Dirac equation in a de Sitter expansion for massive neutrinos from modern Kaluza-Klein theory
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.
On Charge Conjugation, Chirality and Helicity of the Dirac and Majorana Equation for Massive Leptons
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.
Dirac equation for massive neutrinos in a Schwarzschild-de Sitter spacetime from a 5D vacuum
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.
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.
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
Alternatives to the Dirac equation
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
The Dirac equation for accountants
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
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)
Dispersive estimates for massive Dirac operators in dimension two
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.
Rigid particle revisited: Extrinsic curvature yields the Dirac equation
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.
New solitons connected to the Dirac equation
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)
A fractional Dirac equation and its solution
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.
The Dirac equation in classical statistical mechanics
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
The Dirac equation and its solutions
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.
The Dirac equation and its solutions
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.
The Dirac equation and its solutions
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.
New exact solutions of the Dirac equation
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
Scalar potentials and the Dirac equation
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.)
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].
SU(4) proprerties of the Dirac equation
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
New symmetries for the Dirac equation
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
Solvable linear potentials in the Dirac equation
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
Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
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)
Dirac equation on a curved surface
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.
Dirac equation in magnetic-solenoid field
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.)
SU(4) properties of the Dirac equation
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
Probabilistic solution of the Dirac equation
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.)
Dirac equations for generalised Yang-Mills systems
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.)
New exact solutions of the Dirac equation. 8
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
Dirac equation in Kerr space-time
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.
Relativistic space-charge-limited current for massive Dirac fermions
Ang, Y. S.; Zubair, M.; Ang, L. K.
2017-04-01
A theory of relativistic space-charge-limited current (SCLC) is formulated to determine the SCLC scaling, J ∝Vα/Lβ , for a finite band-gap Dirac material of length L biased under a voltage V . In one-dimensional (1D) bulk geometry, our model allows (α ,β ) to vary from (2,3) for the nonrelativistic model in traditional solids to (3/2,2) for the ultrarelativistic model of massless Dirac fermions. For 2D thin-film geometry we obtain α =β , which varies between 2 and 3/2, respectively, at the nonrelativistic and ultrarelativistic limits. We further provide rigorous proof based on a Green's-function approach that for a uniform SCLC model described by carrier-density-dependent mobility, the scaling relations of the 1D bulk model can be directly mapped into the case of 2D thin film for any contact geometries. Our simplified approach provides a convenient tool to obtain the 2D thin-film SCLC scaling relations without the need of explicitly solving the complicated 2D problems. Finally, this work clarifies the inconsistency in using the traditional SCLC models to explain the experimental measurement of a 2D Dirac semiconductor. We conclude that the voltage scaling 3 /2 <α <2 is a distinct signature of massive Dirac fermions in a Dirac semiconductor and is in agreement with experimental SCLC measurements in MoS2.
New experimental proposals for testing Dirac equation
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
Wave Functions for Time-Dependent Dirac Equation under GUP
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
Special function solutions of the free particle Dirac equation
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)
Electronic structure of a graphene superlattice with massive Dirac fermions
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
Multi-component bi-Hamiltonian Dirac integrable equations
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.
Relativistic Spinning Particle without Grassmann Variables and the Dirac Equation
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.
Remarks about singular solutions to the Dirac equation
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
Topological insulators Dirac equation in condensed matter
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...
Topological Insulators Dirac Equation in Condensed Matters
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...
Dirac's equation and the nature of quantum field theory
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.
Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations
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.
The Lorentz-Dirac equation in light of quantum theory
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
Invariance properties of the Dirac equation with external electro ...
. 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 ...
The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
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)
The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
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)].
The Dirac equation in the Lobachevsky space-time
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
Collective modes of massive Dirac fermions in armchair graphene nanoribbons
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.
New exact solutions of the Dirac equation. 11
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
Dirac equation in low dimensions: The factorization method
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.
From a world-sheet supersymmetry to the Dirac equation
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
Relativistic Photoionization Computations with the Time Dependent Dirac Equation
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
Maxwell-Like Equations for Free Dirac Electrons
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").
Ziino, G.
1989-01-01
We assume a strictly invariant definition of the Dirac parity operator under fermion ↔ antifermion exchange. We see that the opposite-intrinsic-parity condition then requires two opposite-mass Dirac equations for the fermion and the antifermion. This leads us to introduce an asymptotically left-handed (fermion) and right-handed (antifermion) chiral field, as just an alternative basis in the internal space spanned by the new pair of charge-conjugate Dirac fields. Hence a dual intrinsic model of a spin - 1/2 massive fermion is drawn: it predicts the coexistence of two anticommuting general varieties of conserved charges, namely a scalar variety, responsible for parity-invariant phenomenology, plus a pseudoscalar one, responsible for chiral phenomenology. In this light, CP-symmetry is seen to be nothing but P-symmetry; and a spontaneous CP-violation mechanism is also derived, that should work in any single process occurring via both scalar-and pseudoscalar-charge interactions. We show, at last, that our scheme automatically yields Weyl's one for a merely left-handed neutrino and a merely right-handed antineutrino, further assigning them the special meaning of pure pseudoscalar-charge objects. Some general consequences as regards magnetic monopoles are briefly discussed too
Inverse scattering scheme for the Dirac equation at fixed energy
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)
General method for reducing the two-body Dirac equation
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)
Dirac equation and optical wave propagation in one dimension
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)
New correct solutions of the Dirac equation. 5
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
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
Spinors, tensors and the covariant form of Dirac's equation
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)
A rational interpretation of the Dirac equation for the electron
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)
Survey on Dirac equation in general relativity theory
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
On the solution of the Dirac equation in de Sitter space
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
Algebraic solution for the vector potential in the Dirac equation
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)
Remarks on a five-dimensional Kaluza-Klein theory of the massive Dirac monopole
Cotaescu, Ion I.
2005-01-01
The Gross-Perry-Sorkin spacetime, formed by the Euclidean Taub-Newman-Unti-Tamburino space with the time trivially added, is the appropriate background of the Dirac magnetic monopole without an explicit mass term. We show that there exists a very simple five-dimensional metric of spacetimes carrying massive magnetic monopoles that is an exact solution of the vacuum Einstein equations. Moreover, the same isometry properties as the original Euclidean Taub-Newman-Unti-Tamburino space are preserved. This leads to an Abelian Kaluza-Klein theory whose metric appears as a combination between the Gross-Perry-Sorkin and Schwarzschild ones. The asymptotic motion of the scalar charged test particles is discussed, now by accounting for the mixing between the gravitational and magnetic effects
New and old symmetries of the Maxwell and Dirac equations
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
Particlelike solutions of the Einstein-Dirac equations
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.
On new and old symmetries of Maxwell and Dirac equations
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
P A M Dirac meets M G Krein: matrix orthogonal polynomials and Dirac's equation
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
Spectral correlations of the massive QCD Dirac operator at finite temperature
Seif, Burkhard; Wettig, Tilo; Guhr, Thomas
1999-01-01
We use the graded eigenvalue method, a variant of the supersymmetry technique, to compute the universal spectral correlations of the QCD Dirac operator in the presence of massive dynamical quarks. The calculation is done for the chiral Gaussian unitary ensemble of random matrix theory with an arbitrary Hermitian matrix added to the Dirac matrix. This case is of interest for schematic models of OCD at finite temperature
Yu Yafei, E-mail: yfyuks@hotmail.com [Laboratory of Nanophotonic Functional Materials and Devices, LQIT and SIPSE, South China Normal University, Guangzhou 510006 (China); Shan Chuanjia [Laboratory of Nanophotonic Functional Materials and Devices, LQIT and SIPSE, South China Normal University, Guangzhou 510006 (China); College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002 (China); Mei Feng; Zhang Zhiming [Laboratory of Nanophotonic Functional Materials and Devices, LQIT and SIPSE, South China Normal University, Guangzhou 510006 (China)
2012-09-15
We propose a simple but feasible experimental scheme to simulate and detect Dirac fermions with cold atoms trapped in one-dimensional optical lattice. In our scheme, through tuning the laser intensity, the one-dimensional optical lattice can have two sites in each unit cell and the atoms around the low energy behave as massive Dirac fermions. Furthermore, we show that these relativistic quasiparticles can be detected experimentally by using atomic density profile measurements and Bragg scattering.
An asymptotic formula for Weyl solutions of the dirac equations
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
How (not) to teach Lorentz covariance of the Dirac equation
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)
Dirac equation in noncommutative space for hydrogen atom
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.
Dirac equation in noncommutative space for hydrogen atom
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.
Two-body Dirac equations for nucleon-nucleon scattering
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
Noncommutativity into Dirac Equation with mass dependent on the position
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)
The Schroedinger and Dirac free particle equations without quantum mechanics
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
The square root of the Dirac operator on superspace and the Maxwell equations
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
The square root of the Dirac operator on superspace and the Maxwell equations
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.
The square root of the Dirac operator on the superspace and the Maxwell equations
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.
The square root of the Dirac operator on superspace and the Maxwell equations
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.
Approximate Treatment of the Dirac Equation with Hyperbolic Potential Function
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.
The supersymmetric Dirac equation the application to hydrogenic atoms
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.
A novel quantum-mechanical interpretation of the Dirac equation
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.
Considerations concering the generalization of the Dirac equations to unstable fermions
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.
Difference equations in massive higher order calculations
Bierenbaum, I.; Bluemlein, J.; Klein, S.; Schneider, C.
2007-07-01
The calculation of massive 2-loop operator matrix elements, required for the higher order Wilson coefficients for heavy flavor production in deeply inelastic scattering, leads to new types of multiple infinite sums over harmonic sums and related functions, which depend on the Mellin parameter N. We report on the solution of these sums through higher order difference equations using the summation package Sigma. (orig.)
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)
Analytical solutions for Dirac and Klein-Gordon equations using Backlund transformations
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)
Coexistence of Dirac and massive carriers in α-(BEDT-TTF){sub 2}I{sub 3} under hydrostatic pressure
Navarin, Fabien; Tisserond, Emilie [Laboratoire de Physique des Solides, UMR 8502, CNRS-Université Paris-Sud, Orsay F-91405 (France); Auban-Senzier, Pascale, E-mail: pascale.senzier@u-psud.fr [Laboratoire de Physique des Solides, UMR 8502, CNRS-Université Paris-Sud, Orsay F-91405 (France); Mézière, Cécile; Batail, Patrick [MOLTECH-Anjou, UMR 6200, CNRS-Université d' Angers, Bat. K, Angers F-49045 (France); Pasquier, Claude; Monteverde, Miguel [Laboratoire de Physique des Solides, UMR 8502, CNRS-Université Paris-Sud, Orsay F-91405 (France)
2015-03-01
We present magnetotransport measurements of α-(BEDT-TTF){sub 2}I{sub 3} crystals under hydrostatic pressure larger than 1.5 GPa where Dirac carriers are present. We show not only the existence of high-mobility Dirac carriers but we also prove experimentally the presence of low-mobility massive carriers, in agreement with band-structure calculations.
The nonlinear Dirac equation and the study of effective many-particle interactions in QED
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
Quantum effects of a massive 3-form coupled to a Dirac field
Aurilia, Antonio; Spallucci, Euro
2004-01-01
The computation of the quantum vacuum pressure must take into account the contribution of zero-point oscillations of a rank-three gauge field A μνρ . This result was established in a previous paper where we calculated both the Casimir pressure within a region of vacuum simulating a hadronic bag and the Wilson factor for the three-index potential associated with the boundary of the bag. The resulting 'volume law' satisfied by the Wilson loop is consistent with the basic confining requirement that the static interquark potential increases with the distance between two test charges. As a sequel to that paper, we consider here the coupling of A μνρ to the generic current of a matter field, later identified with the spin density current of a Dirac field. In fact, one of the objectives of this paper is to investigate the impact of the quantum fluctuations of A μνρ on the effective dynamics of the spinor field. The consistency of the field equations, even at the classical level, requires the introduction of a mass term for A μνρ . In this case, the Casimir vacuum pressure includes a contribution that is explicitly dependent on the mass of A μνρ and leads us to conclude that the mass term plays the same role as the infrared cutoff needed to regularize the finite volume partition functional previously calculated in the massless case. Remarkably, even in the presence of a mass term, A μνρ contains a mixture of massless and massive spin-0 fields so that the resulting equation is still gauge invariant. This is yet another peculiar, but physically relevant property of A μνρ since it is reflected in the effective dynamics of the spinor fields and confirms the confining property of A μνρ already expected from the earlier calculation of the Wilson loop
Quantum mechanics of Yano tensors: Dirac equation in curved spacetime
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
Dirac equation in very special relativity for hydrogen atom
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.
Numerical implementation of the Dirac equation on hypercube multicomputers
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
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.
An integrodifferential Dirac equation with quantized charge in one space dimension
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.)
Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations
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
Covariant differential calculus on quantum Minkowski space and the q-analogue of Dirac equation
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.)
Imaginary Time Step Method to Solve the Dirac Equation with Nonlocal Potential
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.
Massively Parallel Algorithms for Solution of Schrodinger Equation
Fijany, Amir; Barhen, Jacob; Toomerian, Nikzad
1994-01-01
In this paper massively parallel algorithms for solution of Schrodinger equation are developed. Our results clearly indicate that the Crank-Nicolson method, in addition to its excellent numerical properties, is also highly suitable for massively parallel computation.
Exact solution of the N-dimensional generalized Dirac-Coulomb equation
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)
Basic quantum mechanics for three Dirac equations in a curved spacetime
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)
Relativistic two-body equation for one Dirac and one Duffin-Kemmer particle
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)
Simulation of Zitterbewegung by modelling the Dirac equation in Metamaterials
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-...
Relativistic quantum vorticity of the quadratic form of the Dirac equation
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)
P A M Dirac meets M G Krein: matrix orthogonal polynomials and Dirac's equation
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.
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)
Generalized Solutions of the Dirac Equation, W Bosons, and Beta Decay
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.
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
Dirac Equation in (1 +1 )-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model
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.
Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
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
Solution of the Lorentz-Dirac equation based on a new momentum expression
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)
Prolonged photo-carriers generated in a massive-and-anisotropic Dirac material.
Nurmamat, Munisa; Ishida, Yukiaki; Yori, Ryohei; Sumida, Kazuki; Zhu, Siyuan; Nakatake, Masashi; Ueda, Yoshifumi; Taniguchi, Masaki; Shin, Shik; Akahama, Yuichi; Kimura, Akio
2018-06-13
Transient electron-hole pairs generated in semiconductors can exhibit unconventional excitonic condensation. Anisotropy in the carrier mass is considered as the key to elongate the life time of the pairs, and hence to stabilize the condensation. Here we employ time- and angle-resolved photoemission spectroscopy to explore the dynamics of photo-generated carriers in black phosphorus. The electronic structure above the Fermi level has been successfully observed, and a massive-and-anisotropic Dirac-type dispersions are confirmed; more importantly, we directly observe that the photo-carriers generated across the direct band gap have the life time exceeding 400 ps. Our finding confirms that black phosphorus is a suitable platform for excitonic condensations, and also open an avenue for future applications in broadband mid-infrared BP-based optoelectronic devices.
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.
Expressing Solutions of the Dirac Equation in Terms of Feynman Path Integral
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...
Exact solutions of the Dirac equation with a Coulomb plus scalar potential in 2 + 1 dimensions
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)
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.
The Dirac-Kaehler equation and fermions on the lattice
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.)
The Dirac equation in external fields: Variable separation in Cartesian coordinates
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
Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics
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)
Su(4) properties of the Dirac-Kaehler equation
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)
Spin eigen-states of Dirac equation for quasi-two-dimensional electrons
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.
Bound states of the Dirac equation with some physical potentials by the Nikiforov-Uvarov method
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.
Overcritical PT-symmetric square well potential in the Dirac equation
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.
Interpretation of the evolution parameter of the Feynman parametrization of the Dirac equation
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.))
Exact solutions of time-dependent Dirac equations and the quantum-classical correspondence
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
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)
Spinor-electron wave guided modes in coupled quantum wells structures by solving the Dirac equation
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.
Particle-like solutions of the Einstein-Dirac-Maxwell equations
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.
Nuclear structure information studied through Dirac equation with deformed mean fields
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)
Generalized Lorentz-Dirac Equation for a Strongly Coupled Gauge Theory
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.
Generalized Lorentz-Dirac Equation for a Strongly Coupled Gauge Theory
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.
Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations
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.
Moving potential for Dirac and Klein–Gordon equations
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.
Fermion unification model based on the intrinsic SU(8 symmetry of a generalized Dirac equation
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.
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
Dirac equation of spin particles and tunneling radiation from a Kinnersly black hole
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.)
Application of a Lorentz transformation in six dimensions to an extension of dirac equation
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
Single-site Green function of the Dirac equation for full-potential electron scattering
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.)
Single-site Green function of the Dirac equation for full-potential electron scattering
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.)
Quasi-classical derivation of the Dirac and one-particle Schroedinger equations
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
A new approach to the I/N-expansion for the Dirac equation
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)
Path space measures for Dirac and Schroedinger equations: Nonstandard analytical approach
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
Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential
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.
