A Dirac-Dunkl Equation on S 2 and the Bannai-Ito Algebra
NASA Astrophysics Data System (ADS)
De Bie, Hendrik; Genest, Vincent X.; Vinet, Luc
2016-05-01
The Dirac-Dunkl operator on the two-sphere associated to the Z23 reflection group is considered. Its symmetries are found and are shown to generate the Bannai-Ito algebra. Representations of the Bannai-Ito algebra are constructed using ladder operators. Eigenfunctions of the spherical Dirac-Dunkl operator are obtained using a Cauchy-Kovalevskaia extension theorem. These eigenfunctions, which correspond to Dunkl monogenics, are seen to support finite-dimensional irreducible representations of the Bannai-Ito algebra.
Dunkl-Type Operators with Projections Terms Associated to Orthogonal Subsystems in Roots System
NASA Astrophysics Data System (ADS)
Bouzeffour, Fethi
2013-10-01
In this paper, we introduce a new differential-difference operator T_ξ(ξ in {R}^N) by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute and we construct an intertwining operator between T_ξ and the directional derivative partial_ξ. In the case of one variable, we prove that the Kummer functions are eigenfunctions of this operator.
NASA Astrophysics Data System (ADS)
Moroz, Alexander
2016-03-01
A discrete parity {Z}2 -symmetry of a two-parameter extension of the quantum Rabi model which smoothly interpolates between the latter and the Jaynes-Cummings model, and of the two-photon and the two-mode quantum Rabi models, enables their diagonalization in the spin subspace. A more general statement is that the respective sets of 2× 2 Hermitian operators of the Fulton-Gouterman type and those diagonal in the spin subspace are unitary equivalent. The diagonalized representation makes it transparent that any question about integrability and solvability can be addressed only at the level of ordinary differential operators of Dunkl type. Braak's definition of integrability is shown i) to contradict earlier numerical studies and ii) to imply that any physically reasonable differential operator of Fulton-Gouterman type is integrable.
On Dunkl angular momenta algebra
NASA Astrophysics Data System (ADS)
Feigin, Misha; Hakobyan, Tigran
2015-11-01
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
Two-step asymptotics of scaled Dunkl processes
NASA Astrophysics Data System (ADS)
Andraus, Sergio; Miyashita, Seiji
2015-10-01
Dunkl processes are generalizations of Brownian motion obtained by using the differential-difference operators known as Dunkl operators as a replacement of spatial partial derivatives in the heat equation. Special cases of these processes include Dyson's Brownian motion model and the Wishart-Laguerre eigenvalue processes, which are well-known in random matrix theory. It is known that the dynamics of Dunkl processes is obtained by transforming the heat kernel using Dunkl's intertwining operator. It is also known that, under an appropriate scaling, their distribution function converges to a steady-state distribution which depends only on the coupling parameter β as the process time t tends to infinity. We study scaled Dunkl processes starting from an arbitrary initial distribution, and we derive expressions for the intertwining operator in order to calculate the asymptotics of the distribution function in two limiting situations. In the first one, β is fixed and t tends to infinity (approach to the steady state), and in the second one, t is fixed and β tends to infinity (strong-coupling limit). We obtain the deviations from the limiting distributions in both of the above situations, and we find that they are caused by the two different mechanisms which drive the process, namely, the drift and exchange mechanisms. We find that the deviation due to the drift mechanism decays as t-1, while the deviation due to the exchange mechanism decays as t-1/2.
Eigenvalue asymptotics for Dirac-Bessel operators
NASA Astrophysics Data System (ADS)
Hryniv, Rostyslav O.; Mykytyuk, Yaroslav V.
2016-06-01
In this paper, we establish the eigenvalue asymptotics for non-self-adjoint Dirac-Bessel operators on (0, 1) with arbitrary real angular momenta and square integrable potentials, which gives the first step for solution of the related inverse problem. The approach is based on a careful examination of the corresponding characteristic functions and their zero distribution.
