistent theory for the covariant derivatives of Clifford and spinor fields of all kinds. We emphasize that the DECl l and the DHE, although related, are equations of different mathematical natures. We study also the

  4. Robust Imaging Methodology for Challenging Environments: Wave Equation Dispersion Inversion of Surface Waves

    KAUST Repository

    Li, Jing; Schuster, Gerard T.; Zeng, Zhaofa

    2017-01-01

    A robust imaging technology is reviewed that provide subsurface information in challenging environments: wave-equation dispersion inversion (WD) of surface waves for the shear velocity model. We demonstrate the benefits and liabilities of the method

  5. The role of spin–orbit coupling in topologically protected interface states in Dirac materials

    International Nuclear Information System (INIS)

    Abergel, D S L; Balatsky, Alexander V; Edge, Jonathan M

    2014-01-01

    We highlight the fact that two-dimensional (2D) materials with Dirac-like low energy band structures and spin–orbit coupling (SOC) will produce linearly dispersing topologically protected Jackiw–Rebbi modes at interfaces where the Dirac mass changes sign. These modes may support persistent spin or valley currents parallel to the interface, and the exact arrangement of such topologically protected currents depends crucially on the details of the SOC in the material. As examples, we discuss buckled 2D hexagonal lattices such as silicene or germanene, and transition metal dichalcogenides such as MoS 2 . (paper)

  6. Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves

    DEFF Research Database (Denmark)

    Eldeberky, Y.; Madsen, Per A.

    1999-01-01

    and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement......This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary...... is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic...

  7. Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones

    International Nuclear Information System (INIS)

    Assili, M; Haddad, S

    2013-01-01

    We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT) 2 I 3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed. (paper)

  8. Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones

    Science.gov (United States)

    Assili, M.; Haddad, S.

    2013-09-01

    We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT)2I3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed.

  9. Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones.

    Science.gov (United States)

    Assili, M; Haddad, S

    2013-09-11

    We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT)2I3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed.

  10. Dirac fermions in blue-phosphorus

    International Nuclear Information System (INIS)

    Li, Yuanchang; Chen, Xiaobin

    2014-01-01

    We propose that Dirac cones can be engineered in phosphorene with fourfold-coordinated phosphorus atoms. The key is to separate the energy levels of the in-plane (s, p x , and p y ) and out-of-plane (p z ) oribtals through the sp 2 configuration, yielding respective σ- and π-character Dirac cones, and then quench the latter. As a proof-of-principle study, we create σ-character Dirac cones in hydrogenated and fluorinated phosphorene with a honeycomb lattice. The obtained Dirac cones are at K-points, slightly anisotropic, with Fermi velocities of 0.91 and 1.23 times that of graphene along the ΓK and KM direction, and maintain good linearity up to ∼2 eV for holes. A substantive advantage of a σ-character Dirac cone is its convenience in tuning the Dirac gap via in-plane strain. Our findings pave the way for development of high-performance electronic devices based on Dirac materials. (letter)

  11. Tinene: a two-dimensional Dirac material with a 72 meV band gap.

    Science.gov (United States)

    Cai, Bo; Zhang, Shengli; Hu, Ziyu; Hu, Yonghong; Zou, Yousheng; Zeng, Haibo

    2015-05-21

    Dirac materials have attracted great interest for both fundamental research and electronic devices due to their unique band structures, but the usual near zero bandgap of graphene results in a poor on-off ratio in the corresponding transistors. Here, we report on tinene, monolayer gray tin, as a new two-dimensional material with both Dirac characteristics and a remarkable 72 meV bandgap based on density functional theory calculations. Compared with silicene and germanene, tinene has a similar hexagonal honeycomb monolayer structure, but it has an obviously larger buckling height (∼0.70 Å). Interestingly, such a moderate buckling structure results in phonon dispersion without appreciable imaginary modes, indicating the strong dynamic stability of tinene. Significantly, a distinct transformation is discovered from the band structure that six Dirac cones would appear at high symmetry K points in the first Brillouin zone when gray tin is thinned from the bulk to monolayer, but a bandgap as large as 72 meV is still preserved. Considering the recent successful realization of silicene and germanene with a similar structure, the predicted stable tinene with Dirac characteristics and a suitable bandgap is a possibility for the "more than Moore" materials and devices.

  12. Dynamic conductivity modified by impurity resonant states in doping three-dimensional Dirac semimetals

    Science.gov (United States)

    Li, Shuai; Wang, Chen; Zheng, Shi-Han; Wang, Rui-Qiang; Li, Jun; Yang, Mou

    2018-04-01

    The impurity effect is studied in three-dimensional Dirac semimetals in the framework of a T-matrix method to consider the multiple scattering events of Dirac electrons off impurities. It has been found that a strong impurity potential can significantly restructure the energy dispersion and the density of states of Dirac electrons. An impurity-induced resonant state emerges and significantly modifies the pristine optical response. It is shown that the impurity state disturbs the common longitudinal optical conductivity by creating either an optical conductivity peak or double absorption jumps, depending on the relative position of the impurity band and the Fermi level. More importantly, these conductivity features appear in the forbidden region between the Drude and interband transition, completely or partially filling the Pauli block region of optical response. The underlying physics is that the appearance of resonance states as well as the broadening of the bands leads to a more complicated selection rule for the optical transitions, making it possible to excite new electron-hole pairs in the forbidden region. These features in optical conductivity provide valuable information to understand the impurity behaviors in 3D Dirac materials.

  13. The Dirac equation in electronic structure calculations: Accurate evaluation of DFT predictions for actinides

    International Nuclear Information System (INIS)

    Wills, John M.; Mattsson, Ann E.

    2012-01-01

    Brooks, Johansson, and Skriver, using the LMTO-ASA method and considerable insight, were able to explain many of the ground state properties of the actinides. In the many years since this work was done, electronic structure calculations of increasing sophistication have been applied to actinide elements and compounds, attempting to quantify the applicability of DFT to actinides and actinide compounds and to try to incorporate other methodologies (i.e. DMFT) into DFT calculations. Through these calculations, the limits of both available density functionals and ad hoc methodologies are starting to become clear. However, it has also become clear that approximations used to incorporate relativity are not adequate to provide rigorous tests of the underlying equations of DFT, not to mention ad hoc additions. In this talk, we describe the result of full-potential LMTO calculations for the elemental actinides, comparing results obtained with a full Dirac basis with those obtained from scalar-relativistic bases, with and without variational spin-orbit. This comparison shows that the scalar relativistic treatment of actinides does not have sufficient accuracy to provide a rigorous test of theory and that variational spin-orbit introduces uncontrolled errors in the results of electronic structure calculations on actinide elements.

  14. Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd₃As₂.

    Science.gov (United States)

    Jeon, Sangjun; Zhou, Brian B; Gyenis, Andras; Feldman, Benjamin E; Kimchi, Itamar; Potter, Andrew C; Gibson, Quinn D; Cava, Robert J; Vishwanath, Ashvin; Yazdani, Ali

    2014-09-01

    Condensed-matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations as well as the possibility to manipulate them for potential applications. It has recently been proposed that chiral, massless particles known as Weyl fermions can emerge in certain bulk materials or in topological insulator multilayers and give rise to unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry effectively forming a massless Dirac fermion has been predicted to appear as low-energy excitations in a number of materials termed three-dimensional Dirac semimetals. Here we report scanning tunnelling microscopy measurements at sub-kelvin temperatures and high magnetic fields on the II-V semiconductor Cd3As2. We probe this system down to atomic length scales, and show that defects mostly influence the valence band, consistent with the observation of ultrahigh-mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference, we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a magnetic field applied along the axis of the Dirac points, Weyl fermions are the low-energy excitations in Cd3As2.

  15. Pseudo Dirac dispersion in Mn-intercalated graphene on SiC

    KAUST Repository

    Kahaly, M. Upadhyay

    2013-07-01

    The atomic and electronic structures of bulk C6Mn, bulk C 8Mn, and Mn-intercalated graphene on SiC(0 0 0 1) and SiC(0001̄) are investigated by density functional theory. We find for both configurations of Mn-intercalated graphene a nonmagnetic state, in agreement with the experimental situation for SiC(0 0 0 1), and explain this property. The electronic structures around the Fermi energy are dominated by Dirac-like cones at energies consistent with data from angular resolved photoelectron spectroscopy [Gao et al., ACS Nano. 6 (2012) 6562]. However, our results demonstrate that the corresponding states trace back to hybridized Mn d orbitals, and not to the graphene. © 2013 Elsevier B.V. All rights reserved.

  16. Pseudo Dirac dispersion in Mn-intercalated graphene on SiC

    KAUST Repository

    Kahaly, M. Upadhyay; Kaloni, Thaneshwor P.; Schwingenschlö gl, Udo

    2013-01-01

    The atomic and electronic structures of bulk C6Mn, bulk C 8Mn, and Mn-intercalated graphene on SiC(0 0 0 1) and SiC(0001̄) are investigated by density functional theory. We find for both configurations of Mn-intercalated graphene a nonmagnetic state, in agreement with the experimental situation for SiC(0 0 0 1), and explain this property. The electronic structures around the Fermi energy are dominated by Dirac-like cones at energies consistent with data from angular resolved photoelectron spectroscopy [Gao et al., ACS Nano. 6 (2012) 6562]. However, our results demonstrate that the corresponding states trace back to hybridized Mn d orbitals, and not to the graphene. © 2013 Elsevier B.V. All rights reserved.

  17. Spatial dispersion effects upon local excitation of extrinsic plasmons in a graphene micro-disk

    Science.gov (United States)

    Mencarelli, D.; Bellucci, S.; Sindona, A.; Pierantoni, L.

    2015-11-01

    Excitation of surface plasmon waves in extrinsic graphene is studied using a full-wave electromagnetic field solver as analysis engine. Particular emphasis is placed on the role played by spatial dispersion due to the finite size of the two-dimensional material at the micro-scale. A simple instructive set up is considered where the near field of a wire antenna is held at sub-micrometric distance from a disk-shaped graphene patch. The key-input of the simulation is the graphene conductivity tensor at terahertz frequencies, being modeled by the Boltzmann transport equation for the valence and conduction electrons at the Dirac points (where a linear wave-vector dependence of the band energies is assumed). The conductivity equation is worked out in different levels of approximations, based on the relaxation time ansatz with an additional constraint for particle number conservation. Both drift and diffusion currents are shown to significantly contribute to the spatially dispersive anisotropic features of micro-scale graphene. More generally, spatial dispersion effects are predicted to influence not only plasmon propagation free of external sources, but also typical scanning probe microscopy configurations. The paper sets the focus on plasmon excitation phenomena induced by near field probes, being a central issue for the design of optical devices and photonic circuits.

  18. Three Dimensional Dirac Semimetals

    Science.gov (United States)

    Zaheer, Saad

    2014-03-01

    Dirac points on the Fermi surface of two dimensional graphene are responsible for its unique electronic behavior. One can ask whether any three dimensional materials support similar pseudorelativistic physics in their bulk electronic spectra. This possibility has been investigated theoretically and is now supported by two successful experimental demonstrations reported during the last year. In this talk, I will summarize the various ways in which Dirac semimetals can be realized in three dimensions with primary focus on a specific theory developed on the basis of representations of crystal spacegroups. A three dimensional Dirac (Weyl) semimetal can appear in the presence (absence) of inversion symmetry by tuning parameters to the phase boundary separating a bulk insulating and a topological insulating phase. More generally, we find that specific rules governing crystal symmetry representations of electrons with spin lead to robust Dirac points at high symmetry points in the Brillouin zone. Combining these rules with microscopic considerations identifies six candidate Dirac semimetals. Another method towards engineering Dirac semimetals involves combining crystal symmetry and band inversion. Several candidate materials have been proposed utilizing this mechanism and one of the candidates has been successfully demonstrated as a Dirac semimetal in two independent experiments. Work carried out in collaboration with: Julia A. Steinberg, Steve M. Young, J.C.Y. Teo, C.L. Kane, E.J. Mele and Andrew M. Rappe.

  19. Observation of the anisotropic Dirac cone in the band dispersion of 112-structured iron-based superconductor Ca{sub 0.9}La{sub 0.1}FeAs{sub 2}

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Z. T.; Li, M. Y.; Fan, C. C.; Yang, H. F.; Liu, J. S.; Wang, Z. [State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology (SIMIT), Chinese Academy of Sciences, Shanghai 200050 (China); Xing, X. Z.; Zhou, W.; Sun, Y.; Shi, Z. X. [Department of Physics and Key Laboratory of MEMS of the Ministry of Education, Southeast University, Nanjing 211189 (China); Yao, Q. [State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology (SIMIT), Chinese Academy of Sciences, Shanghai 200050 (China); State Key Laboratory of Surface Physics, Department of Physics, and Advanced Materials Laboratory, Fudan University, Shanghai 200433 (China); Li, W. [State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology (SIMIT), Chinese Academy of Sciences, Shanghai 200050 (China); State Key Laboratory of Surface Physics, Department of Physics, and Advanced Materials Laboratory, Fudan University, Shanghai 200433 (China); CAS-Shanghai Science Research Center, Shanghai 201203 (China); Shen, D. W., E-mail: dwshen@mail.sim.ac.cn [State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology (SIMIT), Chinese Academy of Sciences, Shanghai 200050 (China); CAS-Shanghai Science Research Center, Shanghai 201203 (China); CAS Center for Excellence in Superconducting Electronics (CENSE), Shanghai 200050 (China)

    2016-07-25

    CaFeAs{sub 2} is a parent compound of recently discovered 112-type iron-based superconductors. It is predicted to be a staggered intercalation compound that naturally integrates both quantum spin Hall insulating and superconducting layers and an ideal system for the realization of Majorana modes. We performed a systematical angle-resolved photoemission spectroscopy and first-principles calculation study of the slightly electron-doped CaFeAs{sub 2}. We found that the zigzag As chain of 112-type iron-based superconductors play a considerable role in the low-energy electronic structure, resulting in the characteristic Dirac-cone like band dispersion as the prediction. Our experimental results further confirm that these Dirac cones only exist around the X but not Y points in the Brillouin zone, breaking the S{sub 4} symmetry at iron sites. Our findings present the compelling support to the theoretical prediction that the 112-type iron-based superconductors might host the topological nontrivial edge states. The slightly electron doped CaFeAs{sub 2} would provide us a unique opportunity to realize and explore Majorana fermion physics.

  20. Fermi–Dirac Statistics

    Indian Academy of Sciences (India)

    IAS Admin

    Pauli exclusion principle, Fermi–. Dirac statistics, identical and in- distinguishable particles, Fermi gas. Fermi–Dirac Statistics. Derivation and Consequences. S Chaturvedi and Shyamal Biswas. (left) Subhash Chaturvedi is at University of. Hyderabad. His current research interests include phase space descriptions.

  1. Quantum Radiation Properties of Dirac Particles in General Nonstationary Black Holes

    Directory of Open Access Journals (Sweden)

    Jia-Chen Hua

    2014-01-01

    Full Text Available Quantum radiation properties of Dirac particles in general nonstationary black holes in the general case are investigated by both using the method of generalized tortoise coordinate transformation and considering simultaneously the asymptotic behaviors of the first-order and second-order forms of Dirac equation near the event horizon. It is generally shown that the temperature and the shape of the event horizon of this kind of black holes depend on both the time and different angles. Further, we give a general expression of the new extra coupling effect in thermal radiation spectrum of Dirac particles which is absent from the thermal radiation spectrum of scalar particles. Also, we reveal a relationship that is ignored before between thermal radiation and nonthermal radiation in the case of scalar particles, which is that the chemical potential in thermal radiation spectrum is equal to the highest energy of the negative energy state of scalar particles in nonthermal radiation for general nonstationary black holes.