Analytical solutions of the Dirac equation under Hellmann–Frost–Musulin potential
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.
Investigation of the Dirac Equation by Using the Conformable Fractional Derivative
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.
Spin-curvature interaction from curved Dirac equation: Application to single-wall carbon nanotubes
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.
Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays
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.
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.
Excited TBA equations I: Massive tricritical Ising model
Pearce, Paul A.; Chim, Leung; Ahn, Changrim
2001-01-01
We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator phi (cursive,open) Greek 1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A 4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m,n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r,s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters χ r,s (q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II
Meson spectra from two-body dirac equations with minimal interactions
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
Two-body Dirac equation and its wave function at the origin
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
Algebraic inversion of the Dirac equation for the vector potential in the non-Abelian case
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)
Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
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].
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.
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.
Exact Solution of Klein-Gordon and Dirac Equations with Snyder-de Sitter Algebra
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.
Dirac equation in 5- and 6-dimensional curved space-time manifolds
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
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)
D-Dimensional Dirac Equation for Energy-Dependent Pseudoharmonic and Mie-type Potentials via SUSYQM
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
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.
Some spectral properties of the one-dimensional disordered Dirac equation
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
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.
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.
On a model for baryons based on a Dirac equation with confining potentials
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
A CPT-even and Lorentz-Violating nonminimal coupling in the Dirac equation
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)
A CPT-even and Lorentz-Violating nonminimal coupling in the Dirac equation
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)
FFT-split-operator code for solving the Dirac equation in 2+1 dimensions
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
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.
Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis
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.
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.
Dirac, Weyl, Majorana, a review
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
Relativistic particle in a box: Klein-Gordon versus Dirac equations
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.
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)
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.
General solution of the Dirac equation for quasi-two-dimensional electrons
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.
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.)
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.
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.
Non-existence of black-hole solutions for the electroweak Einstein-Dirac-Yang/Mills equations
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
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...
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.
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.
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.
Landau-level spectroscopy of massive Dirac fermions in single-crystalline ZrTe5 thin flakes
Jiang, Y.; Dun, Z. L.; Zhou, H. D.; Lu, Z.; Chen, K.-W.; Moon, S.; Besara, T.; Siegrist, T. M.; Baumbach, R. E.; Smirnov, D.; Jiang, Z.
2017-07-01
We report infrared magnetospectroscopy studies on thin crystals of an emerging Dirac material ZrTe5 near the intrinsic limit. The observed structure of the Landau-level transitions and zero-field infrared absorption indicate a two-dimensional Dirac-like electronic structure, similar to that in graphene but with a small relativistic mass corresponding to a 9.4-meV energy gap. Measurements with circularly polarized light reveal a significant electron-hole asymmetry, which leads to splitting of the Landau-level transitions at high magnetic fields. Our model, based on the Bernevig-Hughes-Zhang effective Hamiltonian, quantitatively explains all observed transitions, determining the values of the Fermi velocity, Dirac mass (or gap), electron-hole asymmetry, and electron and hole g factors.
Bieniek, Maciej; Korkusiński, Marek; Szulakowska, Ludmiła; Potasz, Paweł; Ozfidan, Isil; Hawrylak, Paweł
2018-02-01
We present here the minimal tight-binding model for a single layer of transition metal dichalcogenides (TMDCs) MX 2(M , metal; X , chalcogen) which illuminates the physics and captures band nesting, massive Dirac fermions, and valley Landé and Zeeman magnetic field effects. TMDCs share the hexagonal lattice with graphene but their electronic bands require much more complex atomic orbitals. Using symmetry arguments, a minimal basis consisting of three metal d orbitals and three chalcogen dimer p orbitals is constructed. The tunneling matrix elements between nearest-neighbor metal and chalcogen orbitals are explicitly derived at K ,-K , and Γ points of the Brillouin zone. The nearest-neighbor tunneling matrix elements connect specific metal and sulfur orbitals yielding an effective 6 ×6 Hamiltonian giving correct composition of metal and chalcogen orbitals but not the direct gap at K points. The direct gap at K , correct masses, and conduction band minima at Q points responsible for band nesting are obtained by inclusion of next-neighbor Mo-Mo tunneling. The parameters of the next-nearest-neighbor model are successfully fitted to MX 2(M =Mo ; X =S ) density functional ab initio calculations of the highest valence and lowest conduction band dispersion along K -Γ line in the Brillouin zone. The effective two-band massive Dirac Hamiltonian for MoS2, Landé g factors, and valley Zeeman splitting are obtained.
The many faces of Maxwell, Dirac and Einstein equations a Clifford bundle approach
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...
Equations of motion for massive spin 2 field coupled to gravity
Buchbinder, I.L.; Gitman, D.M.; Krykhtin, V.A.; Pershin, V.D.
2000-01-01
We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in α' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory
Separation of massive field equation of arbitrary spin in Robertson-Walker space-time
Zecca, A.
2006-01-01
The massive spin-(3/2) field equation is explicitly integrated in the Robertson-Walker space-time by the Newman Penrose formalism. The solution is obtained by extending a separation procedure previously used to solve the spin-1 equation. The separated time dependence results in two coupled equations depending on the cosmological background evolution. The separated angular equations are explicitly integrated and the eigenvalues determined. The separated radial equations are integrated in the flat space-time case. The separation method of solution is then generalized, by induction, to prove the main result, that is the separability of the massive field equations of arbitrary spin in the Robertson-Walker space-time
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)
Steinmann, O [Bielefeld Univ. (F.R. Germany). Fakultaet fuer Physik
1975-01-01
Massive quantum electrodynamics of the electron is formulated as an LSZ theory of the electromagnetic field F(..mu nu..) and the electron-positron fields PSI. The interaction is introduced with the help of mathematically well defined subsidiary conditions. These are: 1) gauge invariance of the first kind, assumed to be generated by a conserved current j(..mu..); 2) the homogeneous Maxwell equations and a massive version of the inhomogeneous Maxwell equations; 3) a minimality condition concerning the high momentum behaviour of the theory. The inhomogeneous Maxwell equation is a linear differential equation connecting Fsub(..mu nu..) with the current Jsub(..mu..). No Lagrangian, no non-linear field equations, and no explicit expression of Jsub(..mu..) in terms of PSI, anti-PSI are needed. It is shown in perturbation theory that the proposed conditions fix the physically relevant (i.e. observable) quantities of the theory uniquely.
Proxy-equation paradigm: A strategy for massively parallel asynchronous computations
Mittal, Ankita; Girimaji, Sharath
2017-09-01
Massively parallel simulations of transport equation systems call for a paradigm change in algorithm development to achieve efficient scalability. Traditional approaches require time synchronization of processing elements (PEs), which severely restricts scalability. Relaxing synchronization requirement introduces error and slows down convergence. In this paper, we propose and develop a novel "proxy equation" concept for a general transport equation that (i) tolerates asynchrony with minimal added error, (ii) preserves convergence order and thus, (iii) expected to scale efficiently on massively parallel machines. The central idea is to modify a priori the transport equation at the PE boundaries to offset asynchrony errors. Proof-of-concept computations are performed using a one-dimensional advection (convection) diffusion equation. The results demonstrate the promise and advantages of the present strategy.
Some solutions of the equations of motion of the relativistic string with massive ends
Barbashov, B.M.
1977-01-01
The classical theory is discussed for the relativistic string with point masses at its ends. The dynamical equations are solved for the class of motions of this system when the time evolution parameter tau is the proper time of both massive string ends. In this case the solution of the boundary equations is given by the almost periodic functions. Constraints on the normal modes resulting from the orthonormal gauge conditions differ essentially from the Virasoro ones. Incidentally one obtains an exact solution for the half-infinite string with mass at one end. It is also proved that the exact solution for the string with massive ends cannot be a periodic function. (Auth.)
Unfolded equations for massive higher spin supermultiplets in AdS{sub 3}
Buchbinder, I.L. [Department of Theoretical Physics, Tomsk State Pedagogical University,60 Kievskaya Str., Tomsk, 634061 (Russian Federation); National Research Tomsk State University,36 Lenina Ave., Tomsk, 634050 (Russian Federation); Snegirev, T.V. [Department of Theoretical Physics, Tomsk State Pedagogical University,60 Kievskaya Str., Tomsk, 634061 (Russian Federation); Department of Higher Mathematics and Mathematical Physics,National Research Tomsk Polytechnic University, 30 Lenina Ave., Tomsk, 634050 (Russian Federation); Zinoviev, Yu.M. [Department of Theoretical Physics,Institute for High Energy Physics of National Research Center “Kurchatov Institute”, 1 Pobedy Str., Protvino, Moscow Region, 142280 (Russian Federation)
2016-08-10
In this paper we give an explicit construction of unfolded equations for massive higher spin supermultiplets of the minimal (1,0) supersymmetry in AdS{sub 3} space. For that purpose we use an unfolded formulation for massive bosonic and fermionic higher spins and find supertransformations leaving appropriate set of unfolded equations invariant. We provide two general supermultiplets (s,s+1/2) and (s,s−1/2) with arbitrary integer s, as well as a number of lower spin examples.
Solution of the Dirac Coulomb equation for helium-like ions in the Poet-Temkin model.
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.
Solution of the Dirac Coulomb equation for helium-like ions in the Poet-Temkin model
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.
Semiclassical solution to the BFKL equation with massive gluons
Levin, Eugene; Lipatov, Lev; Siddikov, Marat
2015-01-01
In this paper we proceed to study the high energy behavior of scattering amplitudes in a simple field model, with the Higgs mechanism for the gauge boson mass. The spectrum of the j-plane singularities of the t-channel partial waves and the corresponding eigenfunctions of the BFKL equation in leading log(1/x) approximation were previously calculated numerically. Here we develop a semiclassical approach to investigate the influence of the exponential decrease of the impact parameter dependence existing in this model, on the high energy asymptotic behavior of the scattering amplitude. This approach is much simpler than our earlier numerical calculations, and it reproduces those results. The analytical (semi-analytical) solutions which have been found in the approximation can be used to incorporate correctly the large impact parameter behavior in the framework of CGC/saturation approach. This behavior is interesting as it provides the high energy amplitude for the electroweak theory, which can be measured experimentally. (orig.)
Potential scattering of Dirac particles
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.)
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
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.
Massively parallel red-black algorithms for x-y-z response matrix equations
Hanebutte, U.R.; Laurin-Kovitz, K.; Lewis, E.E.
1992-01-01
Recently, both discrete ordinates and spherical harmonic (S n and P n ) methods have been cast in the form of response matrices. In x-y geometry, massively parallel algorithms have been developed to solve the resulting response matrix equations on the Connection Machine family of parallel computers, the CM-2, CM-200, and CM-5. These algorithms utilize two-cycle iteration on a red-black checkerboard. In this work we examine the use of massively parallel red-black algorithms to solve response matric equations in three dimensions. This longer term objective is to utilize massively parallel algorithms to solve S n and/or P n response matrix problems. In this exploratory examination, however, we consider the simple 6 x 6 response matrices that are derivable from fine-mesh diffusion approximations in three dimensions
Photoconductivity in Dirac materials
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
Smirne, Andrea; Vacchini, Bassano
2010-01-01
We address the microscopic derivation of a quantum master equation in Lindblad form for the dynamics of a massive test particle with internal degrees of freedom, interacting through collisions with a background ideal gas. When either internal or center-of-mass degrees of freedom can be treated classically, previously established equations are obtained as special cases. If in an interferometric setup the internal degrees of freedom are not detected at the output, the equation can be recast in the form of a generalized Lindblad structure, which describes non-Markovian effects. The effect of internal degrees of freedom on center-of-mass decoherence is considered in this framework.
Exact solutions of the dirac equation for an electron in magnetic field with shape invariant method
Setare, M.R.; Hatami, O.
2008-01-01
Based on the shape invariance property we obtain exact solutions of the Virac equation for an electron moving in the presence of a certain varying magnetic Geld, then we also show its non-relativistic limit. (authors)
Fermi-Dirac-Fokker-Planck equation : well-posedness & long-time asymptotics
Carrillo , José A.; Laurençot , Philippe; Rosado , Jesús
2009-01-01
International audience; A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments are finite, we can show the global existence of weak solutions for this problem. The natural associated entropy of the equation is the main tool to derive uniform in time a priori estimates for the kinetic energy and entropy. As a con...
Fermi-Dirac-Fokker-Planck equation: well-posedness and long-time asymptotics
Carrillo, José A.; Laurençot, Philippe; Rosado, Jesús
2008-01-01
A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments are finite, we can show the global existence of weak solutions for this problem. The natural associated entropy of the equation is the main tool to derive uniform in time a priori estimates for the kinetic energy and entropy. As a consequence, long-time asym...
Equations of motion for massive spin 2 field coupled to gravity
Buchbinder, I.L. E-mail: ilb@mail.tomsknet.ru; Gitman, D.M. E-mail: gitman@fma.if.usp.br; Krykhtin, V.A. E-mail: krykhtin@phys.dfe.tpu.edu.ru; Pershin, V.D. E-mail: pershin@ic.tsu.ru
2000-09-18
We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in {alpha}' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.
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
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
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)
Weak cosmic censorship, dyonic Kerr–Newman black holes and Dirac fields
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)
Wigner function for the Dirac oscillator in spinor space
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)
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 ...
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
Killing vector fields in three dimensions: a method to solve massive gravity field equations
Guerses, Metin, E-mail: gurses@fen.bilkent.edu.t [Department of Mathematics, Faculty of Sciences, Bilkent University, 06800 Ankara (Turkey)
2010-10-21
Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.
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.)
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.)
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...
A Dirac algebraic approach to supersymmetry
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)
Connection between Dirac and matrix Schroedinger inverse-scattering transforms
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)
Guermond, Jean-Luc; Minev, Peter D.; Salgado, Abner J.
2012-01-01
We provide a convergence analysis for a new fractional timestepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization. © 2012 American Mathematical Society.
Effects of acceleration through the Dirac sea
Hacyan, S.
1986-01-01
The effects of acceleration through massive scalar and spin-1/2 fields are investigated. It is shown that the density-of-states factor in a uniformly accelerated frame takes a complicated form, but the energy spectrum exhibits a Bose-Einstein or Fermi-Dirac distribution function. In particular, the Dirac sea shows thermal-like effects
A highly scalable massively parallel fast marching method for the Eikonal equation
Yang, Jianming; Stern, Frederick
2017-03-01
The fast marching method is a widely used numerical method for solving the Eikonal equation arising from a variety of scientific and engineering fields. It is long deemed inherently sequential and an efficient parallel algorithm applicable to large-scale practical applications is not available in the literature. In this study, we present a highly scalable massively parallel implementation of the fast marching method using a domain decomposition approach. Central to this algorithm is a novel restarted narrow band approach that coordinates the frequency of communications and the amount of computations extra to a sequential run for achieving an unprecedented parallel performance. Within each restart, the narrow band fast marching method is executed; simple synchronous local exchanges and global reductions are adopted for communicating updated data in the overlapping regions between neighboring subdomains and getting the latest front status, respectively. The independence of front characteristics is exploited through special data structures and augmented status tags to extract the masked parallelism within the fast marching method. The efficiency, flexibility, and applicability of the parallel algorithm are demonstrated through several examples. These problems are extensively tested on six grids with up to 1 billion points using different numbers of processes ranging from 1 to 65536. Remarkable parallel speedups are achieved using tens of thousands of processes. Detailed pseudo-codes for both the sequential and parallel algorithms are provided to illustrate the simplicity of the parallel implementation and its similarity to the sequential narrow band fast marching algorithm.
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)
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...
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
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.
Dirac and Weyl semimetals with holographic interactions
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
Barbashov, B.M.; Chervyakov, A.M.
1991-01-01
The classical histories of the relativistic string with massive ends in space-time are examined in terms of geometric invariants of both the string world surface and world lines of the point masses at the string ends. In this formulation the string variables are completely defined by means of the constant curvatures and torsions of the endpoint trajectories which are subjected to a system of differential equations with a delayed arguments that incorporates retardation effects of the interaction of two point masses through the string. The well-known example of the rotating straight-line string with massive ends corresponds to a particular solution of this system for the constant torsions. A new exact solution for the periodic torsions of the world trajectories of the massive string ends is found. In this case the string coordinates are represented in terms of normal elliptic integrals and describe a more intricate motion including its transverse vibrations than rotation of a stretched string in a given plane. 17 refs
Crater, Horace W.; Schiermeyer, James
2010-01-01
In a previous paper, Crater and Van Alstine applied the two-body Dirac equations of constraint dynamics to quark-antiquark bound states using a relativistic extention of the Adler-Piran potential and compared their spectral results to those from other approaches which also considered meson spectroscopy as a whole and not in parts. In this paper, we explore in more detail the differences and similarities in an important subset of those approaches, the quasipotential approach. In the earlier paper, the transformation properties of the quark-antiquark potentials were limited to a scalar and an electromagnetic-like four-vector, with the former accounting for the confining aspects of the overall potential, and the latter the short range portion. The static Adler-Piran potential was first given an invariant form and then apportioned between those two different types of potentials. Here, we make a change in this apportionment that leads to a substantial improvement in the resultant spectroscopy by including a timelike confining vector potential over and above the scalar confining one and the electromagnetic-like vector potential. Our fit includes 19 more mesons than the earlier results and we modify the scalar portion of the potential in such a way that allows this formalism to account for the isoscalar mesons η and η ' not included in the previous work. Continuing the comparisons of formalisms and spectral results made in the previous paper with other approaches to meson spectroscopy, we examine in this paper the quasipotential approach of Ebert, Faustov, and Galkin.