Spin operator in the Dirac theory
NASA Astrophysics Data System (ADS)
Caban, Paweł; Rembieliński, Jakub; Włodarczyk, Marta
2013-08-01
We find all spin operators for a Dirac particle satisfying the following very general conditions: (i) spin does not convert positive (negative) energy states into negative (positive) energy states, (ii) spin is a pseudovector, and (iii) eigenvalues of the projection of a spin operator in an arbitrary direction are independent of this direction (isotropy condition). We show that there are four such operators and all of them fulfill the standard su(2) Lie algebra commutation relations. Nevertheless, only one of them has a proper nonrelativistic limit and acts in the same way on negative and positive energy states. We show also that this operator is equivalent to the Newton-Wigner spin operator and Foldy-Wouthuysen mean-spin operator. We also discuss another operator proposed in the literature.
Microscopic Spectrum of the Wilson Dirac Operator
Damgaard, P. H.; Splittorff, K.; Verbaarschot, J. J. M.
2010-10-15
We calculate the leading contribution to the spectral density of the Wilson Dirac operator using chiral perturbation theory where volume and lattice spacing corrections are given by universal scaling functions. We find analytical expressions for the spectral density on the scale of the average level spacing, and introduce a chiral random matrix theory that reproduces these results. Our work opens up a novel approach to the infinite-volume limit of lattice gauge theory at finite lattice spacing and new ways to extract coefficients of Wilson chiral perturbation theory.
Spectrum of the Wilson Dirac operator at finite lattice spacings
Akemann, G.; Damgaard, P. H.; Splittorff, K.; Verbaarschot, J. J. M.
2011-04-15
We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral perturbation theory and chiral random matrix theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral random matrix theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral perturbation theory. All results are obtained for a fixed index of the Wilson Dirac operator. The low-energy constants of Wilson chiral perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac operator.
NASA Astrophysics Data System (ADS)
Fakhri, Hossein; Imaanpur, Ali
2003-03-01
In this article we construct the chirality and Dirac operators on noncommutative AdS2. We also derive the discrete spectrum of the Dirac operator which is important in the study of the spectral triple associated to AdS2. It is shown that the degeneracy of the spectrum present in the commutative AdS2 is lifted in the noncommutative case. The way we construct the chirality operator is suggestive of how to introduce the projector operators of the corresponding projective modules on this space.
Generalized Yang-Mills actions from Dirac operator determinants
NASA Astrophysics Data System (ADS)
Langmann, Edwin
2001-11-01
We consider the quantum effective action of Dirac fermions on four-dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R4 twisted by generalized Yang-Mills fields. According to physics folklore, the logarithmic divergent part of this effective action in the pure vector case is proportional to the Yang-Mills action. We present a simple explicit computation proving this fact and extending it to the chiral case. We use an efficient computation method for quantum effective actions which is based on calculation rules for pseudo-differential operators and which yields an expansion of the logarithm of Dirac operators in local and quasi-gauge invariant polynomials of decreasing scaling dimension.
Dirac operators on quasi-Hamiltonian G-spaces
NASA Astrophysics Data System (ADS)
Song, Yanli
2016-08-01
We construct twisted spinor bundles as well as twisted pre-quantum bundles on quasi-Hamiltonian G-spaces, using the spin representation of loop group and the Hilbert space of Wess-Zumino-Witten model. We then define a Hilbert space together with a Dirac operator acting on it. The main result of this paper is that we show the Dirac operator has a well-defined index given by positive energy representation of the loop group. This generalizes the geometric quantization of Hamiltonian G-spaces to quasi-Hamiltonian G-spaces.
Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator
Babich, R.; Brower, R. C.; Rebbi, C.; Brannick, J.; Clark, M. A.; Manteuffel, T. A.; McCormick, S. F.; Osborn, J. C.
2010-11-12
We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called {gamma}{sub 5}-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume.
Adaptive multigrid algorithm for the lattice Wilson-Dirac operator.
Babich, R; Brannick, J; Brower, R C; Clark, M A; Manteuffel, T A; McCormick, S F; Osborn, J C; Rebbi, C
2010-11-12
We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called γ5-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume. PMID:21231217
Dirac operator on a disk with global boundary conditions
Falomir, H.; Gamboa Saravi, R.E.; Santangelo, E.M.