  2. On the Mo-Papas equation

    Science.gov (United States)

    Aguirregabiria, J. M.; Chamorro, A.; Valle, M. A.

    1982-05-01

    A new heuristic derivation of the Mo-Papas equation for charged particles is given. It is shown that this equation cannot be derived for a point particle by closely following Dirac's classical treatment of the problem. The Mo-Papas theory and the Bonnor-Rowe-Marx variable mass dynamics are not compatible.

  3. Dirac or Majorana nature and mass effects on the neutrino behaviour; Effets de la nature de Dirac ou de Majorana, ainsi que de la masse, sur le comportement du neutrino

    Energy Technology Data Exchange (ETDEWEB)

    Campagne, J E

    1995-04-01

    This work deals with the Dirac or Majorana nature and mass effects on the neutrino behaviour. In the first part of this study are given the Dirac equation properties and the Majorana neutrino definition. As the difference between a Dirac and a Majorana neutrino has only a sense if their masses are not equal to zero, the second part presents a generalization of the Dirac mass term and the different ways to generate a neutrino mass. Several comparisons are made in the third part between quarks and leptons families mixtures which are linked intimately to masses generation. The fourth part gives an example of masses possible values and neutrinos particles mixtures matrix elements predicting. The neutrino electromagnetic and weak interactions are then considered as well as the neutrinos production by the neutral currents. The charged currents are however better to discriminate the Dirac or Majorana nature. The neutrinos propagation in the matter and in the vacuum are analyzed (the case of neutrino oscillations more particularly) under the result of recent experimental observations. At last, are presented the evaluation of neutrino mass (if it exists) through the analysis of double beta decay and the sensibility of future experiments. (O.L.). 164 refs., 73 figs., 20 tabs.

  4. Modulating Functions Based Algorithm for the Estimation of the Coefficients and Differentiation Order for a Space-Fractional Advection-Dispersion Equation

    KAUST Repository

    Aldoghaither, Abeer

    2015-12-01

    In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton\\'s iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.

  5. Modulating Functions Based Algorithm for the Estimation of the Coefficients and Differentiation Order for a Space-Fractional Advection-Dispersion Equation

    KAUST Repository

    Aldoghaither, Abeer; Liu, Da-Yan; Laleg-Kirati, Taous-Meriem

    2015-01-01

    In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton's iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.

  6. The Dirac Sea

    OpenAIRE

    Dimock, J.

    2010-01-01

    We give an alternate definition of the free Dirac field featuring an explicit construction of the Dirac sea. The treatment employs a semi-infinite wedge product of Hilbert spaces. We also show that the construction is equivalent to the standard Fock space construction.

  7. Graphene based d-character Dirac Systems

    Science.gov (United States)

    Li, Yuanchang; Zhang, S. B.; Duan, Wenhui

    From graphene to topological insulators, Dirac material continues to be the hot topics in condensed matter physics. So far, almost all of the theoretically predicted or experimentally observed Dirac materials are composed of sp -electrons. By using first-principles calculations, we find the new Dirac system of transition-metal intercalated epitaxial graphene on SiC(0001). Intrinsically different from the conventional sp Dirac system, here the Dirac-fermions are dominantly contributed by the transition-metal d-electrons, which paves the way to incorporate correlation effect with Dirac-cone physics. Many intriguing quantum phenomena are proposed based on this system, including quantum spin Hall effect with large spin-orbital gap, quantum anomalous Hall effect, 100% spin-polarized Dirac fermions and ferromagnet-to-topological insulator transition.

  8. A Differential Quadrature Procedure with Regularization of the Dirac-delta Function for Numerical Solution of Moving Load Problem

    Directory of Open Access Journals (Sweden)

    S. A. Eftekhari

    Full Text Available AbstractThe differential quadrature method (DQM is one of the most elegant and efficient methods for the numerical solution of partial differential equations arising in engineering and applied sciences. It is simple to use and also straightforward to implement. However, the DQM is well-known to have some difficulty when applied to partial differential equations involving singular functions like the Dirac-delta function. This is caused by the fact that the Dirac-delta function cannot be directly discretized by the DQM. To overcome this difficulty, this paper presents a simple differential quadrature procedure in which the Dirac-delta function is replaced by regularized smooth functions. By regularizing the Dirac-delta function, such singular function is treated as non-singular functions and can be easily and directly discretized using the DQM. To demonstrate the applicability and reliability of the proposed method, it is applied here to solve some moving load problems of beams and rectangular plates, where the location of the moving load is described by a time-dependent Dirac-delta function. The results generated by the proposed method are compared with analytical and numerical results available in the literature. Numerical results reveal that the proposed method can be used as an efficient tool for dynamic analysis of beam- and plate-type structures traversed by moving dynamic loads.

  9. Equazione di Dirac

    CERN Document Server

    Monti, Dalida

    1996-01-01

    Relativamente poco noto al gran pubblico, il premio Nobel Paul Adrien Maurice Dirac appartiene a quel gruppo di uomini di ingegno che nei primi decenni del secolo contribuirono a dare alla nostra concezione del mondo fisico la sua impronta attuale. Assolutamente cruciali, per una valutazione dell'opera di Dirac, sono gli anni compresi tra il 1925 e il 1931: un periodo in cui il fisico fornisce la prima spiegazione chiara e coerente delle proprietà di spin dell'elettrone (equazione di Dirac) e perviene, in forza della pura deduzione matematica, alla scoperta dell'esistenza dell'elettrone positivo o positrone.

  10. Constructing anisotropic single-Dirac-cones in Bi(1-x)Sb(x) thin films.

    Science.gov (United States)

    Tang, Shuang; Dresselhaus, Mildred S

    2012-04-11

    The electronic band structures of Bi(1-x)Sb(x) thin films can be varied as a function of temperature, pressure, stoichiometry, film thickness, and growth orientation. We here show how different anisotropic single-Dirac-cones can be constructed in a Bi(1-x)Sb(x) thin film for different applications or research purposes. For predicting anisotropic single-Dirac-cones, we have developed an iterative-two-dimensional-two-band model to get a consistent inverse-effective-mass-tensor and band gap, which can be used in a general two-dimensional system that has a nonparabolic dispersion relation as in the Bi(1-x)Sb(x) thin film system. © 2012 American Chemical Society

  11. Status of the DIRAC Project

    International Nuclear Information System (INIS)

    Casajus, A; Ciba, K; Fernandez, V; Graciani, R; Hamar, V; Mendez, V; Poss, S; Sapunov, M; Stagni, F; Tsaregorodtsev, A; Ubeda, M

    2012-01-01

    The DIRAC Project was initiated to provide a data processing system for the LHCb Experiment at CERN. It provides all the necessary functionality and performance to satisfy the current and projected future requirements of the LHCb Computing Model. A considerable restructuring of the DIRAC software was undertaken in order to turn it into a general purpose framework for building distributed computing systems that can be used by various user communities in High Energy Physics and other scientific application domains. The CLIC and ILC-SID detector projects started to use DIRAC for their data production system. The Belle Collaboration at KEK, Japan, has adopted the Computing Model based on the DIRAC system for its second phase starting in 2015. The CTA Collaboration uses DIRAC for the data analysis tasks. A large number of other experiments are starting to use DIRAC or are evaluating this solution for their data processing tasks. DIRAC services are included as part of the production infrastructure of the GISELA Latin America grid. Similar services are provided for the users of the France-Grilles and IBERGrid National Grid Initiatives in France and Spain respectively. The new communities using DIRAC started to provide important contributions to its functionality. Among recent additions can be mentioned the support of the Amazon EC2 computing resources as well as other Cloud management systems; a versatile File Replica Catalog with File Metadata capabilities; support for running MPI jobs in the pilot based Workload Management System. Integration with existing application Web Portals, like WS-PGRADE, is demonstrated. In this paper we will describe the current status of the DIRAC Project, recent developments of its framework and functionality as well as the status of the rapidly evolving community of the DIRAC users.

  12. Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations

    Science.gov (United States)

    Novruzov, Emil

    2017-11-01

    This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, ut -uxxt +[ f (u) ] x -[ f (u) ] xxx +[ g (u) + f″/(u) 2 ux2 ] x = 0 that includes the Camassa-Holm equation as well as the hyperelastic-rod wave equation (f (u) = ku2 / 2 and g (u) = (3 - k) u2 / 2) as special cases. We establish some a local-in-space blow-up criterion (i.e., a criterion involving only the properties of the data u0 in a neighborhood of a single point) simplifying and precising earlier blow-up criteria for this equation.

  13. Liouville equation of relativistic charged fermion

    International Nuclear Information System (INIS)

    Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming

    1991-01-01

    As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function

  14. Two simple ansaetze for obtaining exact solutions of high dispersive nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Palacios, Sergio L.

    2004-01-01

    We propose two simple ansaetze that allow us to obtain different analytical solutions of the high dispersive cubic and cubic-quintic nonlinear Schroedinger equations. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media

  15. A Formulation of Quantum Field Theory Realizing a Sea of Interacting Dirac Particles

    Science.gov (United States)

    Finster, Felix

    2011-08-01

    In this survey article, we explain a few ideas behind the fermionic projector approach and summarize recent results which clarify the connection to quantum field theory. The fermionic projector is introduced, which describes the physical system by a collection of Dirac states, including the states of the Dirac sea. Formulating the interaction by an action principle for the fermionic projector, we obtain a consistent description of interacting quantum fields which reproduces the results of perturbative quantum field theory. We find a new mechanism for the generation of boson masses and obtain small corrections to the field equations which violate causality.

  16. Paul Dirac lectures at CERN

    CERN Multimedia

    CERN Bulletin

    2010-01-01

    When a group of physicists entered the Main Auditorium, during the evening of 29 June, they felt they had opened a time portal.   Paul Dirac in front of a blackboard showing his formula. ©Sandra Hoogeboom An attentive audience, dressed in early 1900 costumes, were watching a lecture by the elusive Paul Dirac, presenting for the first time his famous formula on the blackboard. Paul Adrien Maurice Dirac (1902-1984) was a British mathematical physicist at Cambridge, and one of the "fathers" of quantum mechanics. When he first wrote it, in 1928, Dirac was not sure what his formula really meant. As demonstrated by Andersson four year later, what Dirac had written on the blackboard was the first definition of a positron, hence he is credited with having anticipated the existence of antimatter. The actor John Kohl performs as Paul Dirac. ©Sandra Hoogeboom What the group of puzzled physicists were really observing when they entered the CERN Auditorium was the shoo...

  17. The investigation for (2+1)-dimensional Eckhaus-type extension of the dispersive long wave equation

    International Nuclear Information System (INIS)

    Yan Zhenya

    2004-01-01

    The (2+1)-dimensional Eckhaus-type extension of the dispersive long wave (EEDLW) equation is investigated, which was obtained in the appropriate approximation from the basic equations of hydrodynamics. Though it has no Painleve property, we gain an auto-Baecklund transformation (aBT) by truncating the Laurent series expansion at O(w 0 ). In particular, the special one of the aBT establishes a relationship between the EEDLW equation and a set of three linear partial differential equations involving the well-known heat equation. Finally many types of new exact solutions of the EEDLW equation are found from the obtained aBT and some proper ansaetze, which may be useful to explain some physical phenomena

  18. Dirac Particle for the Position Dependent Mass in the Generalized Asymmetric Woods-Saxon Potential

    Directory of Open Access Journals (Sweden)

    Soner Alpdoğan

    2014-01-01

    Full Text Available The one-dimensional Dirac equation with position dependent mass in the generalized asymmetric Woods-Saxon potential is solved in terms of the hypergeometric functions. The transmission and reflection coefficients are obtained by considering the one-dimensional electric current density for the Dirac particle and the equation describing the bound states is found by utilizing the continuity conditions of the obtained wave function. Also, by using the generalized asymmetric Woods-Saxon potential solutions, the scattering states are found out without making calculation for the Woods-Saxon, Hulthen, cusp potentials, and so forth, which are derived from the generalized asymmetric Woods-Saxon potential and the conditions describing transmission resonances and supercriticality are achieved. At the same time, the data obtained in this work are compared with the results achieved in earlier studies and are observed to be consistent.

  19. DIRAC in Large Particle Physics Experiments

    Science.gov (United States)

    Stagni, F.; Tsaregorodtsev, A.; Arrabito, L.; Sailer, A.; Hara, T.; Zhang, X.; Consortium, DIRAC

    2017-10-01

    The DIRAC project is developing interware to build and operate distributed computing systems. It provides a development framework and a rich set of services for both Workload and Data Management tasks of large scientific communities. A number of High Energy Physics and Astrophysics collaborations have adopted DIRAC as the base for their computing models. DIRAC was initially developed for the LHCb experiment at LHC, CERN. Later, the Belle II, BES III and CTA experiments as well as the linear collider detector collaborations started using DIRAC for their computing systems. Some of the experiments built their DIRAC-based systems from scratch, others migrated from previous solutions, ad-hoc or based on different middlewares. Adaptation of DIRAC for a particular experiment was enabled through the creation of extensions to meet their specific requirements. Each experiment has a heterogeneous set of computing and storage resources at their disposal that were aggregated through DIRAC into a coherent pool. Users from different experiments can interact with the system in different ways depending on their specific tasks, expertise level and previous experience using command line tools, python APIs or Web Portals. In this contribution we will summarize the experience of using DIRAC in particle physics collaborations. The problems of migration to DIRAC from previous systems and their solutions will be presented. An overview of specific DIRAC extensions will be given. We hope that this review will be useful for experiments considering an update, or for those designing their computing models.

  20. Dirac fields in loop quantum gravity and big bang nucleosynthesis

    International Nuclear Information System (INIS)

    Bojowald, Martin; Das, Rupam; Scherrer, Robert J.

    2008-01-01

    Big bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions. Several corrections to equation of state parameters arise from classical and quantum physics, which are derived here from a canonical perspective. In particular, loop quantum gravity allows one to compute quantum gravity corrections for Maxwell and Dirac fields. Although the classical actions are very different, quantum corrections to the equation of state are remarkably similar. To lowest order, these corrections take the form of an overall expansion-dependent multiplicative factor in the total density. We use these results, along with the predictions of big bang nucleosynthesis, to place bounds on these corrections and especially the patch size of discrete quantum gravity states.

  1. Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations

    International Nuclear Information System (INIS)

    Yarmohammadi, Mohsen; Zareyan, Malek

    2016-01-01

    In graphene, conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature. For this reason, the bounding of electrons in graphene in the form of geometries of quantum dots is impossible. In gapless graphene, due to its unique electronic band structure, there is a minimal conductivity at Dirac points, that is, in the limit of zero doping. This creates a problem for using such a highly motivated new material in electronic devices. One of the ways to overcome this problem is the creation of a band gap in the graphene band structure, which is made by inversion symmetry breaking (symmetry of sublattices). We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for “local chemical potential” and “local gap”. The calculated energy spectrum exhibits quite different features with and without the perturbations. A characteristic equation for bound states (BSs) has been obtained. It is surprisingly found that the relation between the radial functions of sublattices wave functions, i.e., , , and , , can be established by SO (2) group. (paper)

  2. Dirac perturbations on Schwarzschild-anti-de Sitter spacetimes: Generic boundary conditions and new quasinormal modes

    Science.gov (United States)

    Wang, Mengjie; Herdeiro, Carlos; Jing, Jiliang

    2017-11-01

    We study Dirac quasinormal modes of Schwarzschild-anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015)., 10.1103/PhysRevD.92.124006]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.

  3. A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices

    Science.gov (United States)

    AlQurashi, Ahmed; Selvakumar, C. R.