On Huygens' principle for Dirac operators associated to electromagnetic fields
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.
Nakatsuji, Hiroshi
2012-09-18
Just as Newtonian law governs classical physics, the Schrödinger equation (SE) and the relativistic Dirac equation (DE) rule the world of chemistry. So, if we can solve these equations accurately, we can use computation to predict chemistry precisely. However, for approximately 80 years after the discovery of these equations, chemists believed that they could not solve SE and DE for atoms and molecules that included many electrons. This Account reviews ideas developed over the past decade to further the goal of predictive quantum chemistry. Between 2000 and 2005, I discovered a general method of solving the SE and DE accurately. As a first inspiration, I formulated the structure of the exact wave function of the SE in a compact mathematical form. The explicit inclusion of the exact wave function's structure within the variational space allows for the calculation of the exact wave function as a solution of the variational method. Although this process sounds almost impossible, it is indeed possible, and I have published several formulations and applied them to solve the full configuration interaction (CI) with a very small number of variables. However, when I examined analytical solutions for atoms and molecules, the Hamiltonian integrals in their secular equations diverged. This singularity problem occurred in all atoms and molecules because it originates from the singularity of the Coulomb potential in their Hamiltonians. To overcome this problem, I first introduced the inverse SE and then the scaled SE. The latter simpler idea led to immediate and surprisingly accurate solution for the SEs of the hydrogen atom, helium atom, and hydrogen molecule. The free complement (FC) method, also called the free iterative CI (free ICI) method, was efficient for solving the SEs. In the FC method, the basis functions that span the exact wave function are produced by the Hamiltonian of the system and the zeroth-order wave function. These basis functions are called complement
Solving the Fokker-Planck equation on a massively parallel computer
Mirin, A.A.
1990-01-01
The Fokker-Planck package FPPAC had been converted to the Connection Machine 2 (CM2). For fine mesh cases the CM2 outperforms the Cray-2 when it comes to time-integrating the difference equations. For long Legendre expansions the CM2 is also faster at computing the Fokker-Planck coefficients. 3 refs
A Structural Equation Modelling Approach for Massive Blended Synchronous Teacher Training
Kannan, Kalpana; Narayanan, Krishnan
2015-01-01
This paper presents a structural equation modelling (SEM) approach for blended synchronous teacher training workshop. It examines the relationship among various factors that influence the Satisfaction (SAT) of participating teachers. Data were collected with the help of a questionnaire from about 500 engineering college teachers. These teachers…
Resolution of the neutron transport equation by massively parallel computer in the Cronos code
Zardini, D.M.
1996-01-01
The feasibility of neutron transport problems parallel resolution by CRONOS code's SN module is here studied. In this report we give the first data about the parallel resolution by angular variable decomposition of the transport equation. Problems about parallel resolution by spatial variable decomposition and memory stage limits are also explained here. (author)
Paul Dirac: the purest soul in physics
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)
A new type of massive spin-one boson: And its relation with Maxwell equations
Ahluwalia, D.V.
1995-01-01
First, the author showed that in the (1, 0) circle-plus (0, 1) representation space there exist not one but two theories for charged particles. In the Weinberg construct, the boson and its antiboson carry same relative intrinsic parity, whereas in the author's construct the relative intrinsic parities of the boson and its antiboson are opposite. These results originate from the commutativity of the operations of Charge conjugation and Parity in Weinberg's theory, and from the anti-commutativity of the operations of Charge conjugation and Parity in the author's theory. The author thus claims that he has constructed a first non-trivial quantum theory of fields for the Wigner-type particles. Second, the massless limit of both theories seems formally identical and suggests a fundamental modification of Maxwell equations. At its simplest level, the modification to Maxwell equations enters via additional boundary condition(s)
Symmetries and Dirac equation solutions
Souza, Marcio Lima de.
1991-06-01
The purpose of this thesis is the extension to be relativistic case of a method that has proved useful for the solution of various potential problems in non relativistic situation. This method, the method of dynamical symmetries, is based on the Baker-Campbell-Hausdorf formulae and developed first for the particular example of the relativistic Coulomb problem. Here we generalize the method for a Hamiltonian that can be written as a linear combination of generators of the SO(2,1) group. As illustrative examples, we solve the problem of a charged particle in a constant magnetic field and the exponential magnetic field. (author). 21 refs
Hybrid massively parallel fast sweeping method for static Hamilton–Jacobi equations
Detrixhe, Miles, E-mail: mdetrixhe@engineering.ucsb.edu [Department of Mechanical Engineering (United States); University of California Santa Barbara, Santa Barbara, CA, 93106 (United States); Gibou, Frédéric, E-mail: fgibou@engineering.ucsb.edu [Department of Mechanical Engineering (United States); University of California Santa Barbara, Santa Barbara, CA, 93106 (United States); Department of Computer Science (United States); Department of Mathematics (United States)
2016-10-01
The fast sweeping method is a popular algorithm for solving a variety of static Hamilton–Jacobi equations. Fast sweeping algorithms for parallel computing have been developed, but are severely limited. In this work, we present a multilevel, hybrid parallel algorithm that combines the desirable traits of two distinct parallel methods. The fine and coarse grained components of the algorithm take advantage of heterogeneous computer architecture common in high performance computing facilities. We present the algorithm and demonstrate its effectiveness on a set of example problems including optimal control, dynamic games, and seismic wave propagation. We give results for convergence, parallel scaling, and show state-of-the-art speedup values for the fast sweeping method.
Hybrid massively parallel fast sweeping method for static Hamilton–Jacobi equations
Detrixhe, Miles; Gibou, Frédéric
2016-01-01
The fast sweeping method is a popular algorithm for solving a variety of static Hamilton–Jacobi equations. Fast sweeping algorithms for parallel computing have been developed, but are severely limited. In this work, we present a multilevel, hybrid parallel algorithm that combines the desirable traits of two distinct parallel methods. The fine and coarse grained components of the algorithm take advantage of heterogeneous computer architecture common in high performance computing facilities. We present the algorithm and demonstrate its effectiveness on a set of example problems including optimal control, dynamic games, and seismic wave propagation. We give results for convergence, parallel scaling, and show state-of-the-art speedup values for the fast sweeping method.
Optical analogue of relativistic Dirac solitons in binary waveguide arrays
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.
A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations
Guermond, J.L.
2011-06-01
We introduce in this paper a new direction splitting algorithm for solving the incompressible Navier-Stokes equations. The main originality of the method consists of using the operator (I-∂xx)(I-∂yy)(I-∂zz) for approximating the pressure correction instead of the Poisson operator as done in all the contemporary projection methods. The complexity of the proposed algorithm is significantly lower than that of projection methods, and it is shown the have the same stability properties as the Poisson-based pressure-correction techniques, either in standard or rotational form. The first-order (in time) version of the method is proved to have the same convergence properties as the classical first-order projection techniques. Numerical tests reveal that the second-order version of the method has the same convergence rate as its second-order projection counterpart as well. The method is suitable for parallel implementation and preliminary tests show excellent parallel performance on a distributed memory cluster of up to 1024 processors. The method has been validated on the three-dimensional lid-driven cavity flow using grids composed of up to 2×109 points. © 2011 Elsevier B.V.
Mass and oscillations of Dirac neutrinos
Collot, J.
1989-01-01
In the most economical extension of the standard model, we have presented the theory of massive Dirac neutrinos. We have particularly emphasized that, in this model, a complete analogy between quarks and leptons can be erected and predicts neutrino flavor oscillations. We have reviewed the last experimental results concerning kinetic neutrino mass experiments and neutrino oscillation investigations
Azmy, Yousry
2014-06-10
We employ the Integral Transport Matrix Method (ITMM) as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells' fluxes and between the cells' and boundary surfaces' fluxes. The main goals of this work are to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and parallel performance of the developed methods with increasing number of processes, P. The fastest observed parallel solution method, Parallel Gauss-Seidel (PGS), was used in a weak scaling comparison with the PARTISN transport code, which uses the source iteration (SI) scheme parallelized with the Koch-baker-Alcouffe (KBA) method. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method- even without acceleration/preconditioning-is completitive for optically thick problems as P is increased to the tens of thousands range. For the most optically thick cells tested, PGS reduced execution time by an approximate factor of three for problems with more than 130 million computational cells on P = 32,768. Moreover, the SI-DSA execution times's trend rises generally more steeply with increasing P than the PGS trend. Furthermore, the PGS method outperforms SI for the periodic heterogeneous layers (PHL) configuration problems. The PGS method outperforms SI and SI-DSA on as few as P = 16 for PHL problems and reduces execution time by a factor of ten or more for all problems considered with more than 2 million computational cells on P = 4.096.
Counter-diabatic driving for Dirac dynamics
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.
Quantum geometry of the Dirac fermions
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
On an uninterpretated tensor in Dirac's theory
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
Leptons as systems of Dirac particles
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
Zerr, Robert Joseph
2011-12-01
The integral transport matrix method (ITMM) has been used as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells and between the cells and boundary surfaces. The main goals of this work were to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and performance of the developed methods for increasing number of processes. This project compares the effectiveness of the ITMM with the SI scheme parallelized with the Koch-Baker-Alcouffe (KBA) method. The primary parallel solution method involves a decomposition of the domain into smaller spatial sub-domains, each with their own transport matrices, and coupled together via interface boundary angular fluxes. Each sub-domain has its own set of ITMM operators and represents an independent transport problem. Multiple iterative parallel solution methods have investigated, including parallel block Jacobi (PBJ), parallel red/black Gauss-Seidel (PGS), and parallel GMRES (PGMRES). The fastest observed parallel solution method, PGS, was used in a weak scaling comparison with the PARTISN code. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method without acceleration/preconditioning is not competitive for any problem parameters considered. The best comparisons occur for problems that are difficult for SI DSA, namely highly scattering and optically thick. SI DSA execution time curves are generally steeper than the PGS ones. However, until further testing is performed it cannot be concluded that SI DSA does not outperform the ITMM with PGS even on several thousand or tens of
Are Dirac electrons faster than light?
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
March, N.H.
2009-08-01
In this Journal, March and Suhai have earlier set up a first-order Dirac idempotent density matrix theory for one- and two-level occupancy in which the only input required is the nonrelativistic ground-state electron density. Here, an analytic generalization is provided for the case of spherical electron densities for arbitrary level occupancy. Be-like atomic ions are referred to as an example, but 'almost spherical' molecules like SiH 4 and GeH 4 also become accessible. (author)
DIRAC distributed secure framework
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.
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.
Bound-state Dirac eigenvalues for scalar potentials
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)
Becar, Ramon [Universidad Catolica de Temuco, Departamento de Ciencias Matematicas y Fisicas, Temuco (Chile); Gonzalez, P.A. [Universidad Diego Portales, Facultad de Ingenieria, Santiago (Chile); Saavedra, Joel [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Vasquez, Yerko [Universidad de La Serena, Departamento de Fisica, Facultad de Ciencias, La Serena (Chile)
2015-02-01
We study massive charged fermionic perturbations in the background of a charged two-dimensional dilatonic black hole, and we solve the Dirac equation analytically. Then we compute the reflection and transmission coefficients and the absorption cross section for massive charged fermionic fields, and we show that the absorption cross section vanishes at the low- and high-frequency limits. However, there is a range of frequencies where the absorption cross section is not null. Furthermore, we study the effect of the mass and electric charge of the fermionic field over the absorption cross section. (orig.)
A matricial approach for the Dirac-Kahler formalism
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
Quantum equations from Brownian motions
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)
Majorana mass term, Dirac neutrinos and selective neutrino oscillations
Leung, C.N.
1987-01-01
In a theory of neutrino mixing via a Majorana mass term involving only the left-handed neutrinos there exist selection rules for neutrino oscillations if true Dirac and/or exactly zero mass eigenstates are present. In the case of three neutrino flavours no oscillation is allowed if the mass spectrum contains one Dirac and one nondegenerate Majorana massive neutrino. The origin of these selection rules and their implications are discussed and the number of possible CP-violating phases in the lepton mixing matrix when Dirac and Majorana mass eigenstates coexist is given. (orig.)
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.
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.
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 ...
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)
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 ...
Tunnelling of Massive/Massless Bosons from the Apparent Horizon of FRW Universe
Kimet Jusufi
2017-01-01
Full Text Available We investigate the Hawking radiation of vector particles from the apparent horizon of a Friedmann-Robertson-Walker (FRW universe in the framework of quantum tunnelling method. Furthermore we use Proca equation, a relativistic wave equation for a massive/massless spin-1 particle (massless γ photons, weak massive W± and Z0 bosons, strong massless gluons, and ρ and ω mesons together with a Painlevé space-time metric for the FRW universe. We solve the Proca equation via Hamilton-Jacobi (HJ equation and the WKB approximation method. We recover the same result for the Hawking temperature associated with vector particles as in the case of scalar and Dirac particles tunnelled from outside to the inside of the apparent horizon in a FRW universe.
Hawking radiation of Dirac particles in the hot NUT-Kerr-Newman spacetime
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.)
Dirac's aether in relativistic quantum mechanics
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.)
Higher dimensional supersymmetric quantum mechanics and Dirac ...
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.
On Kaehler's geometric description of dirac fields
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)
Avoid the tsunami of the Dirac sea in the imaginary time step method
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)
On the confinement of a Dirac particle to a two-dimensional ring
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.
Three Dimensional Dirac Semimetals
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.
Axial anomaly and index theorem for Dirac-Kaehler fermions
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
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.
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.
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
DIRAC distributed computing services
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.
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.
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.
Particles and Dirac-type operators on curved spaces
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)
A Route to Dirac Liquid Theory: A Fermi Liquid Description for Dirac Materials
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.
Vacuum state of the Dirac field in de Sitter space and entanglement entropy
Kanno, Sugumi [Department of Theoretical Physics and History of Science,University of the Basque Country,48080 Bilbao (Spain); IKERBASQUE, Basque Foundation for Science,Maria Diaz de Haro 3, 48013, Bilbao (Spain); Sasaki, Misao [Center for Gravitational Physics,Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); Tanaka, Takahiro [Department of Physics, Kyoto University,Kyoto 606-8502 (Japan); Center for Gravitational Physics,Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan)
2017-03-13
We compute the entanglement entropy of a free massive Dirac field between two causally disconnected open charts in de Sitter space. We first derive the Bunch-Davies vacuum mode functions of the Dirac field. We find there exists no supercurvature mode for the Dirac field. We then give the Bogoliubov transformation between the Bunch-Davies vacuum and the open chart vacua that makes the reduced density matrix diagonal. We find that the Dirac field becomes more entangled than a scalar field as m{sup 2}/H{sup 2} becomes small, and the difference is maximal in the massless limit.
The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states
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.
The interaction of Dirac particles with non-abelian gauge fields and gravity - bound 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.
The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states
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
DIRAC optimized workload management
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 ...
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.)
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.)
Topological Crystalline Insulators and Dirac Octets in Anti-perovskites
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.
Einstein-Cartan-Dirac theory in (1+2)-dimensions
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.)
Classical electromagnetic radiation of the Dirac electron
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.
Faria, F. F.
2014-01-01
We construct a massive theory of gravity that is invariant under conformal transformations. The massive action of the theory depends on the metric tensor and a scalar field, which are considered the only field variables. We find the vacuum field equations of the theory and analyze its weak-field approximation and Newtonian limit.
Time-dependent massless Dirac fermions in graphene
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.
New symmetries for the Dirac equation
Linhares, C.A.; Mignaco, J.A.
1990-06-01
We study through both the matrix and differential-form formalism the SU(4) symmetry relating spin 1/2 particles. Minimal left ideals of the Clifford algebra are shown to be irreducible representations of these particles. Their physical interpretation relies on their mutual relationship via parity, time reversal and their product. The implication of these features on the spectrum proliferation problem on the lattice is emphasized. (author)
Zero Point Energy and the Dirac Equation
Forouzbakhsh, Farshid
2007-01-01
Zero Point Energy (ZPE) describes the random electromagnetic oscillations that are left in the vacuum after all other energy has been removed. One way to explain this is by means of the uncertainty principle of quantum physics, which implies that it is impossible to have a zero energy condition.I this article, the ZPE is explained by using a novel description of the graviton. This is based on the behavior of photons in gravitational field, leading to a new definition of the graviton. In effec...
Joshipura, A.S.; Rindani, S.D.
1991-01-01
The consequences of imposing an exact L e +L τ -L μ symmetry on a 6x6 matrix describing neutrino masses are discussed. The presence of right-handed neutrinos avoids the need of introducing any SU(2) Higgs triplet. Hence the conflict with the CERN LEP data on the Z width found in earlier models with L e +L τ -L μ symmetry is avoided. The L e +L τ -L μ symmetry provides an interesting realization of a recent proposal of Glashow to accommodate the 17-keV Dirac neutrino in the SU(2)xU(1) theory. All the neutrinos in this model are Dirac particles. The solar-neutrino problem can be solved in an extension of the model which generates a large (∼10 -11 μ B ) magnetic moment for the electron neutrino
Sheka, Elena F.