1998-01-01
We compute the functional determinant for a Dirac operator in the presence of an Abelian gauge field on a bidimensional disk, under global boundary conditions of the type introduced by Atiyah{endash}Patodi{endash}Singer. We also discuss the connection between our result and the index theorem. {copyright} {ital 1998 American Institute of Physics.}
Global boundary conditions for a Dirac operator on the solid torus
Klimek, Slawomir; McBride, Matt
2011-06-15
We study a Dirac operator subject to Atiayh-Patodi-Singer-like boundary conditions on the solid torus and shows that the corresponding boundary value problem is elliptic in the sense that the Dirac operator has a compact parametrix.
An uncertainty inequality for Fourier-Dunkl series
NASA Astrophysics Data System (ADS)
Ciaurri, Óscar; Varona, Juan L.
2010-01-01
An uncertainty inequality for the Fourier-Dunkl series, introduced by the authors in [Ó. Ciaurri, J.L. Varona, A Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transform, Proc. Amer. Math. Soc. 135 (2007) 2939-2947], is proved. This result is an extension of the classical uncertainty inequality for the Fourier series.
Spectral functionals, nonholonomic Dirac operators, and noncommutative Ricci flows
Vacaru, Sergiu I.
2009-07-15
We formulate a noncommutative generalization of the Ricci flow theory in the framework of spectral action approach to noncommutative geometry. Grisha Perelman's functionals are generated as commutative versions of certain spectral functionals defined by nonholonomic Dirac operators and corresponding spectral triples. We derive the formulas for spectral averaged energy and entropy functionals and state the conditions when such values describe (non)holonomic Riemannian configurations.
A priori estimates for the Hill and Dirac operators
NASA Astrophysics Data System (ADS)
Korotyaev, E.
2008-09-01
The Hill operator Ty = -y″ + q'( t) y is considered in L 2(ℝ), where q ∈ L 2(0, 1) is a periodic real potential. The spectrum of T is absolutely continuous and consists of bands separated by gaps. We obtain a priori estimates of gap lengths, effective masses, and action variables for the KDV equation. In the proof of these results, the analysis of a conformal mapping corresponding to quasimomentum of the Hill operator is used. Similar estimates for the Dirac operator are obtained.
NASA Astrophysics Data System (ADS)
Isaac, Phillip S.; Marquette, Ian
2016-03-01
We generalize the construction of integrals of motion for quantum superintegrable models and the deformed oscillator algebra approach. This is presented in the context of 1D systems admitting ladder operators satisfying a parabosonic algebra involving reflection operators and more generally {c}λ extended oscillator algebras with grading. We apply the construction on two-dimensional {c}λ oscillators. We also introduce two new superintegrable Hamiltonians that are the anisotropic Dunkl and the singular Dunkl oscillators. Integrals are constructed by extending the approach of Daskaloyannis to include grading. An algebraic derivation of the energy spectra of the two models is presented, making use of finite dimensional unitary representations. We show how the spectra divide into sectors, and make comparisons with the physical case.
Dirac operator on the sphere with attached wires
NASA Astrophysics Data System (ADS)
E, N. Grishanov; D, A. Eremin; D, A. Ivanov; I, Yu Popov
2016-04-01
An explicitly solvable model for tunnelling of relativistic spinless particles through a sphere is suggested. The model operator is constructed by an operator extensions theory method from the orthogonal sum of the Dirac operators on a semi-axis and on the sphere. The transmission coefficient is obtained. The dependence of the transmission coefficient on the particle energy has a resonant character. One observes pairs of the Breit–Wigner and the Fano resonances. It correlates with the corresponding results for a non-relativistic particle. Project partially financially supported by the Funds from the Government of the Russian Federation (Grant No. 074-U01), the Funds from the Ministry of Education and Science of the Russian Federation (GOSZADANIE 2014/190) (Grant Nos. 14.Z50.31.0031 and 1.754.2014/K), and the President Foundation of the Russian Federation (Grant No. MK-5001.2015.1).
Symmetry operators for Dirac's equation on two-dimensional spin manifolds
NASA Astrophysics Data System (ADS)
Fatibene, Lorenzo; McLenaghan, Raymond G.; Rastelli, Giovanni; Smith, Shane N.
2009-05-01
It is shown that the second order symmetry operators for the Dirac equation on a general two-dimensional spin manifold may be expressed in terms of Killing vectors and valence 2 Killing tensors. The role of these operators in the theory of separation of variables for the Dirac equation is studied.