    2018-06-01

    There had been tremendous growth in the field of Integrated circuits (ICs) in the past fifty years. Scaling laws mandated both lateral and vertical dimensions to be reduced and a steady increase in doping densities. Most of the modern semiconductor devices have invariably heavily doped regions where Fermi-Dirac Integrals are required. Several attempts have been devoted to developing analytical approximations for Fermi-Dirac Integrals since numerical computations of Fermi-Dirac Integrals are difficult to use in semiconductor devices, although there are several highly accurate tabulated functions available. Most of these analytical expressions are not sufficiently suitable to be employed in semiconductor device applications due to their poor accuracy, the requirement of complicated calculations, and difficulties in differentiating and integrating. A new approximation has been developed for the Fermi-Dirac integrals of the order 1/2 by using Prony's method and discussed in this paper. The approximation is accurate enough (Mean Absolute Error (MAE) = 0.38%) and easy enough to be used in semiconductor device equations. The new approximation of Fermi-Dirac Integrals is applied to a more generalized Einstein Relation which is an important relation in semiconductor devices.

  4. Dirac gauginos, gauge mediation and unification

    Energy Technology Data Exchange (ETDEWEB)

    Benakli, K. [UPMC Univ. Paris 06 (France). Laboratoire de Physique Theorique et Hautes Energies, CNRS; Goodsell, M.D. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2010-03-15

    We investigate the building of models with Dirac gauginos and perturbative gauge coupling unification. Here, in contrast to the MSSM, additional fields are required for unification, and these can naturally play the role of the messengers of supersymmetry breaking. We present a framework within which such models can be constructed, including the constraints that the messenger sector must satisfy; and the renormalisation group equations for the soft parameters, which differ from those of the MSSM. For illustration, we provide the spectrum at the electroweak scale for explicit models whose gauge couplings unify at the scale predicted by heterotic strings. (orig.)

  5. Dirac Gauginos, Gauge Mediation and Unification

    CERN Document Server

    Benakli, K

    2010-01-01

    We investigate the building of models with Dirac gauginos and perturbative gauge coupling unification. Here, in contrast to the MSSM, additional fields are required for unification, and these can naturally play the role of the messengers of supersymmetry breaking. We present a framework within which such models can be constructed, including the constraints that the messenger sector must satisfy; and the renormalisation group equations for the soft parameters, which differ from those of the MSSM. For illustration, we provide the spectrum at the electroweak scale for explicit models whose gauge couplings unify at the scale predicted by heterotic strings.

  6. Dirac gauginos, gauge mediation and unification

    International Nuclear Information System (INIS)

    Benakli, K.

    2010-03-01

    We investigate the building of models with Dirac gauginos and perturbative gauge coupling unification. Here, in contrast to the MSSM, additional fields are required for unification, and these can naturally play the role of the messengers of supersymmetry breaking. We present a framework within which such models can be constructed, including the constraints that the messenger sector must satisfy; and the renormalisation group equations for the soft parameters, which differ from those of the MSSM. For illustration, we provide the spectrum at the electroweak scale for explicit models whose gauge couplings unify at the scale predicted by heterotic strings. (orig.)

  7. Confinement limit of a Dirac particle in two and three dimensions

    International Nuclear Information System (INIS)

    Toyama, F.M.; Nogami, Y.

    2010-01-01

    Consider a particle that is in a stationary state described by the Dirac equation with a finite-range potential. In two and three dimensions the particle can be confined to an arbitrarily small spatial region. This is in contrast to the one-dimensional case in which the confinement region cannot be much narrower than the Compton wavelength.

  8. 1-Soliton solution of the generalized Zakharov-Kuznetsov equation with nonlinear dispersion and time-dependent coefficients

    International Nuclear Information System (INIS)

    Biswas, Anjan

    2009-01-01

    In this Letter, the 1-soliton solution of the Zakharov-Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.

  9. Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves

    International Nuclear Information System (INIS)

    Webb, G. M.; Brio, M.; Zank, G. P.

    1996-01-01

    A formulation of Hamiltonian and Lagrangian variational principles, Lie point symmetries and conservation laws for the triple degenerate DNLS equations describing the propagation of weakly nonlinear dispersive MHD waves along the ambient magnetic field, in β∼1 plasmas is given. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic point, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a g 2 =V A 2 where a g is the gas sound speed and V A is the Alfven speed. A discussion is given of the travelling wave similarity solutions of the equations, which include solitary wave and periodic traveling waves. Strongly compressible solutions indicate the necessity for the insertion of shocks in the flow, whereas weakly compressible, near Alfvenic solutions resemble similar, shock free travelling wave solutions of the DNLS equation

  10. Power counting of various Dirac covariants in hadronic Bethe–Salpeter wave functions for pseudoscalar meson decays

    International Nuclear Information System (INIS)

    Bhatnagar, S.; Li, Shiyuan; Mahecha, J.

    2011-01-01

    We have employed the framework of Bethe–Salpeter equation under covariant instantaneous ansatz to calculate leptonic decay constants of unequal mass pseudoscalar mesons like π ± , K, D, D S and B, and radiative decay constants of neutral pseudoscalar mesons like π 0 and η c into two photons. In the Dirac structure of hadronic Bethe–Salpeter wave function, the covariants are incorporated from their complete set in accordance with a recently proposed power counting rule. The contribution of both leading order and next-to-leading order Dirac covariants to decay constants are studied. The results are found to improve and hence validating the power counting rule which provides a practical means of incorporating Dirac covariants in the Bethe–Salpeter wave function for a hadron. (author)

  11. Quasi-Dirac neutrino oscillations

    Science.gov (United States)

    Anamiati, Gaetana; Fonseca, Renato M.; Hirsch, Martin

    2018-05-01

    Dirac neutrino masses require two distinct neutral Weyl spinors per generation, with a special arrangement of masses and interactions with charged leptons. Once this arrangement is perturbed, lepton number is no longer conserved and neutrinos become Majorana particles. If these lepton number violating perturbations are small compared to the Dirac mass terms, neutrinos are quasi-Dirac particles. Alternatively, this scenario can be characterized by the existence of pairs of neutrinos with almost degenerate masses, and a lepton mixing matrix which has 12 angles and 12 phases. In this work we discuss the phenomenology of quasi-Dirac neutrino oscillations and derive limits on the relevant parameter space from various experiments. In one parameter perturbations of the Dirac limit, very stringent bounds can be derived on the mass splittings between the almost degenerate pairs of neutrinos. However, we also demonstrate that with suitable changes to the lepton mixing matrix, limits on such mass splittings are much weaker, or even completely absent. Finally, we consider the possibility that the mass splittings are too small to be measured and discuss bounds on the new, nonstandard lepton mixing angles from current experiments for this case.

  12. Analytical Solution of Dirac Equation for q-Deformed Hyperbolic Manning-Rosen Potential in D Dimensions using SUSY QM and its Thermodynamics Application

    International Nuclear Information System (INIS)

    Cari, C; Suparmi, A; Yunianto, M; Pratiwi, B N

    2016-01-01

    The Dirac equation of q-deformed hyperbolic Manning Rosen potential in D dimension was solved by using Supersymmetric Quantum Mechanics (SUSY QM). The D dimensional relativistic energy spectra were obtained by using SUSY QM and shape invariant properties and D dimensional wave functions of q-deformed hyperbolic Manning Rosen potential were obtained by using the SUSY raising and lowering operators. In the nonrelativistic limit, the relativistic energy spectra for exact spin symmetry case reduced into nonrelativistic energy spectra and so for the wave functions. In the classical regime, the partition function, the vibrational specific heat, and the vibrational mean energy of some diatomic molecules were calculated from the non-relativistic energy spectra with the help of error function and imaginary error function. (paper)

  13. LHCbDIRAC as Apache Mesos microservices

    Science.gov (United States)

    Haen, Christophe; Couturier, Benjamin

    2017-10-01

    The LHCb experiment relies on LHCbDIRAC, an extension of DIRAC, to drive its offline computing. This middleware provides a development framework and a complete set of components for building distributed computing systems. These components are currently installed and run on virtual machines (VM) or bare metal hardware. Due to the increased workload, high availability is becoming more and more important for the LHCbDIRAC services, and the current installation model is showing its limitations. Apache Mesos is a cluster manager which aims at abstracting heterogeneous physical resources on which various tasks can be distributed thanks to so called “frameworks” The Marathon framework is suitable for long running tasks such as the DIRAC services, while the Chronos framework meets the needs of cron-like tasks like the DIRAC agents. A combination of the service discovery tool Consul together with HAProxy allows to expose the running containers to the outside world while hiding their dynamic placements. Such an architecture brings a greater flexibility in the deployment of LHCbDirac services, allowing for easier deployment maintenance and scaling of services on demand (e..g LHCbDirac relies on 138 services and 116 agents). Higher reliability is also easier, as clustering is part of the toolset, which allows constraints on the location of the services. This paper describes the investigations carried out to package the LHCbDIRAC and DIRAC components into Docker containers and orchestrate them using the previously described set of tools.

  14. In the Dirac tradition

    Energy Technology Data Exchange (ETDEWEB)

    Anon.

    1988-04-15

    It was Paul Dirac who cast quantum mechanics into the form we now use, and many generations of theoreticians openly acknowledge his influence on their thinking. When Dirac died in 1984, St. John's College, Cambridge, his base for most of his lifetime, instituted an annual lecture in his memory at Cambridge. The first lecture, in 1986, attracted two heavyweights - Richard Feynman and Steven Weinberg. Far from using the lectures as a platform for their own work, in the Dirac tradition they presented stimulating material on deep underlying questions.

  15. In the Dirac tradition

    International Nuclear Information System (INIS)

    Anon.

    1988-01-01

    It was Paul Dirac who cast quantum mechanics into the form we now use, and many generations of theoreticians openly acknowledge his influence on their thinking. When Dirac died in 1984, St. John's College, Cambridge, his base for most of his lifetime, instituted an annual lecture in his memory at Cambridge. The first lecture, in 1986, attracted two heavyweights - Richard Feynman and Steven Weinberg. Far from using the lectures as a platform for their own work, in the Dirac tradition they presented stimulating material on deep underlying questions

  16. What is between Fermi-Dirac and Bose-Einstein Statistics?

    OpenAIRE

    Byczuk, Krzysztof; Spalek, Jozef; Joyce, Geoffrey; Sarkar, Sarben

    2004-01-01

    We overwiev the properties of a quantum gas of particles with the intermediate statistics defined by Haldane. Although this statistics has no direct connection to the symmetry of the multiparticle wave function, the statistical distribution function interpolates continuously between the Fermi-Dirac and the Bose-Einstein limits. We present an explicit solution of the transcendental equation for the didtribution function in a general case, as well as determine the thermodynamic properties in bo...

  17. Bohr and Dirac*

    Indian Academy of Sciences (India)

    IAS Admin

    We present an account of the work of Niels Bohr and Paul Dirac, their interactions and personal- ities. 1. Introduction. In this essay I would like to convey to my readers some- thing about the personalities and work of Niels Bohr and Paul Dirac, juxtaposed against one another. Let me hope that the portraits I will paint of these ...

  18. Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

    Science.gov (United States)

    Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

    2015-07-01

    Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

  19. Smooth and non-smooth traveling wave solutions of a class of nonlinear dispersive equation

    International Nuclear Information System (INIS)

    Zhao Xiaoshan; Wu Aidi; He Wenzhang

    2009-01-01

    There is the widespread existence of wave phenomena in physics, mechanics. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In this paper, we study a nonlinear dispersive K(n,-n,2n) equation, which can be regarded as a generalized K(n,n) equation. Applying the bifurcation theory and the method of phase portraits analysis, we obtain the dynamical behavior and special exact solutions of the K(n,-n,2n) equation. As a result, the conditions under which peakon and compacton solutions appear are also given and the analytic expressions of peakon solutions, compacton and periodic cusp wave solutions are obtained.

  20. New Equations for Calculating Principal and Fine-Structure Atomic Spectra for Single and Multi-Electron Atoms

    Energy Technology Data Exchange (ETDEWEB)

    Surdoval, Wayne A. [National Energy Technology Lab. (NETL), Pittsburgh, PA, (United States); Berry, David A. [National Energy Technology Lab. (NETL), Morgantown, WV (United States); Shultz, Travis R. [National Energy Technology Lab. (NETL), Morgantown, WV (United States)

    2018-03-09

    A set of equations are presented for calculating atomic principal spectral lines and fine-structure energy splits for single and multi-electron atoms. Calculated results are presented and compared to the National Institute of Science and Technology database demonstrating very good accuracy. The equations do not require fitted parameters. The only experimental parameter required is the Ionization energy for the electron of interest. The equations have comparable accuracy and broader applicability than the single electron Dirac equation. Three Appendices discuss the origin of the new equations and present calculated results. New insights into the special relativistic nature of the Dirac equation and its relationship to the new equations are presented.

  1. On the Dirac oscillator

    International Nuclear Information System (INIS)

    Rodrigues, R. de Lima

    2007-01-01

    In the present work we obtain a new representation for the Dirac oscillator based on the Clifford algebra C 7. The symmetry breaking and the energy eigenvalues for our model of the Dirac oscillator are studied in the non-relativistic limit. (author)

  2. Double Dirac cones in phononic crystals

    KAUST Repository

    Li, Yan

    2014-07-07

    A double Dirac cone is realized at the center of the Brillouin zone of a two-dimensional phononic crystal (PC) consisting of a triangular array of core-shell-structure cylinders in water. The double Dirac cone is induced by the accidental degeneracy of two double-degenerate Bloch states. Using a perturbation method, we demonstrate that the double Dirac cone is composed of two identical and overlapping Dirac cones whose linear slopes can also be accurately predicted from the method. Because the double Dirac cone occurs at a relatively low frequency, a slab of the PC can be mapped onto a slab of zero refractive index material by using a standard retrieval method. Total transmission without phase change and energy tunneling at the double Dirac point frequency are unambiguously demonstrated by two examples. Potential applications can be expected in diverse fields such as acoustic wave manipulations and energy flow control.

  3. Double Dirac cones in phononic crystals

    KAUST Repository

    Li, Yan; Wu, Ying; Mei, Jun

    2014-01-01

    A double Dirac cone is realized at the center of the Brillouin zone of a two-dimensional phononic crystal (PC) consisting of a triangular array of core-shell-structure cylinders in water. The double Dirac cone is induced by the accidental degeneracy of two double-degenerate Bloch states. Using a perturbation method, we demonstrate that the double Dirac cone is composed of two identical and overlapping Dirac cones whose linear slopes can also be accurately predicted from the method. Because the double Dirac cone occurs at a relatively low frequency, a slab of the PC can be mapped onto a slab of zero refractive index material by using a standard retrieval method. Total transmission without phase change and energy tunneling at the double Dirac point frequency are unambiguously demonstrated by two examples. Potential applications can be expected in diverse fields such as acoustic wave manipulations and energy flow control.

  4. Van der Waals equation of state revisited: importance of the dispersion correction.

    Science.gov (United States)

    de Visser, Sam P

    2011-04-28

    One of the most basic equations of state describing nonideal gases and liquids is the van der Waals equation of state, and as a consequence, it is generally taught in most first year undergraduate chemistry courses. In this work, we show that the constants a and b in the van der Waals equation of state are linearly proportional to the polarizability volume of the molecules in a gas or liquid. Using this information, a new thermodynamic one-parameter equation of state is derived that contains experimentally measurable variables and physics constants only. This is the first equation of state apart from the Ideal Gas Law that contains experimentally measurable variables and physics constants only, and as such, it may be a very useful and practical equation for the description of dilute gases and liquids. The modified van der Waals equation of state describes pV as the sum of repulsive and attractive intermolecular interaction energies that are represented by an exponential repulsion function between the electron clouds of the molecules and a London dispersion component, respectively. The newly derived equation of state is tested against experimental data for several gas and liquid examples, and the agreement is satisfactory. The description of the equation of state as a one-parameter function also has implications on other thermodynamic functions, such as critical parameters, virial coefficients, and isothermal compressibilities. Using our modified van der Waals equation of state, we show that all of these properties are a function of the molecular polarizability volume. Correlations of experimental data confirm the derived proportionalities.