2016-01-01
The paper presents the author view on spin-rooted properties of graphene supported by numerous experimental and calculation evidences. Dirac fermions of crystalline graphene and local spins of graphene molecules are suggested to meet a strict demand - different orbitals for different spins- which leads to a large spectrum of effects caused by spin polarization of electronic states. The consequent topological non-triviality, making graphene topological insulator, and local spins, imaging graph...
Quantum transport through 3D Dirac materials
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.
Quantum transport through 3D Dirac materials
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
Dirac vacuum: Acceleration and external-field effects
Jauregui, R.; Torres, M.; Hacyan, S.
1991-01-01
The quantization of the massive spin-1/2 field in Rindler coordinates is considered, including the effects of a background magnetic field. We calculate the expectation values of conserved quantities such as the stress-energy tensor, current density, and spin distribution, as detected by an accelerated observer. The ratio of the energy and particle densities is given by a Fermi-Dirac distribution, but the spectrum of these quantities takes in general a complicated form that cannot be simply interpreted as a thermal spectrum. For the free-particle case the spectrum of the energy-stress tensor has a Fermi-Dirac form only in the massless limit. In the presence of the magnetic field the Dirac vacuum is magnetized and exhibits plasmalike properties
Dirac potentials in a coupled channel approach to inelastic scattering
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
Dirac fermions in nontrivial topology black hole backgrounds
Gozdz, Marek; Nakonieczny, Lukasz; Rogatko, Marek
2010-01-01
We discuss the behavior of the Dirac fermions in a general spherically symmetric black hole background with a nontrivial topology of the event horizon. Both massive and massless cases are taken into account. We will conduct an analytical study of intermediate and late-time behavior of massive Dirac hair in the background of a black hole with a global monopole and dilaton black hole pierced by a cosmic string. In the case of a global monopole swallowed by a static black hole, the intermediate late-time behavior depends on the mass of the Dirac field, the multiple number of the wave mode, and the global monopole parameter. The late-time behavior is quite independent of these factors and has a decay rate proportional to t -5/6 . As far as the black hole pierced by a cosmic string is concerned, the intermediate late-time behavior depends only on the hair mass and the multipole number of the wave mode, while the late-time behavior dependence is the same as in the previous case. The main modification stems from the topology of the S 2 sphere pierced by a cosmic string. This factor modifies the eigenvalues of the Dirac operator acting on the transverse manifold.
Leo, Stefano de; Rotelli, Pietro
2009-01-01
We present the results of the planar diffusion of a Dirac particle by step and barrier potentials, when the incoming wave impinges at an arbitrary angle with the potential. Except for right-angle incidence this process is characterized by the appearance of spin flip terms. For the step potential, spin flip occurs for both transmitted and reflected waves. However, we find no spin flip in the transmitted barrier result. This is surprising because the barrier result may be derived directly from a two-step calculation. We demonstrate that the spin flip cancellation indeed occurs for each ''particle'' (wave packet) contribution. (orig.)
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
LHCb: DIRAC Secure Distributed Platform
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...
Electric-dipole-induced universality for Dirac fermions in graphene.
De Martino, Alessandro; Klöpfer, Denis; Matrasulov, Davron; Egger, Reinhold
2014-05-09
We study electric dipole effects for massive Dirac fermions in graphene and related materials. The dipole potential accommodates towers of infinitely many bound states exhibiting a universal Efimov-like scaling hierarchy. The dipole moment determines the number of towers, but there is always at least one tower. The corresponding eigenstates show a characteristic angular asymmetry, observable in tunnel spectroscopy. However, charge transport properties inferred from scattering states are highly isotropic.
Aoki, Katsuki; Maeda, Kei-ichi; Misonoh, Yosuke; Okawa, Hirotada
2018-02-01
We find vacuum solutions such that massive gravitons are confined in a local spacetime region by their gravitational energy in asymptotically flat spacetimes in the context of the bigravity theory. We call such self-gravitating objects massive graviton geons. The basic equations can be reduced to the Schrödinger-Poisson equations with the tensor "wave function" in the Newtonian limit. We obtain a nonspherically symmetric solution with j =2 , ℓ=0 as well as a spherically symmetric solution with j =0 , ℓ=2 in this system where j is the total angular momentum quantum number and ℓ is the orbital angular momentum quantum number, respectively. The energy eigenvalue of the Schrödinger equation in the nonspherical solution is smaller than that in the spherical solution. We then study the perturbative stability of the spherical solution and find that there is an unstable mode in the quadrupole mode perturbations which may be interpreted as the transition mode to the nonspherical solution. The results suggest that the nonspherically symmetric solution is the ground state of the massive graviton geon. The massive graviton geons may decay in time due to emissions of gravitational waves but this timescale can be quite long when the massive gravitons are nonrelativistic and then the geons can be long-lived. We also argue possible prospects of the massive graviton geons: applications to the ultralight dark matter scenario, nonlinear (in)stability of the Minkowski spacetime, and a quantum transition of the spacetime.
DIRAC: data production management
Smith, A C; Tsaregorodtsev, A
2008-01-01
The LHCb Computing Model describes the dataflow for all stages in the processing of real and simulated events, and defines the role of LHCb associated Tier-1 and Tier-2 computing centers. The WLCG 'Dress Rehearsal' exercise aims to allow LHC experiments to deploy the full chain of their Computing Models, making use of all underlying WLCG services and resources, in preparation for real data taking. During this exercise simulated RAW physics data, matching the properties of eventual real data, will be uploaded from the LHCb Online storage system to Grid enabled storage. This data will then be replicated to LHCb Tier-1 centers and subsequently processed (reconstructed and stripped). The product of this processing is user analysis data that are distributed to all LHCb Tier-1 centers. DIRAC, LHCbs Workload and Data Management System, supports the implementation of the Computing Model in a data driven, real time and coordinated fashion. In this paper the LHCb Computing Model will be reviewed and the DIRAC components providing the needed functionality to support the Computing Model will be detailed. An evaluation of the preparedness for real data taking will also be given
DIRAC: data production management
Smith, A C [CERN, CH-1211, Geneva (Switzerland); Tsaregorodtsev, A [CPPM, Marseille (France)], E-mail: a.smith@cern.ch, E-mail: atsareg@in2p3.fr
2008-07-15
The LHCb Computing Model describes the dataflow for all stages in the processing of real and simulated events, and defines the role of LHCb associated Tier-1 and Tier-2 computing centers. The WLCG 'Dress Rehearsal' exercise aims to allow LHC experiments to deploy the full chain of their Computing Models, making use of all underlying WLCG services and resources, in preparation for real data taking. During this exercise simulated RAW physics data, matching the properties of eventual real data, will be uploaded from the LHCb Online storage system to Grid enabled storage. This data will then be replicated to LHCb Tier-1 centers and subsequently processed (reconstructed and stripped). The product of this processing is user analysis data that are distributed to all LHCb Tier-1 centers. DIRAC, LHCbs Workload and Data Management System, supports the implementation of the Computing Model in a data driven, real time and coordinated fashion. In this paper the LHCb Computing Model will be reviewed and the DIRAC components providing the needed functionality to support the Computing Model will be detailed. An evaluation of the preparedness for real data taking will also be given.
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.
Dirac gauginos, gauge mediation and unification
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.)
Dirac gauginos, gauge mediation and unification
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.)
Dirac Gauginos, Gauge Mediation and Unification
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.
DIRAC data production management
Smith, A C
2008-01-01
The LHCb Computing Model describes the dataflow for all stages in the processing of real and simulated events, and defines the role of LHCb associated Tier-1 and Tier-2 computing centers. The WLCG 'Dress Rehearsal' exercise aims to allow LHC experiments to deploy the full chain of their Computing Models, making use of all underlying WLCG services and resources, in preparation for real data taking. During this exercise simulated RAW physics data, matching the properties of eventual real data, will be uploaded from the LHCb Online storage system to Grid enabled storage. This data will then be replicated to LHCb Tier-1 centers and subsequently processed (reconstructed and stripped). The product of this processing is user analysis data that are distributed to all LHCb Tier-1 centers. DIRAC, LHCbs Workload and Data Management System, supports the implementation of the Computing Model in a data driven, real time and coordinated fashion.
Smith, A C
2007-01-01
The LHCb experiment being built to utilize CERN’s flagship Large Hadron Collider will generate data to be analysed by a community of over 600 physicists worldwide. DIRAC, LHCb’s Workload and Data Management System, facilitates the use of underlying EGEE Grid resources to generate, process and analyse this data in the distributed environment. The Data Management System, presented here, provides real-time, data-driven distribution in accordance with LHCb’s Computing Model. The data volumes produced by the LHC experiments are unprecedented, rendering individual institutes and even countries, unable to provide the computing and storage resources required to make full use of the produced data. EGEE Grid resources allow the processing of LHCb data possible in a distributed fashion and LHCb’s Computing Model is based on this approach. Data Management in this environment requires reliable and high-throughput transfer of data, homogeneous access to storage resources and the cataloguing of data replicas, all of...
Stagni, F.; McNab, A.; Luzzi, C.; Krzemien, W.; Consortium, DIRAC
2017-10-01
In the last few years, new types of computing models, such as IAAS (Infrastructure as a Service) and IAAC (Infrastructure as a Client), gained popularity. New resources may come as part of pledged resources, while others are in the form of opportunistic ones. Most but not all of these new infrastructures are based on virtualization techniques. In addition, some of them, present opportunities for multi-processor computing slots to the users. Virtual Organizations are therefore facing heterogeneity of the available resources and the use of an Interware software like DIRAC to provide the transparent, uniform interface has become essential. The transparent access to the underlying resources is realized by implementing the pilot model. DIRAC’s newest generation of generic pilots (the so-called Pilots 2.0) are the “pilots for all the skies”, and have been successfully released in production more than a year ago. They use a plugin mechanism that makes them easily adaptable. Pilots 2.0 have been used for fetching and running jobs on every type of resource, being it a Worker Node (WN) behind a CREAM/ARC/HTCondor/DIRAC Computing element, a Virtual Machine running on IaaC infrastructures like Vac or BOINC, on IaaS cloud resources managed by Vcycle, the LHCb High Level Trigger farm nodes, and any type of opportunistic computing resource. Make a machine a “Pilot Machine”, and all diversities between them will disappear. This contribution describes how pilots are made suitable for different resources, and the recent steps taken towards a fully unified framework, including monitoring. Also, the cases of multi-processor computing slots either on real or virtual machines, with the whole node or a partition of it, is discussed.
Levinson theorem for Dirac particles in n dimensions
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
Spacetime structure of massive Majorana particles and massive gravitino
Ahluwalia, D.V.; Kirchbach, M. [Theoretical Physics Group, Facultad de Fisica, Universidad Autonoma de Zacatecas, A.P. 600, 98062 Zacatecas (Mexico)
2003-07-01
The profound difference between Dirac and Majorana particles is traced back to the possibility of having physically different constructs in the (1/2, 0) 0 (0,1/2) representation space. Contrary to Dirac particles, Majorana-particle propagators are shown to differ from the simple linear {gamma} {mu} p{sub {mu}}, structure. Furthermore, neither Majorana particles, nor their antiparticles can be associated with a well defined arrow of time. The inevitable consequence of this peculiarity is the particle-antiparticle metamorphosis giving rise to neutrinoless double beta decay, on the one side, and enabling spin-1/2 fields to act as gauge fields, gauginos, on the other side. The second part of the lecture notes is devoted to massive gravitino. We argue that a spin measurement in the rest frame for an unpolarized ensemble of massive gravitino, associated with the spinor-vector [(1/2, 0) 0 (0,1/2)] 0 (1/2,1/2) representation space, would yield the results 3/2 with probability one half, and 1/2 with probability one half. The latter is distributed uniformly, i.e. as 1/4, among the two spin-1/2+ and spin-1/2- states of opposite parities. From that we draw the conclusion that the massive gravitino should be interpreted as a particle of multiple spin. (Author)
Relativistic Dirac-Fock and many-body perturbation calculations on He, He-like ions, Ne, and Ar
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
Dirac charge dynamics in graphene by infrared spectroscopy
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
de Rham, Claudia
2014-01-01
We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali–Gabadadze–Porrati model (DGP), cascading gravity, and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware–Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally, we present alt...
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...
Bergshoeff, E.; Ortin, T.
1998-01-01
We investigate the effective world-volume theories of branes in a background given by (the bosonic sector of) 10-dimensional massive IIA supergravity (''''massive branes'''') and their M-theoretic origin. In the case of the solitonic 5-brane of type IIA superstring theory the construction of the Wess-Zumino term in the world-volume action requires a dualization of the massive Neveu-Schwarz/Neveu-Schwarz target space 2-form field. We find that, in general, the effective world-volume theory of massive branes contains new world-volume fields that are absent in the massless case, i.e. when the mass parameter m of massive IIA supergravity is set to zero. We show how these new world-volume fields can be introduced in a systematic way. (orig.)
LHCb: LHCbDirac is a DIRAC extension to support LHCb specific workflows
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...
A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene
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.
Yan, Weixian, E-mail: wxyansxu@gmail.com
2017-01-01
The tunneling of the massless and massive Dirac particle through the strained barriers driven by the time-periodic scalar potentials and the static vector potentials is investigated, where the interrelationships among the strain, the incidence angle, the dynamic scalar potential, the magnetic field and the transmission of the Dirac particle have been discussed. In either massless or massive case, the intersection angle between the obliquely incident Dirac particle and strain determines the extent of deviation of the tunneling profiles from the strainless case. The time-periodic scalar potentials can enhance the capability of the Dirac particle to surmount the energy gap induced by the mass, reflecting quantum nature of the photon-assisted tunneling. When the magnetic field is switched on, the transmission overall presents a remarkably different profile, and decreases with the increase of the magnetic fields due to the conservation of the transverse momentum, which reduces the number of the side-band channels for tunneling.
The strangest man. The hidden life of Paul Dirac
Farmelo, Graham
2016-01-01
The Strangest Man is the Costa Biography Award-winning account of Paul Dirac, the famous physicist sometimes called the British Einstein. He was one of the leading pioneers of the greatest revolution in twentieth-century science: quantum mechanics. The youngest theoretician ever to win the Nobel Prize for Physics, he was also pathologically reticent, strangely literal-minded and legendarily unable to communicate or empathize. Through his greatest period of productivity, his postcards home contained only remarks about the weather. Based on a previously undiscovered archive of family papers, Graham Farmelo celebrates Dirac's massive scientific achievement while drawing a compassionate portrait of his life and work. Farmelo shows a man who, while hopelessly socially inept, could manage to love and sustain close friendship. The Strangest Man is an extraordinary and moving human story, as well as a study of one of the most exciting times in scientific history.
Quasi-Dirac neutrino oscillations
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.
Farmelo, Graham
2016-07-01
The Strangest Man is the Costa Biography Award-winning account of Paul Dirac, the famous physicist sometimes called the British Einstein. He was one of the leading pioneers of the greatest revolution in twentieth-century science: quantum mechanics. The youngest theoretician ever to win the Nobel Prize for Physics, he was also pathologically reticent, strangely literal-minded and legendarily unable to communicate or empathize. Through his greatest period of productivity, his postcards home contained only remarks about the weather. Based on a previously undiscovered archive of family papers, Graham Farmelo celebrates Dirac's massive scientific achievement while drawing a compassionate portrait of his life and work. Farmelo shows a man who, while hopelessly socially inept, could manage to love and sustain close friendship. The Strangest Man is an extraordinary and moving human story, as well as a study of one of the most exciting times in scientific history.
Fermi field and Dirac oscillator in a Som-Raychaudhuri space-time
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.
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.
A sequence of Clifford algebras and three replicas of Dirac particle
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)
Spacetime structure of massive Majorana particles and massive gravitino
Ahluwalia, D V
2003-01-01
The profound difference between Dirac and Majorana particles is traced back to the possibility of having physically different constructs in the (1/2, 0) 0 (0,1/2) representation space. Contrary to Dirac particles, Majorana-particle propagators are shown to differ from the simple linear gamma mu p submu, structure. Furthermore, neither Majorana particles, nor their antiparticles can be associated with a well defined arrow of time. The inevitable consequence of this peculiarity is the particle-antiparticle metamorphosis giving rise to neutrinoless double beta decay, on the one side, and enabling spin-1/2 fields to act as gauge fields, gauginos, on the other side. The second part of the lecture notes is devoted to massive gravitino. We argue that a spin measurement in the rest frame for an unpolarized ensemble of massive gravitino, associated with the spinor-vector [(1/2, 0) 0 (0,1/2)] 0 (1/2,1/2) representation space, would yield the results 3/2 with probability one half, and 1/2 with probability one half. The ...
The Dirac medals of the ICTP. 1993
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
Quantum tunneling effect of Dirac particles in a Schwarzschild-Godel space-time
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)
On the equation of motion in electrodynamics
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
Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones
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...