Symmetry operators for Dirac's equation on two-dimensional spin manifolds
Fatibene, Lorenzo; McLenaghan, Raymond G.; Smith, Shane N.; Rastelli, Giovanni
2009-05-15
It is shown that the second order symmetry operators for the Dirac equation on a general two-dimensional spin manifold may be expressed in terms of Killing vectors and valence 2 Killing tensors. The role of these operators in the theory of separation of variables for the Dirac equation is studied.
A dynamical time operator in Dirac's relativistic quantum mechanics
NASA Astrophysics Data System (ADS)
Bauer, M.
2014-03-01
A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.
Dynamical representation of the operators for the Dirac particle in the field of a plane wave
NASA Astrophysics Data System (ADS)
Lobanov, A. E.
2015-01-01
We find an explicit form of the integrals of motion for a Dirac particle placed in a plane-wave field. These operators are a realization of the Lie algebra of the Poincaré group in the case where the representation space consists of solutions of the Dirac-Pauli equation for the particle in a plane-wave field.
Finiteness of the L2-index of the Dirac operator of generalized Euclidean Taub NUT metrics
NASA Astrophysics Data System (ADS)
Moroianu, Sergiu; Visinescu, Mihai
2006-05-01
We prove that the axial anomaly, interpreted as the L2-index of the chiral Dirac operator, for the standard Taub-NUT metric on {\\bb R}^4 , vanishes. We show that the essential spectrum of the Dirac operator of the generalized Taub-NUT metrics introduced by Iwai and Katayama is the whole real line. We also show that the axial anomaly for the generalized Taub-NUT metric is finite although the Dirac operator is not Fredholm in L^2({\\bb R}^4,\\Sigma_4,{ds_K}^2) .
Decomposition of the polynomial kernel of arbitrary higher spin Dirac operators
Eelbode, D.; Raeymaekers, T.; Van der Jeugt, J.
2015-10-15
In a series of recent papers, we have introduced higher spin Dirac operators, which are generalisations of the classical Dirac operator. Whereas the latter acts on spinor-valued functions, the former acts on functions taking values in arbitrary irreducible half-integer highest weight representations for the spin group. In this paper, we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group. We will hereby make use of results from representation theory.
NASA Astrophysics Data System (ADS)
Carignano, Alberto; Fatibene, Lorenzo; McLenaghan, Raymond G.; Rastelli, Giovanni
2011-06-01
A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal frames and metrics that permit the solution of Dirac's equation by separation of variables in the case where a second-order symmetry operator underlies the separation. Separation of variables in complex variables on two-dimensional Minkowski space is also considered.
Block-Diagonalization of Operators with Gaps, with Applications to Dirac Operators
NASA Astrophysics Data System (ADS)
Cuenin, Jean-Claude
2012-09-01
We present new results on the block-diagonalization of operators with spectral gaps, based on a method of Langer and Tretter, and apply them to Dirac operators on three-dimensional Euclidean space with unbounded potentials. For the Coulomb potential, we achieve an exact diagonalization up to nuclear charge Z = 124 (which covers all chemical elements) and prove the convergence of an approximate block-diagonalization up to Z = 62, thus considerably improving the upper bounds Z = 93 and Z = 51, respectively, established by Siedentop and Stockmeyer.
The local counting function of operators of Dirac and Laplace type
NASA Astrophysics Data System (ADS)
Li, Liangpan; Strohmaier, Alexander
2016-06-01
Let P be a non-negative self-adjoint Laplace type operator acting on sections of a hermitian vector bundle over a closed Riemannian manifold. In this paper we review the close relations between various P-related coefficients such as the mollified spectral counting coefficients, the heat trace coefficients, the resolvent trace coefficients, the residues of the spectral zeta function as well as certain Wodzicki residues. We then use the Wodzicki residue to obtain results about the local counting function of operators of Dirac and Laplace type. In particular, we express the second term of the mollified spectral counting function of Dirac type operators in terms of geometric quantities and characterize those Dirac type operators for which this coefficient vanishes.
On Some Algebraic and Combinatorial Properties of Dunkl Elements
NASA Astrophysics Data System (ADS)
Kirillov, Anatol N.