  5. Executor Framework for DIRAC

    Science.gov (United States)

    Casajus Ramo, A.; Graciani Diaz, R.

    2012-12-01

    DIRAC framework for distributed computing has been designed as a group of collaborating components, agents and servers, with persistent database back-end. Components communicate with each other using DISET, an in-house protocol that provides Remote Procedure Call (RPC) and file transfer capabilities. This approach has provided DIRAC with a modular and stable design by enforcing stable interfaces across releases. But it made complicated to scale further with commodity hardware. To further scale DIRAC, components needed to send more queries between them. Using RPC to do so requires a lot of processing power just to handle the secure handshake required to establish the connection. DISET now provides a way to keep stable connections and send and receive queries between components. Only one handshake is required to send and receive any number of queries. Using this new communication mechanism DIRAC now provides a new type of component called Executor. Executors process any task (such as resolving the input data of a job) sent to them by a task dispatcher. This task dispatcher takes care of persisting the state of the tasks to the storage backend and distributing them among all the Executors based on the requirements of each task. In case of a high load, several Executors can be started to process the extra load and stop them once the tasks have been processed. This new approach of handling tasks in DIRAC makes Executors easy to replace and replicate, thus enabling DIRAC to further scale beyond the current approach based on polling agents.

  6. Executor Framework for DIRAC

    International Nuclear Information System (INIS)

    Casajus Ramo, A; Graciani Diaz, R

    2012-01-01

    DIRAC framework for distributed computing has been designed as a group of collaborating components, agents and servers, with persistent database back-end. Components communicate with each other using DISET, an in-house protocol that provides Remote Procedure Call (RPC) and file transfer capabilities. This approach has provided DIRAC with a modular and stable design by enforcing stable interfaces across releases. But it made complicated to scale further with commodity hardware. To further scale DIRAC, components needed to send more queries between them. Using RPC to do so requires a lot of processing power just to handle the secure handshake required to establish the connection. DISET now provides a way to keep stable connections and send and receive queries between components. Only one handshake is required to send and receive any number of queries. Using this new communication mechanism DIRAC now provides a new type of component called Executor. Executors process any task (such as resolving the input data of a job) sent to them by a task dispatcher. This task dispatcher takes care of persisting the state of the tasks to the storage backend and distributing them among all the Executors based on the requirements of each task. In case of a high load, several Executors can be started to process the extra load and stop them once the tasks have been processed. This new approach of handling tasks in DIRAC makes Executors easy to replace and replicate, thus enabling DIRAC to further scale beyond the current approach based on polling agents.

  7. Generalised master equations for wave equation separation in a Kerr or Kerr-Newman black hole background

    International Nuclear Information System (INIS)

    Carter, B.; McLenaghan, R.G.

    1982-01-01

    It is shown how previous general formulae for the separated radial and angular parts of the massive, charged scalar (Klein, Gordon) wave equation on one hand, and of the zero mass, neutral, but higher spin (neutrino, electromagnetic and gravitational) wave equations on the other hand may be combined in a more general formula which also covers the case of the full massive charged Dirac equation in a Kerr or Kerr-Newman background space. (Auth.)

  8. The determination of an unknown source for a space fractional advection dispersion equation

    KAUST Repository

    Aldoghaither, Abeer

    2014-09-01

    In this paper, we are interested in the estimation of the source term for a space fractional advection dispersion equation using concentration and flux measurements at final time. An example of application is the identification of contamination source in groundwater transport. We propose to use the socalled modulating functions method which has been introduced for parameters estimation. This method allows to transfer the estimation problem into solving a system of algebraic equations. Numerical examples are given to illustrate the effectiveness and the robustness of the proposed method. Finally, a comparison between a Tikhonov-based optimization method and the modulating functions approach is presented.

  9. Dispersion equations for field-aligned cyclotron waves in axisymmetric magnetospheric plasmas

    Directory of Open Access Journals (Sweden)

    N. I. Grishanov

    2006-03-01

    Full Text Available In this paper, we derive the dispersion equations for field-aligned cyclotron waves in two-dimensional (2-D magnetospheric plasmas with anisotropic temperature. Two magnetic field configurations are considered with dipole and circular magnetic field lines. The main contribution of the trapped particles to the transverse dielectric permittivity is estimated by solving the linearized Vlasov equation for their perturbed distribution functions, accounting for the cyclotron and bounce resonances, neglecting the drift effects, and assuming the weak connection of the left-hand and right-hand polarized waves. Both the bi-Maxwellian and bi-Lorentzian distribution functions are considered to model the ring current ions and electrons in the dipole magnetosphere. A numerical code has been developed to analyze the dispersion characteristics of electromagnetic ion-cyclotron waves in an electron-proton magnetospheric plasma with circular magnetic field lines, assuming that the steady-state distribution function of the energetic protons is bi-Maxwellian. As in the uniform magnetic field case, the growth rate of the proton-cyclotron instability (PCI in the 2-D magnetospheric plasmas is defined by the contribution of the energetic ions/protons to the imaginary part of the transverse permittivity elements. We demonstrate that the PCI growth rate in the 2-D axisymmetric plasmasphere can be significantly smaller than that for the straight magnetic field case with the same macroscopic bulk parameters.

  10. The DIRAC Data Management System (poster)

    CERN Document Server

    Haen, Christophe

    2015-01-01

    The DIRAC Interware provides a development framework and a complete set of components for building distributed computing systems. The DIRAC Data Management System (DMS) offers all the necessary tools to ensure data handling operations for small and large user communities. It supports transparent access to storage resources based on multiple technologies, and is easily expandable. The information on data files and replicas is kept in a File Catalog of which DIRAC offers a powerful and versatile implementation (DFC). Data movement can be performed using third party services including FTS3. Bulk data operations are resilient with respect to failures due to the use of the Request Management System (RMS) that keeps track of ongoing tasks. In this contribution we will present an overview of the DIRAC DMS capabilities and its connection with other DIRAC subsystems such as the Transformation System. The DIRAC DMS is in use by several user communities now. The contribution will present the experience of the LHCb exper...

  11. DIRAC distributed computing services

    International Nuclear Information System (INIS)

    Tsaregorodtsev, A

    2014-01-01

    DIRAC Project provides a general-purpose framework for building distributed computing systems. It is used now in several HEP and astrophysics experiments as well as for user communities in other scientific domains. There is a large interest from smaller user communities to have a simple tool like DIRAC for accessing grid and other types of distributed computing resources. However, small experiments cannot afford to install and maintain dedicated services. Therefore, several grid infrastructure projects are providing DIRAC services for their respective user communities. These services are used for user tutorials as well as to help porting the applications to the grid for a practical day-to-day work. The services are giving access typically to several grid infrastructures as well as to standalone computing clusters accessible by the target user communities. In the paper we will present the experience of running DIRAC services provided by the France-Grilles NGI and other national grid infrastructure projects.

  12. Nonlocal Symmetries, Conservation Laws and Interaction Solutions of the Generalised Dispersive Modified Benjamin-Bona-Mahony Equation

    Science.gov (United States)

    Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Wang, Xiu-Bin; Zhang, Tian-Tian

    2018-05-01

    We consider the generalised dispersive modified Benjamin-Bona-Mahony equation, which describes an approximation status for long surface wave existed in the non-linear dispersive media. By employing the truncated Painlevé expansion method, we derive its non-local symmetry and Bäcklund transformation. The non-local symmetry is localised by a new variable, which provides the corresponding non-local symmetry group and similarity reductions. Moreover, a direct method can be provided to construct a kind of finite symmetry transformation via the classic Lie point symmetry of the normal prolonged system. Finally, we find that the equation is a consistent Riccati expansion solvable system. With the help of the Jacobi elliptic function, we get its interaction solutions between solitary waves and cnoidal periodic waves.

  13. Robust Imaging Methodology for Challenging Environments: Wave Equation Dispersion Inversion of Surface Waves

    KAUST Repository

    Li, Jing

    2017-12-22

    A robust imaging technology is reviewed that provide subsurface information in challenging environments: wave-equation dispersion inversion (WD) of surface waves for the shear velocity model. We demonstrate the benefits and liabilities of the method with synthetic seismograms and field data. The benefits of WD are that 1) there is no layered medium assumption, as there is in conventional inversion of dispersion curves, so that the 2D or 3D S-velocity model can be reliably obtained with seismic surveys over rugged topography, and 2) WD mostly avoids getting stuck in local minima. The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic media and the inversion of dispersion curves associated with Love wave. The liability is that is almost as expensive as FWI and only recovers the Vs distribution to a depth no deeper than about 1/2~1/3 wavelength.

  14. Direct and inverse source problems for a space fractional advection dispersion equation

    KAUST Repository

    Aldoghaither, Abeer

    2016-05-15

    In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from final observations. We first derive the analytic solution to the direct problem which we use to prove the uniqueness and the unstability of the inverse source problem using final measurements. Finally, we illustrate the results with a numerical example.

  15. P A M Dirac

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education. P A M Dirac. Articles written in Resonance – Journal of Science Education. Volume 8 Issue 8 August 2003 pp 102-110 Classics. XI. The Relation between Mathematics and Physics · P A M Dirac · More Details Fulltext PDF ...

  16. Universal properties of materials with the Dirac dispersion relation of low-energy excitations

    Energy Technology Data Exchange (ETDEWEB)

    Protogenov, A. P., E-mail: alprot@appl.sci-nnov.ru [Russian Academy of Sciences, Institute for Applied Physics (Russian Federation); Chulkov, E. V. [Universidad del Pais Vasco, Departamento de Fisica de Materiales (Spain)

    2015-12-15

    The N-terminal scheme is considered for studying the contribution of edge states to the response of a two-dimensional topological insulator. A universal distribution of the nonlocal resistance between terminals is determined in the ballistic transport approach. The calculated responses are identical to experimentally observed values. The spectral properties of surface electronic states in Weyl semimetals are also studied. The density of surface states is accurately determined. The universal behavior of these characteristics is a distinctive feature of the considered Dirac materials which can be used in practical applications.

  17. Universal properties of materials with the Dirac dispersion relation of low-energy excitations

    International Nuclear Information System (INIS)

    Protogenov, A. P.; Chulkov, E. V.

    2015-01-01

    The N-terminal scheme is considered for studying the contribution of edge states to the response of a two-dimensional topological insulator. A universal distribution of the nonlocal resistance between terminals is determined in the ballistic transport approach. The calculated responses are identical to experimentally observed values. The spectral properties of surface electronic states in Weyl semimetals are also studied. The density of surface states is accurately determined. The universal behavior of these characteristics is a distinctive feature of the considered Dirac materials which can be used in practical applications

  18. Two-Carrier Transport Induced Hall Anomaly and Large Tunable Magnetoresistance in Dirac Semimetal Cd3As2 Nanoplates.

    Science.gov (United States)

    Li, Cai-Zhen; Li, Jin-Guang; Wang, Li-Xian; Zhang, Liang; Zhang, Jing-Min; Yu, Dapeng; Liao, Zhi-Min

    2016-06-28

    Cd3As2 is a model material of Dirac semimetal with a linear dispersion relation along all three directions in the momentum space. The unique band structure of Cd3As2 is made with both Dirac and topological properties. It can be driven into a Weyl semimetal by symmetry breaking or a topological insulator by enhancing the spin-orbit coupling. Here we report the temperature and gate voltage-dependent magnetotransport properties of Cd3As2 nanoplates with Fermi level near the Dirac point. The Hall anomaly demonstrates the two-carrier transport accompanied by a transition from n-type to p-type conduction with decreasing temperature. The carrier-type transition is explained by considering the temperature-dependent spin-orbit coupling. The magnetoresistance exhibits a large nonsaturating value up to 2000% at high temperatures, which is ascribed to the electron-hole compensation in the system. Our results are valuable for understanding the experimental observations related to the two-carrier transport in Dirac/Weyl semimetals, such as Na3Bi, ZrTe5, TaAs, NbAs, and HfTe5.

  19. An alternative derivation of the Dirac operator generating intrinsic Lagrangian local gauge invariance

    Directory of Open Access Journals (Sweden)

    Brian Jonathan Wolk

    2017-01-01

    Full Text Available This paper introduces an alternative formalism for deriving the Dirac operator and equation. The use of this formalism concomitantly generates a separate operator coupled to the Dirac operator. When operating on a Clifford field, this coupled operator produces field components which are formally equivalent to the field components of Maxwell's electromagnetic field tensor. Consequently, the Lagrangian of the associated coupled field exhibits internal local gauge symmetry. The coupled field Lagrangian is seen to be equivalent to the Lagrangian of Quantum Electrodynamics. Received: 8 November 2016, Accepted: 4 January 2017; Edited by: D. Gomez Dumm; DOI: http://dx.doi.org/10.4279/PIP.090002 Cite as: B J Wolk, Papers in Physics 9, 090002 (2017

  20. Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

    Energy Technology Data Exchange (ETDEWEB)

    Cortez, Jerónimo, E-mail: jacq@ciencias.unam.mx [Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, México D.F. 04510 (Mexico); Elizaga Navascués, Beatriz, E-mail: beatriz.elizaga@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Martín-Benito, Mercedes, E-mail: m.martin@hef.ru.nl [Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Heyendaalseweg 135, NL-6525 AJ Nijmegen (Netherlands); Mena Marugán, Guillermo A., E-mail: mena@iem.cfmac.csic.es [Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain); Velhinho, José M., E-mail: jvelhi@ubi.pt [Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001, Covilhã (Portugal)

    2017-01-15

    We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.

  1. Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

    International Nuclear Information System (INIS)

    Cortez, Jerónimo; Elizaga Navascués, Beatriz; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.; Velhinho, José M.

    2017-01-01

    We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.