A toy model for higher spin Dirac operators
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.
Heun Polynomials and Exact Solutions for the Massless Dirac Particle in the C-Metric
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.
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
Dirac, Prof. Paul Adrien Maurice
Home; Fellowship. Fellow Profile. Elected: 1935 Honorary. Dirac, Prof. Paul Adrien Maurice Nobel Laureate (Physics) - 1933. Date of birth: 8 August 1902. Date of death: 20 October 1984. YouTube; Twitter; Facebook; Blog. Academy News. IAS Logo. 29th Mid-year meeting. Posted on 19 January 2018. The 29th Mid-year ...
Dirac, Jordan and quantum fields
Darrigol, O.
1985-01-01
The case of two principal physicists of quantum mechanics is specially chose: Paul Dirac and Pascual Jordan. They gave a signification and an importance very different to the notion of quantum field, and in particular to the quantized matter wave one. Through their formation and motivation differences, such as they are expressed in their writings, this deep difference is tentatively understood [fr
about the Dirac Delta Function(?)
V Balakrishnan is in the. Department of ... and sweet as befits this impatient age. It said (in its en- ... to get down to real work by shutting down the system and reverting to ... the Dirac delta function" - but do note the all-important question mark in ...
Superconductivity in doped Dirac semimetals
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.
Dirac Magnons in Honeycomb Ferromagnets
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
Dirac Magnons in Honeycomb Ferromagnets
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
Radiationless Zitterbewegung of Dirac particles and mass formula
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
Graphene based d-character Dirac Systems
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.
DIRAC pilot framework and the DIRAC Workload Management System
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.
DIRAC pilot framework and the DIRAC Workload Management System
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.
Two-spinor description of massive particles and relativistic spin projection operators
Isaev, A. P.; Podoinitsyn, M. A.
2018-04-01
On the basis of the Wigner unitary representations of the covering group ISL (2 , C) of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinor formalism we construct spin-vectors of polarizations and obtain conditions that fix the corresponding relativistic spin projection operators (Behrends-Fronsdal projection operators). With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends-Fronsdal projection operators) and then find relativistic spin projection operators for half integer spins. These projection operators determine the numerators in the propagators of fields of relativistic particles. We deduce generalizations of the Behrends-Fronsdal projection operators for arbitrary space-time dimensions D > 2.
Constrained dynamics of universally coupled massive spin 2-spin 0 gravities
Pitts, J Brian
2006-01-01
The 2-parameter family of massive variants of Einsteins gravity (on a Minkowski background) found by Ogievetsky and Polubarinov by excluding lower spins can also be derived using universal coupling. A Dirac-Bergmann constrained dynamics analysis seems not to have been presented for these theories, the Freund-Maheshwari-Schonberg special case, or any other massive gravity beyond the linear level treated by Marzban, Whiting and van Dam. Here the Dirac-Bergmann apparatus is applied to these theories. A few remarks are made on the question of positive energy. Being bimetric, massive gravities have a causality puzzle, but it appears soluble by the introduction and judicious use of gauge freedom
Dirac spinors for doubly special relativity and κ-Minkowski noncommutative spacetime
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
Supersymmetric Dirac particles in Riemann-Cartan space-time
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.)
On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk
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
DIRAC in Large Particle Physics Experiments
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.
Halogenated arsenenes as Dirac materials
Tang, Wencheng; Sun, Minglei; Ren, Qingqiang; Wang, Sake; Yu, Jin
2016-01-01
Highlights: • We have revealed the presence of Dirac cone in fully-halogenated arsenene compounds. • All fully-halogenated arsenene except As_2I_2 would spontaneously form and stable in defending the thermal fluctuation in room temperature. - Abstract: Arsenene is the graphene-like arsenic nanosheet, which has been predicted very recently [S. Zhang, Z. Yan, Y. Li, Z. Chen, and H. Zeng, Angewandte Chemie, 127 (2015) 3155–3158]. Using first-principles calculations, we systematically investigate the structures and electronic properties of fully-halogenated arsenenes. Formation energy analysis reveals that all the fully-halogenated arsenenes except iodinated arsenene are energetically favorable and could be synthesized. We have revealed the presence of Dirac cone in fully-halogenated arsenene compounds. They may have great potential applications in next generation of high-performance devices.
Precisely predictable Dirac observables
Cordes, Heinz Otto
2006-01-01
This work presents a "Clean Quantum Theory of the Electron", based on Dirac’s equation. "Clean" in the sense of a complete mathematical explanation of the well known paradoxes of Dirac’s theory, and a connection to classical theory, including the motion of a magnetic moment (spin) in the given field, all for a charged particle (of spin ½) moving in a given electromagnetic field. This theory is relativistically covariant, and it may be regarded as a mathematically consistent quantum-mechanical generalization of the classical motion of such a particle, à la Newton and Einstein. Normally, our fields are time-independent, but also discussed is the time-dependent case, where slightly different features prevail. A "Schroedinger particle", such as a light quantum, experiences a very different (time-dependent) "Precise Predictablity of Observables". An attempt is made to compare both cases. There is not the Heisenberg uncertainty of location and momentum; rather, location alone possesses a built-in uncertainty ...
DIRAC: Secure web user interface
Casajus Ramo, A; Sapunov, M
2010-01-01
Traditionally the interaction between users and the Grid is done with command line tools. However, these tools are difficult to use by non-expert users providing minimal help and generating outputs not always easy to understand especially in case of errors. Graphical User Interfaces are typically limited to providing access to the monitoring or accounting information and concentrate on some particular aspects failing to cover the full spectrum of grid control tasks. To make the Grid more user friendly more complete graphical interfaces are needed. Within the DIRAC project we have attempted to construct a Web based User Interface that provides means not only for monitoring the system behavior but also allows to steer the main user activities on the grid. Using DIRAC's web interface a user can easily track jobs and data. It provides access to job information and allows performing actions on jobs such as killing or deleting. Data managers can define and monitor file transfer activity as well as check requests set by jobs. Production managers can define and follow large data productions and react if necessary by stopping or starting them. The Web Portal is build following all the grid security standards and using modern Web 2.0 technologies which allow to achieve the user experience similar to the desktop applications. Details of the DIRAC Web Portal architecture and User Interface will be presented and discussed.
Photon-Assisted Spectroscopy of Dirac Electrons in Graphene
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.
The causal perturbation expansion revisited: Rescaling the interacting Dirac sea
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.
The causal perturbation expansion revisited: Rescaling the interacting Dirac sea
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.
Double Dirac cones in phononic crystals
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.
Data Management System of the DIRAC Project
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...
The DIRAC Data Management System (poster)
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...
Double Dirac cones in phononic crystals
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.
The Dirac medals of the ICTP. 1993
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
LHCbDIRAC as Apache Mesos microservices
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...
LHCbDIRAC as Apache Mesos microservices
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.
Symmetry and exact solutions of nonlinear spinor equations
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.)
Exact Solutions in 3D New Massive Gravity
Ahmedov, Haji; Aliev, Alikram N.
2011-01-01
We show that the field equations of new massive gravity (NMG) consist of a massive (tensorial) Klein-Gordon-type equation with a curvature-squared source term and a constraint equation. We also show that, for algebraic type D and N spacetimes, the field equations of topologically massive gravity (TMG) can be thought of as the “square root” of the massive Klein-Gordon-type equation. Using this fact, we establish a simple framework for mapping all types D and N solutions of TMG into NMG. Finally, we present new examples of types D and N solutions to NMG.
Fijany, A. [Jet Propulsion Lab., Pasadena, CA (United States); Coley, T.R. [Virtual Chemistry, Inc., San Diego, CA (United States); Cagin, T.; Goddard, W.A. III [California Institute of Technology, Pasadena, CA (United States)
1997-12-31
Successful molecular dynamics (MD) simulation of large systems (> million atoms) for long times (> nanoseconds) requires the integration of constrained equations of motion (CEOM). Constraints are used to eliminate high frequency degrees of freedom (DOF) and to allow the use of rigid bodies. Solving the CEOM allows for larger integration time-steps and helps focus the simulation on the important collective dynamics of chemical, biological, and materials systems. We explore advances in multibody dynamics which have resulted in O(N) algorithms for propagating the CEOM. However, because of their strictly sequential nature, the computational time required by these algorithms does not scale down with increased numbers of processors. We then present the new constraint force algorithm for solving the CEOM and show that this algorithm is fully parallelizable, leading to a computational cost of O(N/P+IogP) for N DOF on P processors.
Massive gravity from bimetric gravity
Baccetti, Valentina; Martín-Moruno, Prado; Visser, Matt
2013-01-01
We discuss the subtle relationship between massive gravity and bimetric gravity, focusing particularly on the manner in which massive gravity may be viewed as a suitable limit of bimetric gravity. The limiting procedure is more delicate than currently appreciated. Specifically, this limiting procedure should not unnecessarily constrain the background metric, which must be externally specified by the theory of massive gravity itself. The fact that in bimetric theories one always has two sets of metric equations of motion continues to have an effect even in the massive gravity limit, leading to additional constraints besides the one set of equations of motion naively expected. Thus, since solutions of bimetric gravity in the limit of vanishing kinetic term are also solutions of massive gravity, but the contrary statement is not necessarily true, there is no complete continuity in the parameter space of the theory. In particular, we study the massive cosmological solutions which are continuous in the parameter space, showing that many interesting cosmologies belong to this class. (paper)
Holographically viable extensions of topologically massive and minimal massive gravity?
Altas, Emel; Tekin, Bayram
2016-01-01
Recently [E. Bergshoeff et al., Classical Quantum Gravity 31, 145008 (2014)], an extension of the topologically massive gravity (TMG) in 2 +1 dimensions, dubbed as minimal massive gravity (MMG), which is free of the bulk-boundary unitarity clash that inflicts the former theory and all the other known three-dimensional theories, was found. Field equations of MMG differ from those of TMG at quadratic terms in the curvature that do not come from the variation of an action depending on the metric alone. Here we show that MMG is a unique theory and there does not exist a deformation of TMG or MMG at the cubic and quartic order (and beyond) in the curvature that is consistent at the level of the field equations. The only extension of TMG with the desired bulk and boundary properties having a single massive degree of freedom is MMG.
Mitra, Sukanya [Indian Institute of Technology Gandhinagar, Gandhinagar, Gujarat (India)
2018-01-15
The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis' entropy formula, the fundamental principles of thermostatistics are established for a grand canonical system having q-generalized BE/FD degrees of freedom. Many particle kinetic theory is set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws are realized in terms of appropriate moments of the transport equation. The thermodynamic quantities are obtained in a weak non-extensive environment for a massive pion-nucleon and a massless quark-gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the q-modified effective coupling are estimated for a quark-gluon system. (orig.)
Mitra, Sukanya
2018-01-01
The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis' entropy formula, the fundamental principles of thermostatistics are established for a grand canonical system having q-generalized BE/FD degrees of freedom. Many particle kinetic theory is set up in terms of the relativistic transport equation with q-generalized Uehling-Uhlenbeck collision term. The conservation laws are realized in terms of appropriate moments of the transport equation. The thermodynamic quantities are obtained in a weak non-extensive environment for a massive pion-nucleon and a massless quark-gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the q-modified effective coupling are estimated for a quark-gluon system.
Karbstein, Felix
2009-01-01
We introduce a new method for dealing with fermionic quantum field theories amenable to a mean-field-type approximation. In this work we focus on the relativistic Hartree approximation. Our aim is to integrate out the Dirac sea and derive a no-sea effective theory'' with positive energy single particle states only. As the derivation of the no-sea effective theory involves only standard Feynman diagrams, our approach is quite general and not restricted to particular space-time dimensions. We develop and illustrate the approach in the ''large N'' limit of the Gross-Neveu model family in 1+1 dimensions. As the Gross-Neveu model has been intensely studied and several analytical solutions are known for this model, it is an ideal testing ground for our no-sea effective theory approach. The chiral Gross-Neveu model, also referred to as 1+1 dimensional Nambu-Jona-Lasinio model, turns out to be of particular interest. In this case, we explicitly derive a consistent effective theory featuring both elementary ''π meson'' fields and (positive energy) ''quark'' fields, starting from a purely fermionic quantum field theory. In the second part of this work, we apply our approach to the Walecka model in 1+1 and 3+1 dimensions. As the Dirac sea caused considerable difficulties in attempts to base nuclear physics on field theoretic models like the Walecka model, mean-field calculations were typically done without the sea. We confront several of these mean-field theory results with our no-sea effective theory approach. The potential of our approach is twofold. While the no-sea effective theory can be utilized to provide new analytical insights in particular parameter regimes, it also sheds new light on more fundamental issues as the explicit emergence of effective, Dirac-sea induced multi-fermion interactions in an effective theory with positive energy states only. (orig.)
A new formalism for Dirac-like theories with curved space-time
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
Dirac tensor with heavy photon
Bytev, V.V.; Kuraev, E.A. [Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Scherbakova, E.S. [Hamburg Univ. (Germany). 1. Inst. fuer Theoretische Physik
2012-01-15
For the large-angles hard photon emission by initial leptons in process of high energy annihilation of e{sup +}e{sup -} {yields} to hadrons the Dirac tensor is obtained, taking into account the lowest order radiative corrections. The case of large-angles emission of two hard photons by initial leptons is considered. This result is being completed by the kinematics case of collinear hard photons emission as well as soft virtual and real photons and can be used for construction of Monte-Carlo generators. (orig.)
Semi-Dirac points in phononic crystals
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
LHCbDIRAC as Apache Mesos microservices
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...
Dirac operators on coset spaces
Balachandran, A.P.; Immirzi, Giorgio; Lee, Joohan; Presnajder, Peter
2003-01-01
The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact connected Lie groups and G is simple. An elementary discussion of the differential geometric and bundle theoretic aspects of G/H, including its projective modules and complex, Kaehler and Riemannian structures, is presented for this purpose. An attractive feature of our approach is that it transparently shows obstructions to spin- and spin c -structures. When a manifold is spin c and not spin, U(1) gauge fields have to be introduced in a particular way to define spinors, as shown by Avis, Isham, Cahen, and Gutt. Likewise, for manifolds like SU(3)/SO(3), which are not even spin c , we show that SU(2) and higher rank gauge fields have to be introduced to define spinors. This result has potential consequences for string theories if such manifolds occur as D-branes. The spectra and eigenstates of the Dirac operator on spheres S n =SO(n+1)/SO(n), invariant under SO(n+1), are explicitly found. Aspects of our work overlap with the earlier research of Cahen et al
Nonstandard Supersymmetry Breaking and Dirac Gaugino Masses without Supersoftness
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.
The bundles of algebraic and Dirac-Hestenes spinor fields
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
Confinement limit of a Dirac particle in two and three dimensions
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.
Dirac fields in loop quantum gravity and big bang nucleosynthesis
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.
Karbstein, Felix
2009-07-08
We introduce a new method for dealing with fermionic quantum field theories amenable to a mean-field-type approximation. In this work we focus on the relativistic Hartree approximation. Our aim is to integrate out the Dirac sea and derive a no-sea effective theory'' with positive energy single particle states only. As the derivation of the no-sea effective theory involves only standard Feynman diagrams, our approach is quite general and not restricted to particular space-time dimensions. We develop and illustrate the approach in the ''large N'' limit of the Gross-Neveu model family in 1+1 dimensions. As the Gross-Neveu model has been intensely studied and several analytical solutions are known for this model, it is an ideal testing ground for our no-sea effective theory approach. The chiral Gross-Neveu model, also referred to as 1+1 dimensional Nambu-Jona-Lasinio model, turns out to be of particular interest. In this case, we explicitly derive a consistent effective theory featuring both elementary ''{pi} meson'' fields and (positive energy) ''quark'' fields, starting from a purely fermionic quantum field theory. In the second part of this work, we apply our approach to the Walecka model in 1+1 and 3+1 dimensions. As the Dirac sea caused considerable difficulties in attempts to base nuclear physics on field theoretic models like the Walecka model, mean-field calculations were typically done without the sea. We confront several of these mean-field theory results with our no-sea effective theory approach. The potential of our approach is twofold. While the no-sea effective theory can be utilized to provide new analytical insights in particular parameter regimes, it also sheds new light on more fundamental issues as the explicit emergence of effective, Dirac-sea induced multi-fermion interactions in an effective theory with positive energy states only. (orig.)
Dirac matrices for Chern-Simons gravity
Izaurieta, Fernando; Ramirez, Ricardo; Rodriguez, Eduardo [Departamento de Matematica y Fisica Aplicadas, Universidad Catolica de la Santisima Concepcion, Alonso de Ribera 2850, 4090541 Concepcion (Chile)
2012-10-06
A genuine gauge theory for the Poincare, de Sitter or anti-de Sitter algebras can be constructed in (2n- 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices {Gamma}{sub ab} in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices {Gamma}{sub ab} can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient {alpha}{sub s}. We then give a general algorithm that computes the {alpha}-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B{sup ab} with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, 'minimal' algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.
Dirac fermions in blue-phosphorus
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)
Dirac cones in isogonal hexagonal metallic structures
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.
Benoit-Lévy, Aurélien; Chardin, Gabriel
2014-05-01
We study an unconventional cosmology, in which we investigate the consequences that antigravity would pose to cosmology. We present the main characteristics of the Dirac-Milne Universe, a cosmological model where antimatter has a negative active gravitational mass. In this non-standard Universe, separate domains of matter and antimatter coexist at our epoch without annihilation, separated by a gravitationally induced depletion zone. We show that this cosmology does not require a priori the Dark Matter and Dark Energy components of the standard model of cosmology. Additionally, inflation becomes an unnecessary ingredient. Investigating this model, we show that the classical cosmological tests such as primordial nucleosynthesis, Type Ia supernovæ and Cosmic Microwave Background are surprisingly concordant.
On the possibilities of distinguishing Dirac from Majorana neutrinos
Zralek, M.
1997-01-01
The problem if existing neutrinos are Dirac or Majorana particles is considered in a very pedagogical way. After a few historical remarks we recall the theoretical description of neutral spin 1/2 particles, emphasizing the difference between chirality and helicity which is important in our discussion. Next we describe the properties of neutrinos in the cases when their interactions are given by the standard model and by its extensions (massive neutrinos, right-handed currents, electromagnetic neutrino interaction, interaction with scalar particles). Various processes where the different nature of neutrinos could in principle be visible are reviewed. We clear up misunderstandings which have appeared in last suggestions how to distinguish both types of neutrinos. (author)
A Formulation of Quantum Field Theory Realizing a Sea of Interacting Dirac Particles
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.
Symmetries and Dirac equation solutions; Simetrias e solucoes da equacao de Dirac
Souza, Marcio Lima de
1991-06-01
The purpose of this thesis is the extension to be relativistic case of a method that has proved useful for the solution of various potential problems in non relativistic situation. This method, the method of dynamical symmetries, is based on the Baker-Campbell-Hausdorf formulae and developed first for the particular example of the relativistic Coulomb problem. Here we generalize the method for a Hamiltonian that can be written as a linear combination of generators of the SO(2,1) group. As illustrative examples, we solve the problem of a charged particle in a constant magnetic field and the exponential magnetic field. (author). 21 refs.
On the level order for Dirac operators
Grosse, H.
1987-01-01
We start from the Dirac operator for the Coulomb potential and prove within first order perturbation theory that degenerate levels split in a definite way depending on the sign of the Laplacian of the perturbing potential. 9 refs. (Author)
Dirac gap-induced graphene quantum dot in an electrostatic potential
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.
Wave equation of hydrogen atom
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)
Data acquisition software for DIRAC experiment
Ol'shevskij, V.G.; Trusov, S.V.
2000-01-01
The structure and basic processes of data acquisition software of DIRAC experiment for the measurement of π + π - atom life-time are described. The experiment is running on PS accelerator of CERN. The developed software allows one to accept, record and distribute to consumers up to 3 Mbytes of data in one accelerator supercycle of 14.4 s duration. The described system is used successfully in the DIRAC experiment starting from 1998 year
Deuteron stripping reactions using dirac phenomenology
Hawk, E. A.; McNeil, J. A.
2001-04-01
In this work deuteron stripping reactions are studied using the distorted wave born approximation employing dirac phenomenological potentials. In 1982 Shepard and Rost performed zero-range dirac phenomenological stripping calculations and found a dramatic reduction in the predicted cross sections when compared with similar nonrelativistic calculations. We extend the earlier work by including full finite range effects as well as the deuteron's internal D-state. Results will be compared with traditional nonrelativistic approaches and experimental data at low energy.
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.
Dirac Fermions in an Antiferromagnetic Semimetal
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.
Dirac Hamiltonian and Reissner-Nordström metric: Coulomb interaction in curved space-time
Noble, J. H.; Jentschura, U. D.
2016-03-01
We investigate the spin-1 /2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG , where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.
Continuity relations and quantum wave equations
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.
Massive and massless gauge fields of any spin and symmetry
Hussain, F.; Jarvis, P.D.
1988-05-01
An analysis of the BRST approach to massive and massless gauge fields of any spin and symmetry is presented. Previous results on massless gauge fields are extended to totally antisymmetric massless tensors and Kaehler-Dirac particles. Two methods for arriving at a BRST invariant, massive theory from the corresponding massless one are discussed. The first allows for an interpretation in terms of dimensional reduction, while the second keeps the BRST operator of the massless theory, but employs gauge invariant fields. (author). 10 refs
Inversion of reflection for the one-dimensional Dirac equation
Clerk, G.L.; Davies, A.J.
1991-01-01
It is a general result of one-dimensional non-relativistic quantum mechanics that the coefficient of reflection (reflected flux) is the same irrespective of the direction of traversing a potential barrier, a result that is independent of the barrier shape. In this note, the authors consider the transmission coefficient instead, and derive a strong result, namely that the transmission amplitude is independent of the direction of barrier traversal. That is, the transmission amplitude has the same complex phase as well as being unchanged in magnitude by changing the barrier around. This process was called inversion of reflection. 2 refs
Dirac equation, hydrogen atom spectrum and the Lamb shift in ...
commutative spaces (DNCS or τ -space). Using this Hamiltonian we calculate the energy shift of the ground state as well the 2 P 1 / 2 , 2 S 1 / 2 levels. In all the cases, the energy shift depends on the dynamical non-commutative parameter τ .
Moving potential for Dirac and Klein–Gordon equations
2015-11-27
Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science (IWCCMP-2015). Posted on November 27, 2015. Guest Editors: Anurag Srivastava, C. S. Praveen, H. S. Tewari. © 2015 Indian Academy of Sciences, Bengaluru. Contact | Site index.
Dirac equation, hydrogen atom spectrum and the Lamb shift in ...
2017-04-12
Apr 12, 2017 ... Abstract. We derive the relativistic Hamiltonian of hydrogen atom in dynamical non-commutative spaces. (DNCS or τ-space). Using this Hamiltonian we calculate the energy shift of the ground state as well the 2P1/2, 2S1/2 levels. In all the cases, the energy shift depends on the dynamical non-commutative ...
Numerical approach to CP-violating dirac equation
Funakubo, Koichi [Saga Univ. (Japan). Dept. of Physics; Kakuto, Akira; Otsuki, Shoichiro; Toyoda, Fumihiko
1996-05-01
We propose a new method to evaluate the chiral charge flux, which is converted into baryon number in the framework of the charge transport scenario of electroweak baryogenesis. By the new method, one can calculate the flux in the background of any type of bubble wall with any desired accuracy. (author)
Approximate eigensolutions of Dirac equation for the superposition ...
2014-07-02
Jul 2, 2014 ... tion [5], superdeformation [6], identical bands [7] and magnetic moment [8]. ... angular momentum ˜l is nothing but the orbital angular momentum of the lower compo- ... However, the dependence of the quality of PSS on the relativistic effect has not been ... symmetries in the framework of the NU method.
Viability of Dirac phase leptogenesis
Anisimov, Alexey; Blanchet, Steve; Di Bari, Pasquale
2008-01-01
We discuss the conditions for a non-vanishing Dirac phase δ and mixing angle θ 13 , sources of CP violation in neutrino oscillations, to be uniquely responsible for the observed matter–antimatter asymmetry of the Universe through leptogenesis. We show that this scenario, that we call δ-leptogenesis, is viable when the degenerate limit for the heavy right-handed (RH) neutrino spectrum is considered. We derive an interesting joint condition on sinθ 13 and the absolute neutrino mass scale that can be tested in future neutrino oscillation experiments. In the limit of the hierarchical heavy RH neutrino spectrum, we strengthen the previous result that δ-leptogenesis is only very marginally allowed, even when the production from the two heavier RH neutrinos is taken into account. An improved experimental upper bound on sinθ 13 and/or an account of quantum kinetic effects could completely rule out this option in the future. Therefore, δ-leptogenesis can be also regarded as motivation for models with degenerate heavy neutrino spectrum
General-Covariant Quantum Mechanics of Dirac Particle in Curved Space-Times
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
The motion of a Dirac wave packet in a gravitational field
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
Minimal theory of massive gravity
De Felice, Antonio; Mukohyama, Shinji
2016-01-01
We propose a new theory of massive gravity with only two propagating degrees of freedom. While the homogeneous and isotropic background cosmology and the tensor linear perturbations around it are described by exactly the same equations as those in the de Rham–Gabadadze–Tolley (dRGT) massive gravity, the scalar and vector gravitational degrees of freedom are absent in the new theory at the fully nonlinear level. Hence the new theory provides a stable nonlinear completion of the self-accelerating cosmological solution that was originally found in the dRGT theory. The cosmological solution in the other branch, often called the normal branch, is also rendered stable in the new theory and, for the first time, makes it possible to realize an effective equation-of-state parameter different from (either larger or smaller than) −1 without introducing any extra degrees of freedom.
Minimal theory of massive gravity
Antonio De Felice
2016-01-01
Full Text Available We propose a new theory of massive gravity with only two propagating degrees of freedom. While the homogeneous and isotropic background cosmology and the tensor linear perturbations around it are described by exactly the same equations as those in the de Rham–Gabadadze–Tolley (dRGT massive gravity, the scalar and vector gravitational degrees of freedom are absent in the new theory at the fully nonlinear level. Hence the new theory provides a stable nonlinear completion of the self-accelerating cosmological solution that was originally found in the dRGT theory. The cosmological solution in the other branch, often called the normal branch, is also rendered stable in the new theory and, for the first time, makes it possible to realize an effective equation-of-state parameter different from (either larger or smaller than −1 without introducing any extra degrees of freedom.
Relativistic wave equations for particles in electromagnetic fields
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
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.
Relativistic wave equations and compton scattering
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
First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals
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.
First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals
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.
Micromagnetic sensors and Dirac fermions in HgTe heterostructures
Buettner, Bastian
2012-08-06
Within the scope of this thesis two main topics have been investigated: the examination of micromagnetic sensors and transport of massive and massless Dirac fermions in HgTe quantum wells. For the investigation of localized, inhomogeneous magnetic fields, the fabrication and characterization of two different non-invasive and ultra sensitive sensors has been established at the chair ''Experimentelle Physik'' of the University of Wuerzburg. The first sensor is based on the young technique named micro-Hall magnetometry. The necessary semiconductor devices (Hall cross structures) were fabricated by high-resolution electron beam lithography based on two different two dimensional electron gases (2DEGs), namely InAs/(Al,Ga)Sb- and HgTe/(Hg,Cd)Te-heterostructures. The characteristics have been examined in two different ways. Measurements in homogeneous magnetic fields served for characterization of the sensors, whereas the investigation of artificially produced sub-{mu}m magnets substantiates the suitability of the devices for the study of novel nanoscale magnetic materials (e.g. nanowires). Systematic experiments with various magnets are in accordance with the theory of single-domain particles and anisotropic behavior due to shapes with high aspect ratio. The highest sensitivity for strongly localized fields was obtained at T=4.2 K for a (200.200) nm{sup 2} Hall cross - made from shallow, high mobility HgTe 2DEG. Although the field resolution was merely {delta}B{approx}100 {mu}T, the nanoscale sensor size yields an outstanding flux resolution of {delta}{Phi}=2.10{sup -3} {Phi}{sub 0}, where {Phi}{sub 0}=h/2e is the flux quantum. Translating this result in terms of magnetic moment, the sensitivity allows for the detection of magnetization changes of a particle centered on top of the sensor as low as {delta}M{approx}10{sup 2} {mu}{sub B}, with the magnetic moment of a single electron {mu}{sub B}, the Bohr magneton. The further examination of a permalloy nanomagnet with a
Micromagnetic sensors and Dirac fermions in HgTe heterostructures
Buettner, Bastian
2012-01-01
Within the scope of this thesis two main topics have been investigated: the examination of micromagnetic sensors and transport of massive and massless Dirac fermions in HgTe quantum wells. For the investigation of localized, inhomogeneous magnetic fields, the fabrication and characterization of two different non-invasive and ultra sensitive sensors has been established at the chair ''Experimentelle Physik'' of the University of Wuerzburg. The first sensor is based on the young technique named micro-Hall magnetometry. The necessary semiconductor devices (Hall cross structures) were fabricated by high-resolution electron beam lithography based on two different two dimensional electron gases (2DEGs), namely InAs/(Al,Ga)Sb- and HgTe/(Hg,Cd)Te-heterostructures. The characteristics have been examined in two different ways. Measurements in homogeneous magnetic fields served for characterization of the sensors, whereas the investigation of artificially produced sub-μm magnets substantiates the suitability of the devices for the study of novel nanoscale magnetic materials (e.g. nanowires). Systematic experiments with various magnets are in accordance with the theory of single-domain particles and anisotropic behavior due to shapes with high aspect ratio. The highest sensitivity for strongly localized fields was obtained at T=4.2 K for a (200.200) nm 2 Hall cross - made from shallow, high mobility HgTe 2DEG. Although the field resolution was merely δB∼100 μT, the nanoscale sensor size yields an outstanding flux resolution of δΦ=2.10 -3 Φ 0 , where Φ 0 =h/2e is the flux quantum. Translating this result in terms of magnetic moment, the sensitivity allows for the detection of magnetization changes of a particle centered on top of the sensor as low as δM∼10 2 μ B , with the magnetic moment of a single electron μ B , the Bohr magneton. The further examination of a permalloy nanomagnet with a cross-section of (100.20) nm 2 confirms the expected resolution ability
Micromagnetic sensors and Dirac fermions in HgTe heterostructures
Buettner, Bastian
2012-08-06
Within the scope of this thesis two main topics have been investigated: the examination of micromagnetic sensors and transport of massive and massless Dirac fermions in HgTe quantum wells. For the investigation of localized, inhomogeneous magnetic fields, the fabrication and characterization of two different non-invasive and ultra sensitive sensors has been established at the chair ''Experimentelle Physik'' of the University of Wuerzburg. The first sensor is based on the young technique named micro-Hall magnetometry. The necessary semiconductor devices (Hall cross structures) were fabricated by high-resolution electron beam lithography based on two different two dimensional electron gases (2DEGs), namely InAs/(Al,Ga)Sb- and HgTe/(Hg,Cd)Te-heterostructures. The characteristics have been examined in two different ways. Measurements in homogeneous magnetic fields served for characterization of the sensors, whereas the investigation of artificially produced sub-{mu}m magnets substantiates the suitability of the devices for the study of novel nanoscale magnetic materials (e.g. nanowires). Systematic experiments with various magnets are in accordance with the theory of single-domain particles and anisotropic behavior due to shapes with high aspect ratio. The highest sensitivity for strongly localized fields was obtained at T=4.2 K for a (200.200) nm{sup 2} Hall cross - made from shallow, high mobility HgTe 2DEG. Although the field resolution was merely {delta}B{approx}100 {mu}T, the nanoscale sensor size yields an outstanding flux resolution of {delta}{Phi}=2.10{sup -3} {Phi}{sub 0}, where {Phi}{sub 0}=h/2e is the flux quantum. Translating this result in terms of magnetic moment, the sensitivity allows for the detection of magnetization changes of a particle centered on top of the sensor as low as {delta}M{approx}10{sup 2} {mu}{sub B}, with the magnetic moment of a single electron {mu}{sub B}, the Bohr magneton. The further examination of a permalloy
Volfson, Boris
2013-09-01
The hypothesis of transition from a chaotic Dirac Sea, via highly unstable positronium, into a Simhony Model of stable face-centered cubic lattice structure of electrons and positrons securely bound in vacuum space, is considered. 13.75 Billion years ago, the new lattice, which, unlike a Dirac Sea, is permeable by photons and phonons, made the Universe detectable. Many electrons and positrons ended up annihilating each other producing energy quanta and neutrino-antineutrino pairs. The weak force of the electron-positron crystal lattice, bombarded by the chirality-changing neutrinos, may have started capturing these neutrinos thus transforming from cubic crystals into a quasicrystal lattice. Unlike cubic crystal lattice, clusters of quasicrystals are "slippery" allowing the formation of centers of local torsion, where gravity condenses matter into galaxies, stars and planets. In the presence of quanta, in a quasicrystal lattice, the Majorana neutrinos' rotation flips to the opposite direction causing natural transformations in a category comprised of three components; two others being positron and electron. In other words, each particle-antiparticle pair "e-" and "e+", in an individual crystal unit, could become either a quasi- component "e- ve e+", or a quasi- component "e+ - ve e-". Five-to-six six billion years ago, a continuous stimulation of the quasicrystal aetherial lattice by the same, similar, or different, astronomical events, could have triggered Hebbian and anti-Hebbian learning processes. The Universe may have started writing script into its own aether in a code most appropriate for the quasicrystal aether "hardware": Eight three-dimensional "alphabet" characters, each corresponding to the individual quasi-crystal unit shape. They could be expressed as quantum Turing machine qubits, or, alternatively, in a binary code. The code numerals could contain terminal and nonterminal symbols of the Chomsky's hierarchy, wherein, the showers of quanta, forming the
Semi-Dirac points in phononic crystals
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
Generalized nonlinear Proca equation and its free-particle solutions
Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)
2016-06-15
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)
Strain engineering of Dirac cones in graphyne
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.