  2. (2 + 1)-Dimensional Dirac hierarchy and its integrable couplings as well as multi-component integrable system

    International Nuclear Information System (INIS)

    Li Zhu; Dong Huanhe

    2008-01-01

    Under the frame of the (2 + 1)-dimensional zero curvature equation and Tu model, (2 + 1)-dimensional Dirac hierarchy is obtained. Again by use of the expanding loop algebra the integrable coupling system of the above hierarchy is given

  3. The Dirac medals of the ICTP. 1993

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1996-12-31

    The Dirac Medals of the International Centre for Theoretical Physics (ICTP) were instituted in 1985. These are awarded yearly to outstanding physicists, on Dirac`s birthday - 8th August- for contributions to theoretical physics. The document includes the lectures of the three Dirac Medalists for 1993: Professor Sergio Ferrara, Professor Daniel Z. Freedman, and Professor Peter van Nieuwenhuizen. A separate abstract was prepared for each lecture

  4. Smooth and non-smooth travelling waves in a nonlinearly dispersive Boussinesq equation

    International Nuclear Information System (INIS)

    Shen Jianwei; Xu Wei; Lei Youming

    2005-01-01

    The dynamical behavior and special exact solutions of nonlinear dispersive Boussinesq equation (B(m,n) equation), u tt -u xx -a(u n ) xx +b(u m ) xxxx =0, is studied by using bifurcation theory of dynamical system. As a result, all possible phase portraits in the parametric space for the travelling wave system, solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular straight line in the travelling wave system is the reason why smooth waves converge to cusp waves, finally. When parameter are varied, under different parametric conditions, various sufficient conditions guarantee the existence of the above solutions are given

  5. Micromagnetic sensors and Dirac fermions in HgTe heterostructures

    International Nuclear Information System (INIS)

    Buettner, Bastian

    2012-01-01

    , extracted from the noise of the sensor. The observed high signal-to-noise ratio validates the detection limit of this sensor in terms of geometry. This would be reached for a magnet (same material) with quadratic crosssection for an edge length of 3.3 nm. Moreover, the feasibility of this sensor for operation in a wide temperature range (T=mK..>200 K) and high magnetic fields has been confirmed. The second micromagnetic sensor is the micro-SQUID (micro-Superconducting-QUantum-Interference-Device) based on niobium. The typical sensor area of the devices built in this work was (1.0.1.0) μm 2 , with constrictions of about 20 nm. The characterization of this device demonstrates an amazing field sensitivity (regarding its size) of δB -4 Φ 0 and a similar magnetic moment resolution of δM∼10 2 μ B . Furthermore, the introduction of an ellipsoidal permalloy magnet (axes: 200 nm and 400 nm, thickness 30 nm) substantiates the suitability for the detection of minuscule, localized magnetic fields. The second part of the thesis deals with the peculiar transport properties of HgTe quantum wells. These rely on the linear contribution to the band structure inherent to the heterostructure. Therefore the system can be described by an effective Dirac Hamiltonian, whose Dirac mass is tunable by the variation of the quantum well thickness. By fabrication and characterization of a systematical series of substrates, a system with vanishing Dirac mass (zero energy gap) has been confirmed. This heterostructure therefore resembles graphene (a monolayer of graphite), with the difference of exhibiting only one valley in the energy dispersion of the Brillouin zone. Thus parasitical intervalley scattering cannot occur. The existence of this system has been proven by the agreement of theoretical predictions, based on widely accepted band structure calculations with the experiment (Landau level dispersion, conductivity). Furthermore, another particularity of the band structure - the transition from

  6. Strain-induced gap transition and anisotropic Dirac-like cones in monolayer and bilayer phosphorene

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Can; Xia, Qinglin, E-mail: qlxia@csu.edu.cn; Nie, Yaozhuang; Guo, Guanghua, E-mail: guogh@csu.edu.cn [School of Physics and Electronics, Central South University, Changsha 410083 (China)

    2015-03-28

    The electronic properties of two-dimensional monolayer and bilayer phosphorene subjected to uniaxial and biaxial strains have been investigated using first-principles calculations based on density functional theory. Strain engineering has obvious influence on the electronic properties of monolayer and bilayer phosphorene. By comparison, we find that biaxial strain is more effective in tuning the band gap than uniaxial strain. Interestingly, we observe the emergence of Dirac-like cones by the application of zigzag tensile strain in the monolayer and bilayer systems. For bilayer phosphorene, we induce the anisotropic Dirac-like dispersion by the application of appropriate armchair or biaxial compressive strain. Our results present very interesting possibilities for engineering the electronic properties of phosphorene and pave a way for tuning the band gap of future electronic and optoelectronic devices.

  7. An integral transform of the Salpeter equation

    International Nuclear Information System (INIS)

    Krolikowski, W.

    1980-03-01

    We find a new form of relativistic wave equation for two spin-1/2 particles, which arises by an integral transformation (in the position space) of the wave function in the Salpeter equation. The non-locality involved in this transformation is extended practically over the Compton wavelength of the lighter of two particles. In the case of equal masses the new equation assumes the form of the Breit equation with an effective integral interaction. In the one-body limit it reduces to the Dirac equation also with an effective integral interaction. (author)

  8. Dirac cones in isogonal hexagonal metallic structures

    Science.gov (United States)

    Wang, Kang

    2018-03-01

    A honeycomb hexagonal metallic lattice is equivalent to a triangular atomic one and cannot create Dirac cones in its electromagnetic wave spectrum. We study in this work the low-frequency electromagnetic band structures in isogonal hexagonal metallic lattices that are directly related to the honeycomb one and show that such structures can create Dirac cones. The band formation can be described by a tight-binding model that allows investigating, in terms of correlations between local resonance modes, the condition for the Dirac cones and the consequence of the third structure tile sustaining an extra resonance mode in the unit cell that induces band shifts and thus nonlinear deformation of the Dirac cones following the wave vectors departing from the Dirac points. We show further that, under structure deformation, the deformations of the Dirac cones result from two different correlation mechanisms, both reinforced by the lattice's metallic nature, which directly affects the resonance mode correlations. The isogonal structures provide new degrees of freedom for tuning the Dirac cones, allowing adjustment of the cone shape by modulating the structure tiles at the local scale without modifying the lattice periodicity and symmetry.

  9. The causal perturbation expansion revisited: Rescaling the interacting Dirac sea

    International Nuclear Information System (INIS)

    Finster, Felix; Grotz, Andreas

    2010-01-01

    The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.

  10. The causal perturbation expansion revisited: Rescaling the interacting Dirac sea

    Science.gov (United States)

    Finster, Felix; Grotz, Andreas

    2010-07-01

    The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.

  11. LHCbDIRAC as Apache Mesos microservices

    CERN Multimedia

    Couturier, Ben

    2016-01-01

    The LHCb experiment relies on LHCbDIRAC, an extension of DIRAC, to drive its offline computing. This middleware provides a development framework and a complete set of components for building distributed computing systems. These components are currently installed and ran on virtual machines (VM) or bare metal hardware. Due to the increased load of work, high availability is becoming more and more important for the LHCbDIRAC services, and the current installation model is showing its limitations. Apache Mesos is a cluster manager which aims at abstracting heterogeneous physical resources on which various tasks can be distributed thanks to so called "framework". The Marathon framework is suitable for long running tasks such as the DIRAC services, while the Chronos framework meets the needs of cron-like tasks like the DIRAC agents. A combination of the service discovery tool Consul together with HAProxy allows to expose the running containers to the outside world while hiding their dynamic placements. Such an arc...

  12. Low momentum scattering of the Dirac particle with an asymmetric cusp potential

    International Nuclear Information System (INIS)

    Jiang, Yu.; Dong, Shi-Hai; Lozada-Cassou, M.; Antillon, A.

    2006-01-01

    We study the exact solutions of the bound and scattering states of the one-dimensional Dirac equation with an asymmetric cusp potential and derive the condition of the supercriticality for this quantum system. We find that the scattering properties are invariant under reflection of the potential's shape, and the supercritical value for the potential amplitude V 0 varies with the degree of the potential asymmetry. (orig.)

  13. Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma

    Science.gov (United States)

    Seadawy, A. R.; El-Rashidy, K.

    2018-03-01

    The Kadomtsev-Petviashvili (KP) and modified KP equations are two of the most universal models in nonlinear wave theory, which arises as a reduction of system with quadratic nonlinearity which admit weakly dispersive waves. The generalized extended tanh method and the F-expansion method are used to derive exact solitary waves solutions of KP and modified KP equations. The region of solutions are displayed graphically.

  14. Data Management System of the DIRAC Project

    CERN Multimedia

    Haen, Christophe; Tsaregorodtsev, Andrei

    2015-01-01

    The DIRAC Interware provides a development framework and a complete set of components for building distributed computing systems. The DIRAC Data Management System (DMS) offers all the necessary tools to ensure data handling operations for small and large user communities. It supports transparent access to storage resources based on multiple technologies, and is easily expandable. The information on data files and replicas is kept in a File Catalog of which DIRAC offers a powerful and versatile implementation (DFC). Data movement can be performed using third party services including FTS3. Bulk data operations are resilient with respect to failures due to the use of the Request Management System (RMS) that keeps track of ongoing tasks. In this contribution we will present an overview of the DIRAC DMS capabilities and its connection with other DIRAC subsystems such as the Transformation System. The DIRAC DMS is in use by several user communities now. The contribution will present the experience of the LHCb exper...

  15. Dirac bi-spinor entanglement under local noise and its simulation by Jaynes-Cummings interactions

    Science.gov (United States)

    Bittencourt, Victor A. S. V.; Bernardini, Alex E.

    2017-08-01

    A description of the effects of the local noise on the quantum entanglement constraining the internal degrees of freedom of Dirac bi-spinor structures driven by arbitrary Poincaré invariant potentials is proposed. Given that the Dirac equation dynamics including external potentials can be simulated by a suitable four level trapped ion setup, quantum entanglement of two-qubit ionic states with quantum numbers related to the total angular momentum and to its projection onto the direction of the external magnetic field (used for lift the ions degeneracy), are recovered by means of a suitable ansatz. This formalism allows the inclusion of noise effects, which leads to disentanglement in the four level trapped ion quantum system. Our results indicate the role of interactions in bi-spinor entanglement, as well as the description of disentanglement in ionic states under local noises. For a state prepared initially in one of the ionic levels, local noise induces entanglement sudden death followed by sudden revivals driven by the noiseless dynamics of the state. Residual quantum correlations are observed in the intervals where such state is separable. Schrödinger cat and Werner states partially loose their initial entanglement content due to the interaction with the noisy environment but presenting entanglement oscillations without sudden death. Because Dirac equation describes low energy excitations of mono layer and bi-layer graphene, the formalism can also be applied to compute, for instance, electron-hole or electron/electron entanglement in various circumstances.

  16. The DIRAC Web Portal 2.0

    Science.gov (United States)

    Mathe, Z.; Casajus Ramo, A.; Lazovsky, N.; Stagni, F.

    2015-12-01

    For many years the DIRAC interware (Distributed Infrastructure with Remote Agent Control) has had a web interface, allowing the users to monitor DIRAC activities and also interact with the system. Since then many new web technologies have emerged, therefore a redesign and a new implementation of the DIRAC Web portal were necessary, taking into account the lessons learnt using the old portal. These new technologies allowed to build a more compact, robust and responsive web interface that enables users to have better control over the whole system while keeping a simple interface. The web framework provides a large set of “applications”, each of which can be used for interacting with various parts of the system. Communities can also create their own set of personalised web applications, and can easily extend already existing ones with a minimal effort. Each user can configure and personalise the view for each application and save it using the DIRAC User Profile service as RESTful state provider, instead of using cookies. The owner of a view can share it with other users or within a user community. Compatibility between different browsers is assured, as well as with mobile versions. In this paper, we present the new DIRAC Web framework as well as the LHCb extension of the DIRAC Web portal.

  17. A collective variable approach and stabilization for dispersion-managed optical solitons in the quintic complex Ginzburg-Landau equation as perturbations of the nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Fewo, S I; Kenfack-Jiotsa, A; Kofane, T C

    2006-01-01

    With the help of the one-dimensional quintic complex Ginzburg-Landau equation (CGLE) as perturbations of the nonlinear Schroedinger equation (NLSE), we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fibre optic links. The equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance, and also to analyse effects of initial amplitude and width on the propagating pulse. Nonlinear gain is shown to be beneficial in stabilizing DM solitons. A fully numerical simulation of the one-dimensional quintic CGLE as perturbations of NLSE finally tests the results of the CV theory. A good agreement is observed between both methods

  18. easyDiracGauginos

    International Nuclear Information System (INIS)

    Abel, Steven; Goodsell, Mark

    2011-02-01

    A simple and natural model is presented that gives Dirac gauginos. The configuration is related to ''deconstructed gaugino mediation''. A high energy completion is provided based on existing ISS-like models of deconstructed gaugino mediation. This provides a complete picture of Dirac gauginos that includes the necessary extra adjoint fermions (generated as magnetic quarks of the ISS theory) and supersymmetry breaking (via the ISS mechanism). Moreover the screening of the scalar masses means that they can similar to or less than the gaugino masses, even though the supersymmetry breaking is driven by F-terms. (orig.)

  19. Properties of the DKP [Duffin-Kemmer-Petiau] equation

    International Nuclear Information System (INIS)

    Nieto, M.M.

    1988-01-01

    After recalling the development of relativistic quantum mechanics, I elucidating the properties of the Duffin-Kemmer-Petiau first-order wave equation for spin-0 and -1 mesons. The DKP equation is formally compared to the Dirac equation, and physically compared to the Klein-Gordon second-order equation for mesons. I point out where the DKP and KG equations predict the same results, and where their predictions are different. I conclude with an example of where these differences might interest people studying quark models of nuclei. 9 refs

  20. Nonlinear optical observation of coherent acoustic Dirac plasmons in thin-film topological insulators

    Science.gov (United States)

    Glinka, Yuri D.; Babakiray, Sercan; Johnson, Trent A.; Holcomb, Mikel B.; Lederman, David

    2016-09-01

    Low-energy collective electronic excitations exhibiting sound-like linear dispersion have been intensively studied both experimentally and theoretically for a long time. However, coherent acoustic plasmon modes appearing in time-domain measurements are rarely observed due to Landau damping by the single-particle continua. Here we report on the observation of coherent acoustic Dirac plasmon (CADP) modes excited in indirectly (electrostatically) opposite-surface coupled films of the topological insulator Bi2Se3. Using transient second-harmonic generation, a technique capable of independently monitoring the in-plane and out-of-plane electron dynamics in the films, the GHz-range oscillations were observed without corresponding oscillations in the transient reflectivity. These oscillations were assigned to the transverse magnetic and transverse electric guided CADP modes induced by the evanescent guided Lamb acoustic waves and remained Landau undamped due to fermion tunnelling between the opposite-surface Dirac states.

  1. Existence of solution for a general fractional advection-dispersion equation

    Science.gov (United States)

    Torres Ledesma, César E.

    2018-05-01

    In this work, we consider the existence of solution to the following fractional advection-dispersion equation -d/dt ( p {_{-∞}}It^{β }(u'(t)) + q {t}I_{∞}^{β }(u'(t))) + b(t)u = f(t, u(t)),t\\in R where β \\in (0,1) , _{-∞}It^{β } and tI_{∞}^{β } denote left and right Liouville-Weyl fractional integrals of order β respectively, 0continuous functions. Due to the general assumption on the constant p and q, the problem (0.1) does not have a variational structure. Despite that, here we study it performing variational methods, combining with an iterative technique, and give an existence criteria of solution for the problem (0.1) under suitable assumptions.

  2. Photonic band structures in one-dimensional photonic crystals containing Dirac materials

    International Nuclear Information System (INIS)

    Wang, Lin; Wang, Li-Gang

    2015-01-01

    We have investigated the band structures of one-dimensional photonic crystals (1DPCs) composed of Dirac materials and ordinary dielectric media. It is found that there exist an omnidirectional passing band and a kind of special band, which result from the interaction of the evanescent and propagating waves. Due to the interface effect and strong dispersion, the electromagnetic fields inside the special bands are strongly enhanced. It is also shown that the properties of these bands are invariant upon the lattice constant but sensitive to the resonant conditions

  3. Designing Two-Dimensional Dirac Heterointerfaces of Few-Layer Graphene and Tetradymite-Type Sb2Te3 for Thermoelectric Applications.

    Science.gov (United States)

    Jang, Woosun; Lee, Jiwoo; In, Chihun; Choi, Hyunyong; Soon, Aloysius

    2017-12-06

    Despite the ubiquitous nature of the Peltier effect in low-dimensional thermoelectric devices, the influence of finite temperature on the electronic structure and transport in the Dirac heterointerfaces of the few-layer graphene and layered tetradymite, Sb 2 Te 3 (which coincidently have excellent thermoelectric properties) are not well understood. In this work, using the first-principles density-functional theory calculations, we investigate the detailed atomic and electronic structure of these Dirac heterointerfaces of graphene and Sb 2 Te 3 and further re-examine the effect of finite temperature on the electronic band structures using a phenomenological temperature-broadening model based on Fermi-Dirac statistics. We then proceed to understand the underlying charge redistribution process in this Dirac heterointerfaces and through solving the Boltzmann transport equation, we present the theoretical evidence of electron-hole asymmetry in its electrical conductivity as a consequence of this charge redistribution mechanism. We finally propose that the hexagonal-stacked Dirac heterointerfaces are useful as efficient p-n junction building blocks in the next-generation thermoelectric devices where the electron-hole asymmetry promotes the thermoelectric transport by "hot" excited charge carriers.

  4. LHCbDIRAC as Apache Mesos microservices

    OpenAIRE

    Haen, Christophe; Couturier, Benjamin

    2017-01-01

    The LHCb experiment relies on LHCbDIRAC, an extension of DIRAC, to drive its offline computing. This middleware provides a development framework and a complete set of components for building distributed computing systems. These components are currently installed and run on virtual machines (VM) or bare metal hardware. Due to the increased workload, high availability is becoming more and more important for the LHCbDIRAC services, and the current installation model is showing its limitations. A...

  5. Dirac particle on S2

    International Nuclear Information System (INIS)

    Ferreira, P.L.; Palladino, B.E.

    1985-01-01

    The problem of a Dirac particle in stationary motion on S 2 - a two dimensional sphere embedded in Euclidean space E 3 - is discussed. It provides a particularly simple case of an exactly solvable constrained Dirac particle whose properties are here studied, with emphasis on its magnetic moment. (Author) [pt

  6. On the spectral theory and dispersive estimates for a discrete Schroedinger equation in one dimension

    International Nuclear Information System (INIS)

    Pelinovsky, D. E.; Stefanov, A.

    2008-01-01

    Based on the recent work [Komech et al., 'Dispersive estimates for 1D discrete Schroedinger and Klein-Gordon equations', Appl. Anal. 85, 1487 (2006)] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schroedinger operator, Hφ=(-Δ+V)φ=-(φ n+1 +φ n-1 -2φ n )+V n φ n . We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates parallel e itH P a.c. (H) parallel l σ 2 →l -σ 2 -3/2 for any fixed σ>(5/2) and any t>0, where P a.c. (H) denotes the spectral projection to the absolutely continuous spectrum of H. In addition, based on the scattering theory for the discrete Jost solutions and the previous results by Stefanov and Kevrekidis [''Asymptotic behaviour of small solutions for the discrete nonlinear Schroedinger and Klein-Gordon equations,'' Nonlinearity 18, 1841 (2005)], we find new dispersive estimates parallel e itH P a.c. (H) parallel l 1 →l ∞ -1/3 , which are sharp for the discrete Schroedinger operators even for V=0

  7. New solitary solutions with compact support for Boussinesq-like B(2n, 2n) equations with fully nonlinear dispersion

    International Nuclear Information System (INIS)

    Zhu Yonggui; Lu Chao

    2007-01-01

    In this paper, the Boussinesq-like equations with fully nonlinear dispersion, B(2n, 2n) equations: u tt + (u 2n ) xx + (u 2n ) xxxx 0 which exhibit compactons: solitons with compact support, are studied. New exact solitary solutions with compact support are found. The special case B(2, 2) is chosen to illustrate the concrete scheme of the decomposition method in B(2n, 2n) equations. General formulas for the solutions of B(2n, 2n) equations are established

  8. [p,q] {ne} i{Dirac_h}

    Energy Technology Data Exchange (ETDEWEB)

    Costella, J P

    1995-05-22

    In this short note, it is argued that [p, q] {ne} i{Dirac_h}, contrary to the oiginal claims of Born and Jordan, and Dirac. Rather, [p, q] is equal to something that is infinitesimally different from i{Dirac_h}. While this difference is usually harmless, it does provide the solution of the Born-Jordan `trace paradox` of [p, q]. More recently, subtleties of a very similar form have been found to be of fundamental importance in quantum field theory. 3 refs.

  9. DIRAC - The Distributed MC Production and Analysis for LHCb

    CERN Document Server

    Tsaregorodtsev, A

    2004-01-01

    DIRAC is the LHCb distributed computing grid infrastructure for MC production and analysis. Its architecture is based on a set of distributed collaborating services. The service decomposition broadly follows the ARDA project proposal, allowing for the possibility of interchanging the EGEE/ARDA and DIRAC components in the future. Some components developed outside the DIRAC project are already in use as services, for example the File Catalog developed by the AliEn project. An overview of the DIRAC architecture will be given, in particular the recent developments to support user analysis. The main design choices will be presented. One of the main design goals of DIRAC is the simplicity of installation, configuring and operation of various services. This allows all the DIRAC resources to be easily managed by a single Production Manager. The modular design of the DIRAC components allows its functionality to be easily extended to include new computing and storage elements or to handle new tasks. The DIRAC system al...

  10. easyDiracGauginos

    Energy Technology Data Exchange (ETDEWEB)

    Abel, Steven [Durham Univ. (United Kingdom). Inst. for Particle Physics Phenomenology; CERN, Geneva (Switzerland); Goodsell, Mark [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2011-02-15

    A simple and natural model is presented that gives Dirac gauginos. The configuration is related to ''deconstructed gaugino mediation''. A high energy completion is provided based on existing ISS-like models of deconstructed gaugino mediation. This provides a complete picture of Dirac gauginos that includes the necessary extra adjoint fermions (generated as magnetic quarks of the ISS theory) and supersymmetry breaking (via the ISS mechanism). Moreover the screening of the scalar masses means that they can similar to or less than the gaugino masses, even though the supersymmetry breaking is driven by F-terms. (orig.)

  11. Transverse Field Dispersion in the Generalized Nonlinear Schrödinger Equation: Four Wave Mixing in a Higher Order Mode Fiber

    DEFF Research Database (Denmark)

    Pedersen, Martin Erland Vestergaard; Cheng, Ji; Xu, Chris

    2013-01-01

    An improved version of the generalized nonlinear Schrödinger equation is derived, which takes into account the correct dispersion of the transverse field distribution. The new improved version of the generalized nonlinear Schrödinger equation is verified to give the same results as the standard...

  12. Relativistic wave equations for particles in electromagnetic fields

    International Nuclear Information System (INIS)

    Good, R.H. Jr.

    1989-01-01

    A new type of generalization of the Dirac equation of higher spin particles and antiparticles is given, in case only the terms proportional to the external fields need to be retained. copyright 1989 Academic Press, Inc

  13. Prediction of the High Thermoelectric Performance of Pnictogen Dichalcogenide Layered Compounds with Quasi-One-Dimensional Gapped Dirac-like Band Dispersion

    Science.gov (United States)

    Ochi, Masayuki; Usui, Hidetomo; Kuroki, Kazuhiko

    2017-12-01

    Thermoelectric power generation has been recognized as one of the most important technologies, and high-performance thermoelectric materials have long been pursued. However, because of the large number of candidate materials, this quest is extremely challenging, and it has become clear that a firm theoretical concept from the viewpoint of band-structure engineering is needed. We theoretically demonstrate that pnictogen dichalcogenide layered compounds, which originally attracted attention as a family of superconductors and have recently been investigated as thermoelectric materials, can exhibit very high thermoelectric performance with elemental substitution. Specifically, we clarify a promising guiding principle for material design and find that LaOAsSe2, a material that has yet to be synthesized, has a power factor that is 6 times as large as that of the known compound LaOBiS2 and can exhibit a very large Z T under some plausible assumptions. This large enhancement of the thermoelectric performance originates from the quasi-one-dimensional gapped Dirac-like band dispersion, which is realized by the square-lattice network. We offer one ideal limit of the band structure for thermoelectric materials. Because our target materials have high controllability of constituent elements and feasibility of carrier doping, experimental studies along this line are eagerly awaited.

  14. Micromagnetic sensors and Dirac fermions in HgTe heterostructures

    Energy Technology Data Exchange (ETDEWEB)

    Buettner, Bastian

    2012-08-06

    cross-section of (100.20) nm{sup 2} confirms the expected resolution ability, extracted from the noise of the sensor. The observed high signal-to-noise ratio validates the detection limit of this sensor in terms of geometry. This would be reached for a magnet (same material) with quadratic crosssection for an edge length of 3.3 nm. Moreover, the feasibility of this sensor for operation in a wide temperature range (T=mK..>200 K) and high magnetic fields has been confirmed. The second micromagnetic sensor is the micro-SQUID (micro-Superconducting-QUantum-Interference-Device) based on niobium. The typical sensor area of the devices built in this work was (1.0.1.0) {mu}m{sup 2}, with constrictions of about 20 nm. The characterization of this device demonstrates an amazing field sensitivity (regarding its size) of {delta}B<1 {mu}T. Even though the sensor was 25 times larger than the best micro-Hall sensor, it provided an excellent flux resolution in the order of {delta}{Phi}{approx}5.10{sup -4} {Phi}{sub 0} and a similar magnetic moment resolution of {delta}M{approx}10{sup 2} {mu}{sub B}. Furthermore, the introduction of an ellipsoidal permalloy magnet (axes: 200 nm and 400 nm, thickness 30 nm) substantiates the suitability for the detection of minuscule, localized magnetic fields. The second part of the thesis deals with the peculiar transport properties of HgTe quantum wells. These rely on the linear contribution to the band structure inherent to the heterostructure. Therefore the system can be described by an effective Dirac Hamiltonian, whose Dirac mass is tunable by the variation of the quantum well thickness. By fabrication and characterization of a systematical series of substrates, a system with vanishing Dirac mass (zero energy gap) has been confirmed. This heterostructure therefore resembles graphene (a monolayer of graphite), with the difference of exhibiting only one valley in the energy dispersion of the Brillouin zone. Thus parasitical intervalley scattering

  15. Micromagnetic sensors and Dirac fermions in HgTe heterostructures

    Energy Technology Data Exchange (ETDEWEB)

    Buettner, Bastian

    2012-08-06

    nanomagnet with a cross-section of (100.20) nm{sup 2} confirms the expected resolution ability, extracted from the noise of the sensor. The observed high signal-to-noise ratio validates the detection limit of this sensor in terms of geometry. This would be reached for a magnet (same material) with quadratic crosssection for an edge length of 3.3 nm. Moreover, the feasibility of this sensor for operation in a wide temperature range (T=mK..>200 K) and high magnetic fields has been confirmed. The second micromagnetic sensor is the micro-SQUID (micro-Superconducting-QUantum-Interference-Device) based on niobium. The typical sensor area of the devices built in this work was (1.0.1.0) {mu}m{sup 2}, with constrictions of about 20 nm. The characterization of this device demonstrates an amazing field sensitivity (regarding its size) of {delta}B<1 {mu}T. Even though the sensor was 25 times larger than the best micro-Hall sensor, it provided an excellent flux resolution in the order of {delta}{Phi}{approx}5.10{sup -4} {Phi}{sub 0} and a similar magnetic moment resolution of {delta}M{approx}10{sup 2} {mu}{sub B}. Furthermore, the introduction of an ellipsoidal permalloy magnet (axes: 200 nm and 400 nm, thickness 30 nm) substantiates the suitability for the detection of minuscule, localized magnetic fields. The second part of the thesis deals with the peculiar transport properties of HgTe quantum wells. These rely on the linear contribution to the band structure inherent to the heterostructure. Therefore the system can be described by an effective Dirac Hamiltonian, whose Dirac mass is tunable by the variation of the quantum well thickness. By fabrication and characterization of a systematical series of substrates, a system with vanishing Dirac mass (zero energy gap) has been confirmed. This heterostructure therefore resembles graphene (a monolayer of graphite), with the difference of exhibiting only one valley in the energy dispersion of the Brillouin zone. Thus parasitical intervalley

  16. The Dirac medals of the ICTP. 1993

    International Nuclear Information System (INIS)

    1995-01-01

    The Dirac Medals of the International Centre for Theoretical Physics (ICTP) were instituted in 1985. These are awarded yearly to outstanding physicists, on Dirac's birthday - 8th August- for contributions to theoretical physics. The document includes the lectures of the three Dirac Medalists for 1993: Professor Sergio Ferrara, Professor Daniel Z. Freedman, and Professor Peter van Nieuwenhuizen. A separate abstract was prepared for each lecture

  17. A robust and general Schrödinger and Dirac solver for atomic structure calculations

    Czech Academy of Sciences Publication Activity Database

    Čertík, O.; Pask, J.E.; Vackář, Jiří

    2013-01-01

    Roč. 184, č. 7 (2013), s. 1777-1791 ISSN 0010-4655 R&D Projects: GA MŠk(CZ) LC06040; GA ČR GA101/09/1630 Institutional support: RVO:68378271 Keywords : atom * electronic structure * Dirac equation * density-functional theory Subject RIV: BE - Theoretical Physics Impact factor: 2.407, year: 2013 http://www.sciencedirect.com/science/article/pii/S0010465513000714

  18. DIRAC pilot framework and the DIRAC Workload Management System

    International Nuclear Information System (INIS)

    Casajus, Adrian; Graciani, Ricardo; Paterson, Stuart; Tsaregorodtsev, Andrei

    2010-01-01

    DIRAC, the LHCb community Grid solution, has pioneered the use of pilot jobs in the Grid. Pilot Jobs provide a homogeneous interface to an heterogeneous set of computing resources. At the same time, Pilot Jobs allow to delay the scheduling decision to the last moment, thus taking into account the precise running conditions at the resource and last moment requests to the system. The DIRAC Workload Management System provides one single scheduling mechanism for jobs with very different profiles. To achieve an overall optimisation, it organizes pending jobs in task queues, both for individual users and production activities. Task queues are created with jobs having similar requirements. Following the VO policy a priority is assigned to each task queue. Pilot submission and subsequent job matching are based on these priorities following a statistical approach.

  19. DIRAC pilot framework and the DIRAC Workload Management System

    Energy Technology Data Exchange (ETDEWEB)

    Casajus, Adrian; Graciani, Ricardo [Universitat de Barcelona (Spain); Paterson, Stuart [CERN (Switzerland); Tsaregorodtsev, Andrei, E-mail: adria@ecm.ub.e, E-mail: graciani@ecm.ub.e, E-mail: stuart.paterson@cern.c, E-mail: atsareg@in2p3.f [CPPM Marseille (France)

    2010-04-01

    DIRAC, the LHCb community Grid solution, has pioneered the use of pilot jobs in the Grid. Pilot Jobs provide a homogeneous interface to an heterogeneous set of computing resources. At the same time, Pilot Jobs allow to delay the scheduling decision to the last moment, thus taking into account the precise running conditions at the resource and last moment requests to the system. The DIRAC Workload Management System provides one single scheduling mechanism for jobs with very different profiles. To achieve an overall optimisation, it organizes pending jobs in task queues, both for individual users and production activities. Task queues are created with jobs having similar requirements. Following the VO policy a priority is assigned to each task queue. Pilot submission and subsequent job matching are based on these priorities following a statistical approach.

  20. Universal Quantum Criticality in the Metal-Insulator Transition of Two-Dimensional Interacting Dirac Electrons

    Directory of Open Access Journals (Sweden)

    Yuichi Otsuka

    2016-03-01

    Full Text Available The metal-insulator transition has been a subject of intense research since Mott first proposed that the metallic behavior of interacting electrons could turn to an insulating one as electron correlations increase. Here, we consider electrons with massless Dirac-like dispersion in two spatial dimensions, described by the Hubbard models on two geometrically different lattices, and perform numerically exact calculations on unprecedentedly large systems that, combined with a careful finite-size scaling analysis, allow us to explore the quantum critical behavior in the vicinity of the interaction-driven metal-insulator transition. Thereby, we find that the transition is continuous, and we determine the quantum criticality for the corresponding universality class, which is described in the continuous limit by the Gross-Neveu model, a model extensively studied in quantum field theory. Furthermore, we discuss a fluctuation-driven scenario for the metal-insulator transition in the interacting Dirac electrons: The metal-insulator transition is triggered only by the vanishing of the quasiparticle weight, not by the Dirac Fermi velocity, which instead remains finite near the transition. This important feature cannot be captured by a simple mean-field or Gutzwiller-type approximate picture but is rather consistent with the low-energy behavior of the Gross-Neveu model.