Melting of Domain Wall in Charge Ordered Dirac Electron of Organic Conductor α-(BEDT-TTF)2I3
Ohki, Daigo; Matsuno, Genki; Omori, Yukiko; Kobayashi, Akito
2018-05-01
The origin of charge order melting is identified by using the real space dependent mean-field theory in the extended Hubbard model describing an organic Dirac electron system α-(BEDT-TTF)2I3. In this model, the width of a domain wall which arises between different types of the charge ordered phase exhibits a divergent increase with decreasing the strength of electron-electron correlations. By analyzing the finite-size effect carefully, it is shown that the divergence coincides with a topological transition where a pair of Dirac cones merges in keeping with a finite gap. It is also clarified that the gap opening point and the topological transition point are different, which leads to the existence of an exotic massive Dirac electron phase with melted-type domain wall and gapless edge states. The present result also indicated that multiple metastable states are emerged in massive Dirac Electron phase. In the trivial charge ordered phase, the gapless domain-wall bound state takes place instead of the gapless edge states, accompanying with a form change of the domain wall from melted-type into hyperbolic-tangent-type.
Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones
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)
Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones
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.
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.
Dirac operator on spaces with conical singularities
Chou, A.W.
1982-01-01
The Dirac operator on compact spaces with conical singularities is studied via the separation of variables formula and the functional calculus of the Dirac Laplacian on the cone. A Bochner type vanishing theorem which gives topological obstructions to the existence of non-negative scalar curvature k greater than or equal to 0 in the singular case is proved. An index formula relating the index of the Dirac operator to the A-genus and Eta-invariant similar to that of Atiyah-Patodi-Singer is obtained. In an appendix, manifolds with boundary with non-negative scalar curvature k greater than or equal to 0 are studied, and several new results on constructing complete metrics with k greater than or equal to on them are obtained
LHCb: Monitoring the DIRAC Distribution System
Nandakumar, R; Santinelli, R
2009-01-01
DIRAC is the LHCb gateway to any computing grid infrastructure (currently supporting WLCG) and is intended to reliably run large data mining activities. The DIRAC system consists of various services (which wait to be contacted to perform actions) and agents (which carry out periodic activities) to direct jobs as required. An important part of ensuring the reliability of the infrastructure is the monitoring and logging of these DIRAC distributed systems. The monitoring is done collecting information from two sources - one is from pinging the services or by keeping track of the regular heartbeats of the agents, and the other from the analysis of the error messages generated by both agents and services and collected by the logging system. This allows us to ensure that he components are running properly and to collect useful information regarding their operations. The process status monitoring is displayed using the SLS sensor mechanism which also automatically allows one to plot various quantities and also keep ...
DIRAC - Distributed Infrastructure with Remote Agent Control
Tsaregorodtsev, A; Closier, J; Frank, M; Gaspar, C; van Herwijnen, E; Loverre, F; Ponce, S; Graciani Diaz, R.; Galli, D; Marconi, U; Vagnoni, V; Brook, N; Buckley, A; Harrison, K; Schmelling, M; Egede, U; Bogdanchikov, A; Korolko, I; Washbrook, A; Palacios, J P; Klous, S; Saborido, J J; Khan, A; Pickford, A; Soroko, A; Romanovski, V; Patrick, G N; Kuznetsov, G; Gandelman, M
2003-01-01
This paper describes DIRAC, the LHCb Monte Carlo production system. DIRAC has a client/server architecture based on: Compute elements distributed among the collaborating institutes; Databases for production management, bookkeeping (the metadata catalogue) and software configuration; Monitoring and cataloguing services for updating and accessing the databases. Locally installed software agents implemented in Python monitor the local batch queue, interrogate the production database for any outstanding production requests using the XML-RPC protocol and initiate the job submission. The agent checks and, if necessary, installs any required software automatically. After the job has processed the events, the agent transfers the output data and updates the metadata catalogue. DIRAC has been successfully installed at 18 collaborating institutes, including the DataGRID, and has been used in recent Physics Data Challenges. In the near to medium term future we must use a mixed environment with different types of grid mid...
DIRAC - The Distributed MC Production and Analysis for LHCb
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...
Cloud flexibility using DIRAC interware
Albor, Víctor Fernandez; Miguelez, Marcos Seco; Silva, Juan Jose Saborido; Pena, Tomas Fernandez; Muñoz, Victor Mendez; Diaz, Ricardo Graciani
2014-01-01
Communities of different locations are running their computing jobs on dedicated infrastructures without the need to worry about software, hardware or even the site where their programs are going to be executed. Nevertheless, this usually implies that they are restricted to use certain types or versions of an Operating System because either their software needs an definite version of a system library or a specific platform is required by the collaboration to which they belong. On this scenario, if a data center wants to service software to incompatible communities, it has to split its physical resources among those communities. This splitting will inevitably lead to an underuse of resources because the data centers are bound to have periods where one or more of its subclusters are idle. It is, in this situation, where Cloud Computing provides the flexibility and reduction in computational cost that data centers are searching for. This paper describes a set of realistic tests that we ran on one of such implementations. The test comprise software from three different HEP communities (Auger, LHCb and QCD phenomelogists) and the Parsec Benchmark Suite running on one or more of three Linux flavors (SL5, Ubuntu 10.04 and Fedora 13). The implemented infrastructure has, at the cloud level, CloudStack that manages the virtual machines (VM) and the hosts on which they run, and, at the user level, the DIRAC framework along with a VM extension that will submit, monitorize and keep track of the user jobs and also requests CloudStack to start or stop the necessary VM's. In this infrastructure, the community software is distributed via the CernVM-FS, which has been proven to be a reliable and scalable software distribution system. With the resulting infrastructure, users are allowed to send their jobs transparently to the Data Center. The main purpose of this system is the creation of flexible cluster, multiplatform with an scalable method for software distribution for
Cloud flexibility using DIRAC interware
Fernandez Albor, Víctor; Seco Miguelez, Marcos; Fernandez Pena, Tomas; Mendez Muñoz, Victor; Saborido Silva, Juan Jose; Graciani Diaz, Ricardo
2014-06-01
Communities of different locations are running their computing jobs on dedicated infrastructures without the need to worry about software, hardware or even the site where their programs are going to be executed. Nevertheless, this usually implies that they are restricted to use certain types or versions of an Operating System because either their software needs an definite version of a system library or a specific platform is required by the collaboration to which they belong. On this scenario, if a data center wants to service software to incompatible communities, it has to split its physical resources among those communities. This splitting will inevitably lead to an underuse of resources because the data centers are bound to have periods where one or more of its subclusters are idle. It is, in this situation, where Cloud Computing provides the flexibility and reduction in computational cost that data centers are searching for. This paper describes a set of realistic tests that we ran on one of such implementations. The test comprise software from three different HEP communities (Auger, LHCb and QCD phenomelogists) and the Parsec Benchmark Suite running on one or more of three Linux flavors (SL5, Ubuntu 10.04 and Fedora 13). The implemented infrastructure has, at the cloud level, CloudStack that manages the virtual machines (VM) and the hosts on which they run, and, at the user level, the DIRAC framework along with a VM extension that will submit, monitorize and keep track of the user jobs and also requests CloudStack to start or stop the necessary VM's. In this infrastructure, the community software is distributed via the CernVM-FS, which has been proven to be a reliable and scalable software distribution system. With the resulting infrastructure, users are allowed to send their jobs transparently to the Data Center. The main purpose of this system is the creation of flexible cluster, multiplatform with an scalable method for software distribution for several
All-Metallic Vertical Transistors Based on Stacked Dirac Materials
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 ...
A framework for unified Dirac gauginos
Benakli Karim
2017-01-01
Full Text Available We identify the Minimal Dirac Gaugino Supersymmetric Standard Model (MDGSSM as the minimal field content with Dirac gauginos allowing unification of gauge coupling. We stress that its parameter space describes also other most popular models as the MSSM, NMSSM and MRSSM. We discuss the generation of trilinear couplings in models of gauge mediation that has been overlooked in the past. We study the different source of Higgs mixings and constraints from the ƿ parameter. Finally, we provide new experimental limits on the masses of the scalar octets.
Dirac particle tunneling from black rings
Jiang Qingquan
2008-01-01
Recent research shows that Hawking radiation can be treated as a quantum tunneling process, and Hawking temperatures of Dirac particles across the horizon of a black hole can be correctly recovered via the fermion tunneling method. In this paper, motivated by the fermion tunneling method, we attempt to apply the analysis to derive Hawking radiation of Dirac particles via tunneling from black ring solutions of 5-dimensional Einstein-Maxwell-dilaton gravity theory. Finally, it is interesting to find that, as in the black hole case, fermion tunneling can also result in correct Hawking temperatures for the rotating neutral, dipole, and charged black rings.
Kapitza–Dirac effect with traveling waves
Hayrapetyan, Armen G; Götte, Jörg B; Grigoryan, Karen K; Petrosyan, Rubik G
2015-01-01
We report on the possibility of diffracting electrons from light waves traveling inside a dielectric medium. We show that, in the frame of reference which moves with the group velocity of light, the traveling wave acts as a stationary diffraction grating from which electrons can diffract, similar to the conventional Kapitza–Dirac effect. To characterize the Kapitza–Dirac effect with traveling light waves, we make use of the Hamiltonian Analogy between electron optics and quantum mechanics and apply the Helmholtz–Kirchhoff theory of diffraction. (fast track communication)
Bergshoeff, Eric A.; Hohm, Olaf; Townsend, Paul K.
2012-01-01
We present a brief review of New Massive Gravity, which is a unitary theory of massive gravitons in three dimensions obtained by considering a particular combination of the Einstein-Hilbert and curvature squared terms.
Generalization of the Dirac’s Equation and Sea
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...
Kondo effect in three-dimensional Dirac and Weyl systems
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
Dirac cones beyond the honeycomb lattice : a symmetry based approach
Miert, G. van; de Morais Smith, Cristiane
2016-01-01
Recently, several new materials exhibiting massless Dirac fermions have been proposed. However, many of these do not have the typical graphene honeycomb lattice, which is often associated with Dirac cones. Here, we present a classification of these different two-dimensional Dirac systems based on
Dirac Particle for the Position Dependent Mass in the Generalized Asymmetric Woods-Saxon Potential
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.
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.
Intrinsic and extrinsic spin Hall effects of Dirac electrons
Fukazawa, Takaaki; Kohno, Hiroshi; Fujimoto, Junji
2017-01-01
We investigate the spin Hall effect (SHE) of electrons described by the Dirac equation, which is used as an effective model near the L-points in bismuth. By considering short-range nonmagnetic impurities, we calculate the extrinsic as well as intrinsic contributions on an equal footing. The vertex corrections are taken into account within the ladder type and the so-called skew-scattering type. The intrinsic SHE which we obtain is consistent with that of Fuseya et al. It is found that the extrinsic contribution dominates the intrinsic one when the system is metallic. The extrinsic SHE due to the skew scattering is proportional to Δ/n i u, where 2Δ is the band gap, n i is the impurity concentration, and u is the strength of the impurity potential. (author)
Einstein-Dirac theory in spin maximum I
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
Dirac's Dream - the Search for the Magnetic Monopole
Pinfold, James L.
2010-01-01
I first quickly summarize the history of the Magnetic Monopole leading to the quantum theory of magnetic charge that started with a 1931 paper by Paul Dirac who showed that the existence of magnetic monopoles was consistent with Maxwell's equations only if electric charges are quantized. Next I will briefly review the status of monopole searches. Last, but not least I discuss in more detail the MoEDAL experiment--the latest accelerator experiment designed to search for direct production of magnetic monopoles or dyons (particles with electric and magnetic charge) and other highly ionizing particles - such as heavy (pseudo-) stable particles with conventional electric charge - at the LHC. The MoEDAL experiment employs nuclear track-etch detectors deployed in the VELO vertex region of the LHCb experiment.
Finger-gate manipulated quantum transport in Dirac materials
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)
Relativistic quantum Darwinism in Dirac fermion and graphene systems
Ni, Xuan; Huang, Liang; Lai, Ying-Cheng; Pecora, Louis
2012-02-01
We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which are signatures of relativistic quantum Darwinism (RQD). These localized states suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of quantum tunneling. Qualitatively similar phenomena have been observed in graphene. A physical theory is developed to explain relativistic quantum Darwinism and its effects based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the open cavity system.
A robust and general Schrödinger and Dirac solver for atomic structure calculations
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
Low momentum scattering of the Dirac particle with an asymmetric cusp potential
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.)
What is between Fermi-Dirac and Bose-Einstein Statistics?
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...
Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene
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...
Magnetoplasmons of the tilted-anisotropic Dirac cone material $\\alpha-$(BEDT-TTF)$_2$I$_3$
Sári, Judit; Toke, Csaba; Goerbig, Mark O.
2014-01-01
We study the collective modes of a low-energy continuum model of the quasi-two-dimensional electron liquid in a layer of the organic compound $\\alpha-$(BEDT-TTF)$_2$I$_3$ in a perpendicular magnetic field. As testified by zero magnetic field transport experiments and \\textit{ab initio} theory, this material hosts both massless and massive low-energy carriers, the former being described by tilted and anisotropic Dirac cones. The polarizability of these cones is anisotropic, and two sets of mag...
Dirac's minimum degree condition restricted to claws
Broersma, Haitze J.; Ryjacek, Z.; Schiermeyer, I.
1997-01-01
Let G be a graph on n 3 vertices. Dirac's minimum degree condition is the condition that all vertices of G have degree at least . This is a well-known sufficient condition for the existence of a Hamilton cycle in G. We give related sufficiency conditions for the existence of a Hamilton cycle or a
Ferreira, P.L.; Alcaras, J.A.C.
1980-01-01
The group theoretical properties of the Dirac groups of rank n are discussed together with the properties and construction of their IR's. The cases n even and n odd show distinct features. Furthermore, for n odd, the cases n=4K+1 and n=4K+3 exhibit some different properties too. (Author) [pt
Applications of Dirac's Delta Function in Statistics
Khuri, Andre
2004-01-01
The Dirac delta function has been used successfully in mathematical physics for many years. The purpose of this article is to bring attention to several useful applications of this function in mathematical statistics. Some of these applications include a unified representation of the distribution of a function (or functions) of one or several…
The Dirac operator on the Fuzzy sphere
Grosse, H.
1994-01-01
We introduce the Fuzzy analog of spinor bundles over the sphere on which the non-commutative analog of the Dirac operator acts. We construct the complete set of eigenstates including zero modes. In the commutative limit we recover known results. (authors)
First level trigger of the DIRAC experiment
Afanas'ev, L.G.; Karpukhin, V.V.; Kulikov, A.V.; Gallas, M.
2001-01-01
The logic of the first level trigger of the DIRAC experiment at CERN is described. A parallel running of different trigger modes with tagging of events and optional independent prescaling is realized. A CAMAC-based trigger system is completely computer controlled
Evolution kernel for the Dirac field
Baaquie, B.E.
1982-06-01
The evolution kernel for the free Dirac field is calculated using the Wilson lattice fermions. We discuss the difficulties due to which this calculation has not been previously performed in the continuum theory. The continuum limit is taken, and the complete energy eigenfunctions as well as the propagator are then evaluated in a new manner using the kernel. (author)
Poisson geometry from a Dirac perspective
Meinrenken, Eckhard
2018-03-01
We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.
Dirac relaxation of the Israel junction conditions: Unified Randall-Sundrum brane theory
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
The GridPP DIRAC project - DIRAC for non-LHC communities
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...
The GridPP DIRAC project - DIRAC for non-LHC communities
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.
Identifying Dirac cones in carbon allotropes with square symmetry
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.
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
Neutron stars structure in the context of massive gravity
Hendi, S.H.; Bordbar, G.H.; Panah, B. Eslam; Panahiyan, S., E-mail: hendi@shirazu.ac.ir, E-mail: ghbordbar@shirazu.ac.ir, E-mail: behzad.eslampanah@gmail.com, E-mail: sh.panahiyan@gmail.com [Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz 71454 (Iran, Islamic Republic of)
2017-07-01
Motivated by the recent interests in spin−2 massive gravitons, we study the structure of neutron star in the context of massive gravity. The modifications of TOV equation in the presence of massive gravity are explored in 4 and higher dimensions. Next, by considering the modern equation of state for the neutron star matter (which is extracted by the lowest order constrained variational (LOCV) method with the AV18 potential), different physical properties of the neutron star (such as Le Chatelier's principle, stability and energy conditions) are investigated. It is shown that consideration of the massive gravity has specific contributions into the structure of neutron star and introduces new prescriptions for the massive astrophysical objects. The mass-radius relation is examined and the effects of massive gravity on the Schwarzschild radius, average density, compactness, gravitational redshift and dynamical stability are studied. Finally, a relation between mass and radius of neutron star versus the Planck mass is extracted.
Neutron stars structure in the context of massive gravity
Hendi, S. H.; Bordbar, G. H.; Eslam Panah, B.; Panahiyan, S.