  1. Finger-gate manipulated quantum transport in Dirac materials

    International Nuclear Information System (INIS)

    Kleftogiannis, Ioannis; Cheng, Shun-Jen; Tang, Chi-Shung

    2015-01-01

    We investigate the quantum transport properties of multichannel nanoribbons made of materials described by the Dirac equation, under an in-plane magnetic field. In the low energy regime, positive and negative finger-gate potentials allow the electrons to make intra-subband transitions via hole-like or electron-like quasibound states (QBS), respectively, resulting in dips in the conductance. In the high energy regime, double dip structures in the conductance are found, attributed to spin-flip or spin-nonflip inter-subband transitions through the QBSs. Inverting the finger-gate polarity offers the possibility to manipulate the spin polarized electronic transport to achieve a controlled spin-switch. (paper)

  2. Wave equation of hydrogen atom

    International Nuclear Information System (INIS)

    Suwito.

    1977-01-01

    The calculation of the energy levels of the hydrogen atom using Bohr, Schroedinger and Dirac theories is reviewed. The result is compared with that obtained from infinite component wave equations theory which developed recently. The conclusion can be stated that the latter theory is better to describe the composit system than the former. (author)

  3. Strain engineering of Dirac cones in graphyne

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Gaoxue; Kumar, Ashok; Pandey, Ravindra, E-mail: pandey@mtu.edu [Department of Physics, Michigan Technological University, Houghton, Michigan 49931 (United States); Si, Mingsu [Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000 (China)

    2014-05-26

    6,6,12-graphyne, one of the two-dimensional carbon allotropes with the rectangular lattice structure, has two kinds of non-equivalent anisotropic Dirac cones in the first Brillouin zone. We show that Dirac cones can be tuned independently by the uniaxial compressive strain applied to graphyne, which induces n-type and p-type self-doping effect, by shifting the energy of the Dirac cones in the opposite directions. On the other hand, application of the tensile strain results into a transition from gapless to finite gap system for the monolayer. For the AB-stacked bilayer, the results predict tunability of Dirac-cones by in-plane strains as well as the strain applied perpendicular to the plane. The group velocities of the Dirac cones show enhancement in the resistance anisotropy for bilayer relative to the case of monolayer. Such tunable and direction-dependent electronic properties predicted for 6,6,12-graphyne make it to be competitive for the next-generation electronic devices at nanoscale.

  4. Asymptotic solution of the coupled equations for electron collisions with atoms or positive ions using Dirac hamiltonians

    International Nuclear Information System (INIS)

    Grant, I.P.

    1982-01-01

    Possible relativistic effects in low energy electron scattering from atoms or positive ions has been investigated using the Dirac hamiltonian. Single channel formula and many channel expressions indicate that asymptotic estimation of radial wavefunctions can be carried out satisfactorily for most purposes using non-relativistic methods. (U.K.)

  5. A generalization of Dirac non-linear electrodynamics, and spinning charged particles

    International Nuclear Information System (INIS)

    Rodrigues Junior, W.A.; Vaz Junior, J.; Recami, E.

    1992-08-01

    The Dirac non-linear electrodynamics is generalized by introducing two potentials (namely, the vector potential a and the pseudo-vector potential γ 5 B of the electromagnetic theory with charges and magnetic monopoles), and by imposing the pseudoscalar part of the product W W * to BE zero, with W = A + γ 5 B. Also, is demonstrated that the field equations of such a theory posses a soliton-like solution which can represent a priori a charged particle. (L.C.J.A.)

  6. Dirac experiment

    International Nuclear Information System (INIS)

    Gomez, F.; Adeva, B.; Afanasev, L.; Benayoun, M.; Brekhovskikh, V.; Caragheorgheopol, G.; Cechak, T.; Chiba, M.; Constantinescu, S.; Doudarev, A.; Dreossi, D.; Drijard, D.; Ferro-Luzzi, M.; Gallas, M.V.; Gerndt, J.; Giacomich, R.; Gianotti, P.; Goldin, D.; Gorin, A.; Gortchakov, O.; Guaraldo, C.; Hansroul, M.; Hosek, R.; Iliescu, M.; Jabitski, M.; Kalinina, N.; Karpoukhine, V.; Kluson, J.; Kobayashi, M.; Kokkas, P.; Komarov, V.; Koulikov, A.; Kouptsov, A.; Krouglov, V.; Krouglova, L.; Kuroda, K.-I.; Lanaro, A.; Lapshine, V.; Lednicky, R.; Leruste, P.; Levisandri, P.; Lopez Aguera, A.; Lucherini, V.; Maki, T.; Manuilov, I.; Montanet, L.; Narjoux, J.-L.; Nemenov, L.; Nikitin, M.; Nunez Pardo, T.; Okada, K.; Olchevskii, V.; Pazos, A.; Pentia, M.; Penzo, A.; Perreau, J.-M.; Petrascu, C.; Plo, M.; Ponta, T.; Pop, D.; Riazantsev, A.; Rodriguez, J.M.; Rodriguez Fernandez, A.; Rykaline, V.; Santamarina, C.; Saborido, J.; Schacher, J.; Sidorov, A.; Smolik, J.; Takeutchi, F.; Tarasov, A.; Tauscher, L.; Tobar, M.J.; Trusov, S.; Vazquez, P.; Vlachos, S.; Yazkov, V.; Yoshimura, Y.; Zrelov, P.

    2001-01-01

    The main objective of DIRAC experiment is the measurement of the lifetime τ of the exotic hadronic atom consisting of π + and π - mesons. The lifetime of this atom is determined by the decay mode π + π - → π 0 π 0 due to the strong interaction. Through the precise relationship between the lifetime and the S-wave pion-pion scattering length difference |a 0 - a 2 | for isospin 0 and 2 (respectively), a measurement of τ with an accuracy of 10% will allow a determination of |a 0 - a 2 | at a 5% precision level. Pion-pion scattering lengths have been calculated in the framework of chiral perturbation theory with an accuracy below 5%. In this way DIRAC experiment will provide a crucial test of the chiral symmetry breaking scheme in QCD effective theories at low energies

  7. Nonstandard Supersymmetry Breaking and Dirac Gaugino Masses without Supersoftness

    Energy Technology Data Exchange (ETDEWEB)

    Martin, Stephen P. [Northern Illinois U.

    2015-08-05

    I consider models in which nonstandard supersymmetry-breaking terms, including Dirac gaugino masses, arise from F-term breaking mediated by operators with a 1/M3 suppression. In these models, the supersoft properties found in the case of D-term breaking are absent in general, but can be obtained as a special case that is a fixed point of the renormalization group equations. The μ term is replaced by three distinct supersymmetry-breaking parameters, decoupling the Higgs scalar potential from the Higgsino masses. Both holomorphic and nonholomorphic scalar cubic interactions with minimal flavor violation are induced in the supersymmetric Standard Model Lagrangian.

  8. DIRAC optimized workload management

    CERN Document Server

    Paterson, S K

    2008-01-01

    The LHCb DIRAC Workload and Data Management System employs advanced optimization techniques in order to dynamically allocate resources. The paradigms realized by DIRAC, such as late binding through the Pilot Agent approach, have proven to be highly successful. For example, this has allowed the principles of workload management to be applied not only at the time of user job submission to the Grid but also to optimize the use of computing resources once jobs have been acquired. Along with the central application of job priorities, DIRAC minimizes the system response time for high priority tasks. This paper will describe the recent developments to support Monte Carlo simulation, data processing and distributed user analysis in a consistent way across disparate compute resources including individual PCs, local batch systems, and the Worldwide LHC Computing Grid. The Grid environment is inherently unpredictable and whilst short-term studies have proven to deliver high job efficiencies, the system performance over ...

  9. Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations

    KAUST Repository

    Lorz, Alexander; Mirrahimi, Sepideh; Perthame, Benoî t

    2011-01-01

    simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.

  10. Quantum Hall effect of massless Dirac fermions and free fermions in Hofstadter's butterfly

    International Nuclear Information System (INIS)

    Yoshioka, Nobuyuki; Matsuura, Hiroyasu; Ogata, Masao

    2016-01-01

    We propose a new physical interpretation of the Diophantine equation of σ xy for the Hofstadter problem. First, we divide the energy spectrum, or Hofstadter's butterfly, into smaller self-similar areas called 'subcells', which were first introduced by Hofstadter to describe the recursive structure. We find that in the energy gaps between subcells, there are two ways to account for the quantization rule of σ xy , that are consistent with the Diophantine equation: Landau quantization of (1) massless Dirac fermions or (2) free fermions in Hofstadter's butterfly. (author)

  11. A hierarchy of systems of nonlinear equations

    International Nuclear Information System (INIS)

    Falkensteiner, P.; Grosse, H.

    1985-01-01

    Imposing isospectral invariance for the one-dimensional Dirac operator yields an infinite hierarchy of systems of chiral invariant nonlinear partial differential equations. The same system is obtained through a Lax pair construction and finally a formulation in terms of Kac-Moody generators is given. (Author)

  12. Moving potential for Dirac and Klein–Gordon equations

    Indian Academy of Sciences (India)

    and according to our knowledge the mathematical treatment of relativistic ..... the equation with step + Coulomb is soluble in principle, the time-dependent term ... and A R Hibbs, Quantum mechanics and path integrals (McGraw Hill, New.

  13. Identifying Dirac cones in carbon allotropes with square symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Jinying [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); Huang, Huaqing; Duan, Wenhui [Department of Physics, Tsinghua University, Beijing 100084 (China); Liu, Zhirong, E-mail: LiuZhiRong@pku.edu.cn [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); State Key Laboratory for Structural Chemistry of Unstable and Stable Species and Beijing National Laboratory for Molecular Sciences (BNLMS), Peking University, Beijing 100871 (China)

    2013-11-14

    A theoretical study is conducted to search for Dirac cones in two-dimensional carbon allotropes with square symmetry. By enumerating the carbon atoms in a unit cell up to 12, an allotrope with octatomic rings is recognized to possess Dirac cones under a simple tight-binding approach. The obtained Dirac cones are accompanied by flat bands at the Fermi level, and the resulting massless Dirac-Weyl fermions are chiral particles with a pseudospin of S = 1, rather than the conventional S = 1/2 of graphene. The spin-1 Dirac cones are also predicted to exist in hexagonal graphene antidot lattices.

  14. Symanzik approach in modeling of bound states of Dirac particle in singular background

    Directory of Open Access Journals (Sweden)

    Pismak Yu. M.

    2017-01-01

    Full Text Available In the model of interaction of spinor field with homogeneous isotropic material plane constructed in framework of Symanzik approach, the bound states are studied. For localized near plane Dirac particle the expression for current, charge and density are presented. For bound state with massless dispersion law the current, charge and density are calculated for simplified model with 2 parameter exactly.The model can find application to a wide class of phenomena arising by the interaction of fields of quantum electrodynamics with two-dimensional materials.

  15. Split Dirac cones in HgTe/CdTe quantum wells due to symmetry-enforced level anticrossing at interfaces

    Science.gov (United States)

    Tarasenko, S. A.; Durnev, M. V.; Nestoklon, M. O.; Ivchenko, E. L.; Luo, Jun-Wei; Zunger, Alex

    2015-02-01

    HgTe is a band-inverted compound which forms a two-dimensional topological insulator if sandwiched between CdTe barriers for a HgTe layer thickness above the critical value. We describe the fine structure of Dirac states in the HgTe/CdTe quantum wells of critical and close-to-critical thicknesses and show that the necessary creation of interfaces brings in another important physical effect: the opening of a significant anticrossing gap between the tips of the Dirac cones. The level repulsion driven by the natural interface inversion asymmetry of zinc-blende heterostructures considerably modifies the electron states and dispersion but preserves the topological transition at the critical thickness. By combining symmetry analysis, atomistic calculations, and extended k .p theory with interface terms, we obtain a quantitative description of the energy spectrum and extract the interface mixing coefficient. We discuss how the fingerprints of the predicted zero-magnetic-field splitting of the Dirac cones could be detected experimentally by studying magnetotransport phenomena, cyclotron resonance, Raman scattering, and THz radiation absorption.

  16. Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene

    OpenAIRE

    Oettinger, D.; Mendoza, M.; Herrmann, H. J.

    2013-01-01

    We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in m...

  17. Influence of the dispersive and dissipative scales alpha and beta on the energy spectrum of the Navier-Stokes alphabeta equations.

    Science.gov (United States)

    Chen, Xuemei; Fried, Eliot

    2008-10-01

    Lundgren's vortex model for the intermittent fine structure of high-Reynolds-number turbulence is applied to the Navier-Stokes alphabeta equations and specialized to the Navier-Stokes alpha equations. The Navier-Stokes alphabeta equations involve dispersive and dissipative length scales alpha and beta, respectively. Setting beta equal to alpha reduces the Navier-Stokes alphabeta equations to the Navier-Stokes alpha equations. For the Navier-Stokes alpha equations, the energy spectrum is found to obey Kolmogorov's -5/3 law in a range of wave numbers identical to that determined by Lundgren for the Navier-Stokes equations. For the Navier-Stokes alphabeta equations, Kolmogorov's -5/3 law is also recovered. However, granted that beta Navier-Stokes alphabeta equations may have the potential to resolve features smaller than those obtainable using the Navier-Stokes alpha equations.

  18. Dirac experiment

    Energy Technology Data Exchange (ETDEWEB)

    Gomez, F.; Adeva, B.; Afanasev, L.; Benayoun, M.; Brekhovskikh, V.; Caragheorgheopol, G.; Cechak, T.; Chiba, M.; Constantinescu, S.; Doudarev, A.; Dreossi, D.; Drijard, D.; Ferro-Luzzi, M.; Gallas, M.V.; Gerndt, J.; Giacomich, R.; Gianotti, P.; Goldin, D.; Gorin, A.; Gortchakov, O.; Guaraldo, C.; Hansroul, M.; Hosek, R.; Iliescu, M.; Jabitski, M.; Kalinina, N.; Karpoukhine, V.; Kluson, J.; Kobayashi, M.; Kokkas, P.; Komarov, V.; Koulikov, A.; Kouptsov, A.; Krouglov, V.; Krouglova, L.; Kuroda, K.-I.; Lanaro, A.; Lapshine, V.; Lednicky, R.; Leruste, P.; Levisandri, P.; Lopez Aguera, A.; Lucherini, V.; Maki, T.; Manuilov, I.; Montanet, L.; Narjoux, J.-L.; Nemenov, L.; Nikitin, M.; Nunez Pardo, T.; Okada, K.; Olchevskii, V.; Pazos, A.; Pentia, M.; Penzo, A.; Perreau, J.-M.; Petrascu, C.; Plo, M.; Ponta, T.; Pop, D.; Riazantsev, A.; Rodriguez, J.M.; Rodriguez Fernandez, A.; Rykaline, V.; Santamarina, C.; Saborido, J.; Schacher, J.; Sidorov, A.; Smolik, J.; Takeutchi, F.; Tarasov, A.; Tauscher, L.; Tobar, M.J.; Trusov, S.; Vazquez, P.; Vlachos, S.; Yazkov, V.; Yoshimura, Y.; Zrelov, P

    2001-04-01

    The main objective of DIRAC experiment is the measurement of the lifetime {tau} of the exotic hadronic atom consisting of {pi}{sup +} and {pi}{sup -} mesons. The lifetime of this atom is determined by the decay mode {pi}{sup +} {pi}{sup -} {yields} {pi}{sup 0} {pi}{sup 0} due to the strong interaction. Through the precise relationship between the lifetime and the S-wave pion-pion scattering length difference |a{sub 0} - a{sub 2}| for isospin 0 and 2 (respectively), a measurement of {tau} with an accuracy of 10% will allow a determination of |a{sub 0} - a{sub 2}| at a 5% precision level. Pion-pion scattering lengths have been calculated in the framework of chiral perturbation theory with an accuracy below 5%. In this way DIRAC experiment will provide a crucial test of the chiral symmetry breaking scheme in QCD effective theories at low energies.

  19. Quasiparticle dynamics in reshaped helical Dirac cone of topological insulators.

    Science.gov (United States)

    Miao, Lin; Wang, Z F; Ming, Wenmei; Yao, Meng-Yu; Wang, Meixiao; Yang, Fang; Song, Y R; Zhu, Fengfeng; Fedorov, Alexei V; Sun, Z; Gao, C L; Liu, Canhua; Xue, Qi-Kun; Liu, Chao-Xing; Liu, Feng; Qian, Dong; Jia, Jin-Feng

    2013-02-19

    Topological insulators and graphene present two unique classes of materials, which are characterized by spin-polarized (helical) and nonpolarized Dirac cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in topological insulators. Here, we report the experimental observation of the renormalized quasiparticle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi(2)Te(3) substrate from angle-resolved photoemission spectroscopy. First-principles band calculations indicate that the quasiparticle spectra are likely associated with the hybridization between the extrinsic substrate-induced Dirac states of Bi bilayer and the intrinsic surface Dirac states of Bi(2)Te(3) film at close energy proximity. Without such hybridization, only single-particle Dirac spectra are observed in a single Bi bilayer grown on Bi(2)Se(3), where the extrinsic Dirac states Bi bilayer and the intrinsic Dirac states of Bi(2)Se(3) are well separated in energy. The possible origins of many-body interactions are discussed. Our findings provide a means to manipulate topological surface states.

  20. Topology-optimized dual-polarization Dirac cones

    Science.gov (United States)

    Lin, Zin; Christakis, Lysander; Li, Yang; Mazur, Eric; Rodriguez, Alejandro W.; Lončar, Marko

    2018-02-01

    We apply a large-scale computational technique, known as topology optimization, to the inverse design of photonic Dirac cones. In particular, we report on a variety of photonic crystal geometries, realizable in simple isotropic dielectric materials, which exhibit dual-polarization Dirac cones. We present photonic crystals of different symmetry types, such as fourfold and sixfold rotational symmetries, with Dirac cones at different points within the Brillouin zone. The demonstrated and related optimization techniques open avenues to band-structure engineering and manipulating the propagation of light in periodic media, with possible applications to exotic optical phenomena such as effective zero-index media and topological photonics.

  1. Role of four-fermion interaction and impurity in the states of two-dimensional semi-Dirac materials.

    Science.gov (United States)

    Wang, Jing

    2018-03-28

    We study the effects of four-fermion interaction and impurity on the low-energy states of 2D semi-Dirac materials by virtue of the unbiased renormalization group approach. The coupled flow equations that govern the energy-dependent evolutions of all correlated interaction parameters are derived after taking into account one-loop corrections from the interplay between four-fermion interaction and impurity. Whether and how four-fermion interaction and impurity influence the low-energy properties of 2D semi-Dirac materials are discreetly explored and addressed attentively. After carrying out the standard renormalization group analysis, we find that both trivial insulating and nontrivial semimetal states are qualitatively stable against all four kinds of four-fermion interactions. However, while switching on both four-fermion interaction and impurity, certain insulator-semimetal phase transitions and the distance of Dirac nodal points can be respectively induced and modified due to their strong interplay and intimate competition. Moreover, several non-Fermi liquid behaviors that deviate from the conventional Fermi liquids are exhibited at the lowest-energy limit.

  2. Spin and pseudospin symmetric Dirac particles in the field of Tietz—Hua potential including Coulomb tensor interaction

    International Nuclear Information System (INIS)

    Ikhdair, Sameer M.; Hamzavi, Majid

    2013-01-01

    Approximate analytical solutions of the Dirac equation for Tietz—Hua (TH) potential including Coulomb-like tensor (CLT) potential with arbitrary spin—orbit quantum number κ are obtained within the Pekeris approximation scheme to deal with the spin—orbit coupling terms κ(κ ± 1)r −2 . Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov—Uvarov (NU) method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated. (general)

  3. All-Metallic Vertical Transistors Based on Stacked Dirac Materials

    OpenAIRE

    Wang, Yangyang; Ni, Zeyuan; Liu, Qihang; Quhe, Ruge; Zheng, Jiaxin; Ye, Meng; Yu, Dapeng; Shi, Junjie; Yang, Jinbo; Lu, Jing

    2014-01-01

    It is an ongoing pursuit to use metal as a channel material in a field effect transistor. All metallic transistor can be fabricated from pristine semimetallic Dirac materials (such as graphene, silicene, and germanene), but the on/off current ratio is very low. In a vertical heterostructure composed by two Dirac materials, the Dirac cones of the two materials survive the weak interlayer van der Waals interaction based on density functional theory method, and electron transport from the Dirac ...

  4. Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

    Science.gov (United States)

    Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

    2018-06-01

    The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

  5. Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion

    Science.gov (United States)

    Parra-Rivas, P.; Gomila, D.; Gelens, L.; Knobloch, E.

    2018-04-01

    The origin, stability, and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation are studied. This mean field model describes the nonlinear dynamics of light circulating in fiber cavities and microresonators. In the case of anomalous group velocity dispersion and low values of the intracavity phase detuning these bright states are organized in a homoclinic snaking bifurcation structure. We describe how this bifurcation structure is destroyed when the detuning is increased across a critical value, and determine how a bifurcation structure known as foliated snaking emerges.

  6. Kondo effect in three-dimensional Dirac and Weyl systems

    NARCIS (Netherlands)

    Mitchell, Andrew K.; Fritz, Lars

    2015-01-01

    Magnetic impurities in three-dimensional Dirac and Weyl systems are shown to exhibit a fascinatingly diverse range of Kondo physics, with distinctive experimental spectroscopic signatures. When the Fermi level is precisely at the Dirac point, Dirac semimetals are in fact unlikely candidates for a

  7. Nonlinear quantum fluid equations for a finite temperature Fermi plasma

    International Nuclear Information System (INIS)

    Eliasson, Bengt; Shukla, Padma K

    2008-01-01

    Nonlinear quantum electron fluid equations are derived, taking into account the moments of the Wigner equation and by using the Fermi-Dirac equilibrium distribution for electrons with an arbitrary temperature. A simplified formalism with the assumptions of incompressibility of the distribution function is used to close the moments in velocity space. The nonlinear quantum diffraction effects into the fluid equations are incorporated. In the high-temperature limit, we retain the nonlinear fluid equations for a dense hot plasma and in the low-temperature limit, we retain the correct fluid equations for a fully degenerate plasma

  8. Quantum-statistical kinetic equations

    International Nuclear Information System (INIS)

    Loss, D.; Schoeller, H.

    1989-01-01

    Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, the authors derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors, P q -rule, etc.) to nonequilibrium systems described by a density operator ρ(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived

  9. Realization of non-symmorphic Dirac cones in PbFCl materials

    Science.gov (United States)

    Schoop, Leslie

    While most 3D Dirac semimetals require two bands with different orbital character to be protected, there is also the possibility to find 3D Dirac semimetals that are guaranteed to exist in certain space groups. Those are resulting from the non-symmoprhic symmetry of the space group, which forces the bands to degenerate at high symmetry points in the Brillouin zone. Non-symmorphic space groups can force three- four, six and eight fold degeneracies which led to the proposal to find 3D Dirac Semimetals as well as new quasiparticles in such space groups. Problematic for realizing this types of Dirac materials is that they require and odd band filling in order to have the Fermi level located at or also near by the band crossing points. Therefore, although the first prediction for using non-symmoprhic symmetry to create a Dirac material was made in 2012, it took almost four years for an experimental verification of this type of Dirac crossing. In this talk I will introduce the material ZrSiS that has, besides other Dirac features, a Dirac cone protected by non-symmorphic symmetry at about 0.5 eV below the Fermi level and was the first material where this type of Dirac cone was imaged with ARPES. I will then proceed to discuss ways to shift this crossing to the Fermi edge and finally show an experimental verification of a fourfold Dirac crossing, protected by non-symmorphic symmetry, at the Fermi energy.

  10. Dynamical Symmetries of Two-Dimensional Dirac Equation with Screened Coulomb and Isotropic Harmonic Oscillator Potentials

    International Nuclear Information System (INIS)

    Wang Qing; Hou Yu-Long; Jing Jian; Long Zheng-Wen

    2014-01-01

    In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed. (general)

  11. Anisotropic Fermi Surface and Quantum Limit Transport in High Mobility Three-Dimensional Dirac Semimetal Cd_{3}As_{2}

    Directory of Open Access Journals (Sweden)

    Yanfei Zhao

    2015-09-01

    Full Text Available Three-dimensional topological Dirac semimetals have a linear dispersion in 3D momentum space and are viewed as the 3D analogues of graphene. Here, we report angle-dependent magnetotransport on the newly revealed Cd_{3}As_{2} single crystals and clearly show how the Fermi surface evolves with crystallographic orientations. Remarkably, when the magnetic field lies in the [112] or [441[over ¯

  12. Spectrum of the Wilson Dirac operator at finite lattice spacings

    DEFF Research Database (Denmark)

    Akemann, G.; Damgaard, Poul Henrik; Splittorff, Kim

    2011-01-01

    We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator...... as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral Random Matrix Theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral Perturbation Theory. All results are obtained for fixed index...... of the Wilson Dirac operator. The low-energy constants of Wilson chiral Perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac operator....

  13. Asymptotic profile of global solutions to the generalized double dispersion equation via the nonlinear term

    Science.gov (United States)

    Wang, Yu-Zhu; Wei, Changhua

    2018-04-01

    In this paper, we investigate the initial value problem for the generalized double dispersion equation in R^n. Weighted decay estimate and asymptotic profile of global solutions are established for n≥3 . The global existence result was already proved by Kawashima and the first author in Kawashima and Wang (Anal Appl 13:233-254, 2015). Here, we show that the nonlinear term plays an important role in this asymptotic profile.

  14. Role of various Dirac covariants in the BS wave functions in decay constant calculations of pseudoscalar mesons using a power counting scheme

    International Nuclear Information System (INIS)

    Bhatnagar, S.; Mahecha, J.

    2008-09-01

    We have employed the framework of Bethe-Salpeter equation under Covariant Instantaneous Ansatz to calculate the leptonic decay constants of unequal mass pseudoscalar mesons. In the Dirac structure of BS wave function, the covariants are incorporated from their complete set in accordance with a recently proposed power counting rule, order-by-order in powers of inverse of meson mass. The decay constants are calculated incorporating both Leading Order (LO) as well as Next-to-leading Order (NLO) Dirac covariants. The contribution of both LO as well as NLO covariants to decay constants are studied in detail in this paper. The results are found to improve dramatically, and hence validating the power counting rule which also provides a practical means of incorporating Dirac covariants in the BS wave function of a hadron. (author)

  15. Graphene Dirac point tuned by ferroelectric polarization field

    Science.gov (United States)

    Wang, Xudong; Chen, Yan; Wu, Guangjian; Wang, Jianlu; Tian, Bobo; Sun, Shuo; Shen, Hong; Lin, Tie; Hu, Weida; Kang, Tingting; Tang, Minghua; Xiao, Yongguang; Sun, Jinglan; Meng, Xiangjian; Chu, Junhao

    2018-04-01

    Graphene has received numerous attention for future nanoelectronics and optoelectronics. The Dirac point is a key parameter of graphene that provides information about its carrier properties. There are lots of methods to tune the Dirac point of graphene, such as chemical doping, impurities, defects, and disorder. In this study, we report a different approach to tune the Dirac point of graphene using a ferroelectric polarization field. The Dirac point can be adjusted to near the ferroelectric coercive voltage regardless its original position. We have ensured this phenomenon by temperature-dependent experiments, and analyzed its mechanism with the theory of impurity correlation in graphene. Additionally, with the modulation of ferroelectric polymer, the current on/off ratio and mobility of graphene transistor both have been improved. This work provides an effective method to tune the Dirac point of graphene, which can be readily used to configure functional devices such as p-n junctions and inverters.

  16. Saha's ionization equation for high Z elements

    International Nuclear Information System (INIS)

    Godwal, B.K.; Sikka, S.K.

    1977-01-01

    Saha's ionization equation has been solved for high Z elements with the aim of providing input for opacity calculations. Results are presented for two elements, tungsten and uranium. The ionization potentials have been evaluated using the simple Bhor's formula with suitable effective charges for ions. The reliability of the free electron density, ion concentrations, etc., obtained from the Saha's equation solutions has been checked by comparing the P and E computed from them with those given by the Thomas-Fermi-Dirac equation of state. The agreement between the two is good from temperatures above 0.2 keV. (author)

  17. Quantum effects from topological conditions in solutions of Einstein equations

    CERN Document Server

    Patiño, L

    2003-01-01

    In this paper it is shown that Dirac's approach to the quantization of the electric charge can be extended to gravitational configurations by defining a phase-like object related to the curvature of the space-time. Using this phase-like object, Dirac's argument is applied to the Kerr-Newmann and the Taub-NUT solutions to Einstein equations. As a result of this procedure we obtain that certain functions of the parameters entering the metric become quantized. Also, the phase acquired by an observer traveling along a loop around a curvature singularity is quantized. (Author)

  18. Einstein-Dirac theory in spin maximum I

    International Nuclear Information System (INIS)

    Crumeyrolle, A.

    1975-01-01

    An unitary Einstein-Dirac theory, first in spin maximum 1, is constructed. An original feature of this article is that it is written without any tetrapod technics; basic notions and existence conditions for spinor structures on pseudo-Riemannian fibre bundles are only used. A coupling gravitation-electromagnetic field is pointed out, in the geometric setting of the tangent bundle over space-time. Generalized Maxwell equations for inductive media in presence of gravitational field are obtained. Enlarged Einstein-Schroedinger theory, gives a particular case of this E.D. theory. E. S. theory is a truncated E.D. theory in spin maximum 1. A close relation between torsion-vector and Schroedinger's potential exists and nullity of torsion-vector has a spinor meaning. Finally the Petiau-Duffin-Kemmer theory is incorporated in this geometric setting [fr

  19. The NO-pair equation---Fundamental problems, numerical solutions and applications

    International Nuclear Information System (INIS)

    Martensson-Pendrill, A.

    1989-01-01

    The solution of inhomogeneous two-particle differential equations is a powerful method for treating correlation effects in the non-relativistic case and is reviewed briefly. The relativistic generalization, the so-called Dirac-Coulomb equation, is complicated by the need to distinguish between positive and negative energy states. The construction and use of projection operators onto positive energy states are presented and the application of the pair equation to other properties such as parity non-conservation is discussed

  20. Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type

    Science.gov (United States)

    El, G. A.; Nguyen, L. T. K.; Smyth, N. F.

    2018-04-01

    We develop a general approach to the description of dispersive shock waves (DSWs) for a class of nonlinear wave equations with a nonlocal Benjamin-Ono type dispersion term involving the Hilbert transform. Integrability of the governing equation is not a pre-requisite for the application of this method which represents a modification of the DSW fitting method previously developed for dispersive-hydrodynamic systems of Korteweg-de Vries (KdV) type (i.e. reducible to the KdV equation in the weakly nonlinear, long wave, unidirectional approximation). The developed method is applied to the Calogero-Sutherland dispersive hydrodynamics for which the classification of all solution types arising from the Riemann step problem is constructed and the key physical parameters (DSW edge speeds, lead soliton amplitude, intermediate shelf level) of all but one solution type are obtained in terms of the initial step data. The analytical results are shown to be in excellent agreement with results of direct numerical simulations.