2017-07-01
Motivated by the recent interests in spin-2 massive gravitons, we study the structure of neutron star in the context of massive gravity. The modifications of TOV equation in the presence of massive gravity are explored in 4 and higher dimensions. Next, by considering the modern equation of state for the neutron star matter (which is extracted by the lowest order constrained variational (LOCV) method with the AV18 potential), different physical properties of the neutron star (such as Le Chatelier's principle, stability and energy conditions) are investigated. It is shown that consideration of the massive gravity has specific contributions into the structure of neutron star and introduces new prescriptions for the massive astrophysical objects. The mass-radius relation is examined and the effects of massive gravity on the Schwarzschild radius, average density, compactness, gravitational redshift and dynamical stability are studied. Finally, a relation between mass and radius of neutron star versus the Planck mass is extracted.
Neutron stars structure in the context of massive gravity
Hendi, S.H.; Bordbar, G.H.; Panah, B. Eslam; Panahiyan, S.
2017-01-01
Motivated by the recent interests in spin−2 massive gravitons, we study the structure of neutron star in the context of massive gravity. The modifications of TOV equation in the presence of massive gravity are explored in 4 and higher dimensions. Next, by considering the modern equation of state for the neutron star matter (which is extracted by the lowest order constrained variational (LOCV) method with the AV18 potential), different physical properties of the neutron star (such as Le Chatelier's principle, stability and energy conditions) are investigated. It is shown that consideration of the massive gravity has specific contributions into the structure of neutron star and introduces new prescriptions for the massive astrophysical objects. The mass-radius relation is examined and the effects of massive gravity on the Schwarzschild radius, average density, compactness, gravitational redshift and dynamical stability are studied. Finally, a relation between mass and radius of neutron star versus the Planck mass is extracted.
Alishahiha, Mohsen; Naseh, Ali; Shirzad, Ahmad
2014-12-03
We study linearized equations of motion of the newly proposed three dimensional gravity, known as minimal massive gravity, using its metric formulation. We observe that the resultant linearized equations are exactly the same as that of TMG by making use of a redefinition of the parameters of the model. In particular the model admits logarithmic modes at the critical points. We also study several vacuum solutions of the model, specially at a certain limit where the contribution of Chern-Simons term vanishes.
SARAH 3.2: Dirac gauginos, UFO output, and more
Staub, Florian
2013-07-01
. Nature of problem: To use Madgraph for new models it is necessary to provide the corresponding model files which include all information about the interactions of the model. However, the derivation of the vertices for a given model and putting those into model files which can be used with Madgraph is usually very time consuming. Dirac gauginos are not present in the minimal supersymmetric standard model (MSSM) or many extensions of it. Dirac mass terms for vector superfields lead to new structures in the supersymmetric (SUSY) Lagrangian (bilinear mass term between gaugino and matter fermion as well as new D-terms) and modify also the SUSY renormalization group equations (RGEs). The Dirac character of gauginos can change the collider phenomenology. In addition, they come with an extended Higgs sector for which a precise calculation of the 1-loop masses has not happened so far. Solution method: SARAH calculates the complete Lagrangian for a given model whose gauge sector can be any direct product of SU(N) gauge groups. The chiral superfields can transform as any, irreducible representation with respect to these gauge groups and it is possible to handle an arbitrary number of symmetry breakings or particle rotations. Also the gauge fixing is automatically added. Using this information, SARAH derives all vertices for a model. These vertices can be exported to model files in the UFO which is supported by Madgraph and other codes like GoSam, MadAnalysis or ALOHA. The user can also study models with Dirac gauginos. In that case SARAH includes all possible terms in the Lagrangian stemming from the new structures and can also calculate the RGEs. The entire impact of these terms is then taken into account in the output of SARAH to UFO, CalcHep, WHIZARD, FeynArts and SPheno. Reasons for new version: SARAH provides, with this version, the possibility of creating model files in the UFO format. The UFO format is supposed to become a standard format for model files which should be
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.
Prototype of a production system for Cherenkov Telescope Array with DIRAC
Arrabito, L; Bregeon, J; Haupt, A; Graciani Diaz, R; Stagni, F; Tsaregorodtsev, A
2015-01-01
The Cherenkov Telescope Array (CTA) — an array of many tens of Imaging Atmospheric Cherenkov Telescopes deployed on an unprecedented scale — is the next generation instrument in the field of very high energy gamma-ray astronomy. CTA will operate as an open observatory providing data products to the scientific community. An average data stream of about 10 GB/s for about 1000 hours of observation per year, thus producing several PB/year, is expected. Large CPU time is required for data-processing as well for massive Monte Carlo simulations needed for detector calibration purposes. The current CTA computing model is based on a distributed infrastructure for the archive and the data off-line processing. In order to manage the off-line data-processing in a distributed environment, CTA has evaluated the DIRAC (Distributed Infrastructure with Remote Agent Control) system, which is a general framework for the management of tasks over distributed heterogeneous computing environments. In particular, a production system prototype has been developed, based on the two main DIRAC components, i.e. the Workload Management and Data Management Systems. After three years of successful exploitation of this prototype, for simulations and analysis, we proved that DIRAC provides suitable functionalities needed for the CTA data processing. Based on these results, the CTA development plan aims to achieve an operational production system, based on the DIRAC Workload Management System, to be ready for the start of CTA operation phase in 2017-2018. One more important challenge consists of the development of a fully automatized execution of the CTA workflows. For this purpose, we have identified a third DIRAC component, the so-called Transformation System, which offers very interesting functionalities to achieve this automatisation. The Transformation System is a ’data-driven’ system, allowing to automatically trigger data-processing and data management operations according to pre
STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS
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.
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)
Quantum Hall effect of massless Dirac fermions and free fermions in Hofstadter's butterfly
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)
Dirac phenomenology and hyperon-nucleus interactions
Mares, J; Jennings, B K [TRIUMF, Vancouver, British Columbia (Canada); Cooper, E D [Fraser Valley Univ. College, Chilliwack, British Columbia (Canada). Dept. of Physics
1993-05-01
We discuss various aspects of hyperon-nucleus interactions in the relativistic mean field theory. First, characteristics of {Lambda}, {Sigma} and {identical_to} hypernuclei, as well as multi strange baryonic objects, are investigated. The spin-orbit splittings and magnetic moments are shown to be very sensitive to the value of the tensor coupling f{omega}y. Second, optical potentials for {Lambda} and {Sigma} scattering off nuclei are developed based on a global nucleon-nucleon Dirac optical potential and SU(3) symmetry. The tensor coupling has a large effect on the predictions for the analyzing power. Third, the Dirac approach is used in the calculations of the non-mesonic decay of {Lambda} hypernuclei. The large discrepancy between the decay rates and data suggests the need for additional meson exchanges. (authors). 62 refs.,7 figs., 6 tabs.
Dirac neutrino masses from generalized supersymmetry breaking
Demir, D.A.; Everett, L.L.; Langacker, P.
2007-12-01
We demonstrate that Dirac neutrino masses in the experimentally preferred range are generated within supersymmetric gauge extensions of the Standard Model with a generalized supersymmetry breaking sector. If the usual superpotential Yukawa couplings are forbidden by the additional gauge symmetry (such as a U(1) ' ), effective Dirac mass terms involving the ''wrong Higgs'' field can arise either at tree level due to hard supersymmetry breaking fermion Yukawa couplings, or at one-loop due to nonanalytic or ''nonholomorphic'' soft supersymmetry breaking trilinear scalar couplings. As both of these operators are naturally suppressed in generic models of supersymmetry breaking, the resulting neutrino masses are naturally in the sub-eV range. The neutrino magnetic and electric dipole moments resulting from the radiative mechanism also vanish at one-loop order. (orig.)
Floquet-Engineered Valleytronics in Dirac Systems.
Kundu, Arijit; Fertig, H A; Seradjeh, Babak
2016-01-08
Valley degrees of freedom offer a potential resource for quantum information processing if they can be effectively controlled. We discuss an optical approach to this problem in which intense light breaks electronic symmetries of a two-dimensional Dirac material. The resulting quasienergy structures may then differ for different valleys, so that the Floquet physics of the system can be exploited to produce highly polarized valley currents. This physics can be utilized to realize a valley valve whose behavior is determined optically. We propose a concrete way to achieve such valleytronics in graphene as well as in a simple model of an inversion-symmetry broken Dirac material. We study the effect numerically and demonstrate its robustness against moderate disorder and small deviations in optical parameters.
Crucial test of the Dirac cosmologies
Steigman, G.
1978-01-01
In a cosmology consistent with the Cosmological Principle (large scale, statistical isotropy and homogeneity of the universe), a Planck spectrum is not preserved as the universe evolves unless the number of photons in a comoving volume is conserved. It is shown that a large class of cosmological models based on Dirac's Large Numbers Hypothesis (LNH) violate this constraint. The observed isotropy and spectral distribution of the microwave background radiation thus provide a crucial test of such cosmologies. After reviewing the LNH, the general evolution of radiation spectra in cosmologies consistent with the cosmological principle is outlined. It is shown that the predicted deviations from a Planck spectrum for Dirac cosmologies (as well as for ''tired-light'' cosmologies) are enormous. The Planckian (or near-Planckian) spectral form for the microwave radiation provides a crucial test, failed by such cosmologies
Excitation spectrum of correlated Dirac fermions
Jalali, Z.; Jafari, S. A.
2015-04-01
Motivated by the puzzling optical conductivity measurements in graphene, we speculate on the possible role of strong electronic correlations on the two-dimensional Dirac fermions. In this work we employ the slave-particle method to study the excitations of the Hubbard model on honeycomb lattice, away from half-filling. Since the ratio U/t ≈ 3.3 in graphene is not infinite, double occupancy is not entirely prohibited and hence a finite density of doublonscan be generated. We therefore extend the Ioff-Larkin composition rule to include a finite density of doublons. We then investigate the role played by each of these auxiliary particles in the optical absorption of strongly correlated Dirac fermions.
Dirac gauginos in low scale supersymmetry breaking
Goodsell, Mark D.; Tziveloglou, Pantelis
2014-01-01
It has been claimed that Dirac gaugino masses are necessary for realistic models of low-scale supersymmetry breaking, and yet very little attention has been paid to the phenomenology of a light gravitino when gauginos have Dirac masses. We begin to address this deficit by investigating the couplings and phenomenology of the gravitino in the effective Lagrangian approach. We pay particular attention to the phenomenology of the scalar octets, where new decay channels open up. This leads us to propose a new simplified effective scenario including only light gluinos, sgluons and gravitinos, allowing the squarks to be heavy – with the possible exception of the third generation. Finally, we comment on the application of our results to Fake Split Supersymmetry
Dirac operator, chirality and random matrix theory
Pullirsch, R.
2001-05-01
Quantum Chromodynamics (QCD) is considered to be the correct theory which describes quarks and gluons and, thus, all strong interaction phenomena from the fundamental forces of nature. However, important properties of QCD such as the physical mechanism of color confinement and the spontaneous breaking of chiral symmetry are still not completely understood and under extensive discussion. Analytical calculations are limited, because in the low-energy regime where quarks are confined, application of perturbation theory is restricted due to the large gluon coupling. A powerful tool to investigate numerically and analytically the non-perturbative region is provided by the lattice formulation of QCD. From Monte Carlo simulations of lattice QCD we know that chiral symmetry is restored above a critical temperature. As the chiral condensate is connected to the spectral density of the Dirac operator via the Banks-Casher relation, the QCD Dirac spectrum is an interesting object for detailed studies. In search for an analytical expression of the infrared limit of the Dirac spectrum it has been realized that chiral random-matrix theory (chRMT) is a suitable tool to compare with the distribution and the correlations of the small Dirac eigenvalues. Further, it has been shown that the correlations of eigenvalues on the scale of mean level spacings are universal for complex physical systems and are given by random-matrix theory (Rm). This has been formulated as the Baghouse-Giannoni-Schmit conjecture which states that spectral correlations of a classically chaotic system are given by RMT on the quantum level. The aim of this work is to analyze the relationship between chiral phase transitions and chaos to order transitions in quantum field theories. We study the eigenvalues of the Dirac operator for Quantum Electrodynamics (QED) with compact gauge group U(1) on the lattice. This theory shows chiral symmetry breaking and confinement in the strong coupling region. Although being
Renormalization group evolution of Dirac neutrino masses
Lindner, Manfred; Ratz, Michael; Schmidt, Michael Andreas
2005-01-01
There are good reasons why neutrinos could be Majorana particles, but there exist also a number of very good reasons why neutrinos could have Dirac masses. The latter option deserves more attention and we derive therefore analytic expressions describing the renormalization group evolution of mixing angles and of the CP phase for Dirac neutrinos. Radiative corrections to leptonic mixings are in this case enhanced compared to the quark mixings because the hierarchy of neutrino masses is milder and because the mixing angles are larger. The renormalization group effects are compared to the precision of current and future neutrino experiments. We find that, in the MSSM framework, radiative corrections of the mixing angles are for large tan β comparable to the precision of future experiments
LHCb: Pilot Framework and the DIRAC WMS
Graciani, R; Casajus, A
2009-01-01
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. Details of the implementation and the security aspects of this framework will be discussed.
Transversal Dirac families in Riemannian foliations
Glazebrook, J.F.; Kamber, F.W.
1991-01-01
We describe a family of differential operators parametrized by the transversal vector potentials of a Riemannian foliation relative to the Clifford algebra of the foliation. This family is non-elliptic but in certain ways behaves like a standard Dirac family in the absolute case as a result of its elliptic-like regularity properties. The analytic and topological indices of this family are defined as elements of K-theory in the parameter space. We indicate how the cohomology of the parameter space is described via suitable maps to Fredholm operators. We outline the proof of a theorem of Vafa-Witten type on uniform bounds for the eigenvalues of this family using a spectral flow argument. A determinant operator is also defined with the appropriate zeta function regularization dependent on the codimension of the foliation. With respect to a generalized coupled Dirac-Yang-Mills system, we indicate how chiral anomalies are located relative to the foliation. (orig.)
A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices
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.
Permanent Magnet Dipole for DIRAC Design Report
Vorozhtsov, Alexey
2012-01-01
Two dipole magnets including one spare unit are needed for the for the DIRAC experiment. The proposed design is a permanent magnet dipole. The design based on Sm2Co17 blocks assembled together with soft ferromagnetic pole tips. The magnet provides integrated field strength of 24.6 10-3 T×m inside the aperture of 60 mm. This Design Report summarizes the main magnetic and mechanic design parameters of the permanent dipole magnets.
Dirac monopole without strings: monopole harmonics
Wu, T.T.; Yang, C.N.
1983-01-01
Using the ideas developed in a previous paper which are borrowed from the mathematics of fiber bundles, it is shown that the wave function psi of a particle of charge Ze around a Dirac monopole of strength g should be regarded as a section. The section is without discontinuities. Thus the monopole does not possess strings of singularities in the field around it. The eigensections of the angular momentum operators are monopole harmonics which are explicitly exhibited. 7 references, 2 figures, 1 table
Dispersionless wave packets in Dirac materials
Jakubský, Vít; Tušek, Matěj
2017-01-01
We show that a wide class of quantum systems with translational invariance can host dispersionless, soliton-like, wave packets. We focus on the setting where the effective, two-dimensional Hamiltonian acquires the form of the Dirac operator. The proposed framework for construction of the dispersionless wave packets is illustrated on silicene-like systems with topologically nontrivial effective mass. Our analytical predictions are accompanied by a numerical analysis and possible experimental realizations are discussed.
Dirac operators and Killing spinors with torsion
Becker-Bender, Julia
2012-01-01
On a Riemannian spin manifold with parallel skew torsion, we use the twistor operator to obtain an eigenvalue estimate for the Dirac operator with torsion. We consider the equality case in dimensions four and six. In odd dimensions we describe Sasaki manifolds on which equality in the estimate is realized by Killing spinors with torsion. In dimension five we characterize all Killing spinors with torsion and obtain certain naturally reductive spaces as exceptional cases.
Data acquisition software for DIRAC experiment
Olshevsky, V G
2001-01-01
The structure and basic processes of data acquisition software of the DIRAC experiment for the measurement of pi /sup +/ pi /sup -/ atom lifetime are described. The experiment is running on the PS accelerator of CERN. The developed software allows one to accept, record and distribute up to 3 Mbytes of data to consumers in one accelerator supercycle of 14.4 s duration. The described system is successfully in use in the experiment since its startup in 1998. (13 refs).
Data acquisition software for DIRAC experiment
Olshevsky, V.; Trusov, S.
2001-08-01
The structure and basic processes of data acquisition software of the DIRAC experiment for the measurement of π +π - atom lifetime are described. The experiment is running on the PS accelerator of CERN. The developed software allows one to accept, record and distribute up to 3 Mbytes of data to consumers in one accelerator supercycle of 14.4 s duration. The described system is successfully in use in the experiment since its startup in 1998.
Data acquisition software for DIRAC experiment
Olshevsky, V.; Trusov, S.
2001-01-01
The structure and basic processes of data acquisition software of the DIRAC experiment for the measurement of π + π - atom lifetime are described. The experiment is running on the PS accelerator of CERN. The developed software allows one to accept, record and distribute up to 3 Mbytes of data to consumers in one accelerator supercycle of 14.4 s duration. The described system is successfully in use in the experiment since its startup in 1998
Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations
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)
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.
Dirac bi-spinor entanglement under local noise and its simulation by Jaynes-Cummings interactions
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.