2013-06-01
We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147-182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371-383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248]. Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang-Baxter algebra in a connection with the values of the β-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan-Robbins polytope.
On Some Algebraic and Combinatorial Properties of Dunkl Elements
NASA Astrophysics Data System (ADS)
Kirillov, Anatol N.
2012-11-01
We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147-182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371-383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248]. Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang-Baxter algebra in a connection with the values of the β-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan-Robbins polytope.
Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
NASA Astrophysics Data System (ADS)
Cariglia, Marco; Krtouš, Pavel; Kubizňák, David
2011-07-01
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].
On the Hamiltonian and energy operators in a curved spacetime, especially for a Dirac particle
NASA Astrophysics Data System (ADS)
Arminjon, Mayeul
2015-07-01
The definition of the Hamiltonian operator H for a general wave equation in a general spacetime is discussed. We recall that H depends on the coordinate system merely through the corresponding reference frame. When the wave equation involves a gauge choice and the gauge change is time-dependent, H asan operator depends on the gauge choice. This dependence extends to the energy operator E, which is the Hermitian part of H. We distinguish between this ambiguity issue of E and the one that occurs due to a mere change of the “representation” (e.g. transforming the Dirac wave function from the “Dirac representation” to a “Foldy-Wouthuy senre presentation”). We also assert that the energy operator ought to be well defined in a given reference frame at a given time, e.g. by comparing the situation for this operator with the main features of the energy for a classical Hamiltonian particle.
Spectral asymmetry of the massless Dirac operator on a 3-torus
Downes, Robert J. Vassiliev, Dmitri; Levitin, Michael
2013-11-15
Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.
Spectral action for a one-parameter family of Dirac operators on { SU}{(2)} and {SU}{(3)}
NASA Astrophysics Data System (ADS)
Lai, Alan; Teh, Kevin
2013-02-01
The one-parameter family of Dirac operators containing the Levi-Civita, cubic, and the trivial Dirac operators on a compact Lie group is analyzed. The spectra for the one-parameter family of Dirac Laplacians on SU(2) and SU(3) are computed by considering a diagonally embedded Casimir operator. Then the asymptotic expansions of the spectral actions for SU(2) and SU(3) are computed, using the Poisson summation formula and the two-dimensional Euler-Maclaurin formula, respectively. The inflation potential and slow-roll parameters for the corresponding pure gravity inflationary theory are generated, using the full asymptotic expansion of the spectral action on SU(2).
A formula for the first eigenvalue of the Dirac operator on compact spin symmetric spaces
Milhorat, Jean-Louis
2006-04-15
Let G/K be a simply connected spin compact inner irreducible symmetric space, endowed with the metric induced by the Killing form of G sign-changed. We give a formula for the square of the first eigenvalue of the Dirac operator in terms of a root system of G. As an example of application, we give the list of the first eigenvalues for the spin compact irreducible symmetric spaces endowed with a quaternion-Kaehler structure.
Spectrum of the Dirac operator on Gr{sub 2}(C{sup m+2})
Milhorat, J.
1998-01-01
The spectrum of the Dirac operator, acting on the quaternion-Kaehler spin symmetric space Gr{sub 2}(C{sup m+2}), is explicitly computed by harmonic analysis methods: in particular `branching rules` for irreducible representations of the Lie group SU(m+2) and its subgroup S(U(m){times}U(2)), are given. {copyright} {ital 1998 American Institute of Physics.}
Equivalence of Dirac formulations
NASA Astrophysics Data System (ADS)
Joyce, William P.; Martin, Jeremy G.
2002-06-01
We construct general Dirac theories in both ⊗ ℓ(3, 1) and ⊗ ℓ(1, 3) using a first order left acting Dirac operator. Any two such theories are equivalent provided they have the same dimension. We also show that every 16- or 8-dimensional real Dirac theory in ℓ(3, 1) is equivalent to some (complex) Dirac theory in ⊗ ℓ(1, 3). As an immediate consequence of this we have that the Hestenes and original Dirac formulations are equivalent.
Ginsparg-Wilson Dirac operator in monopole backgrounds on the fuzzy 2-sphere
Aoki, Hajime; Maeda, Toshiharu; Iso, Satoshi
2007-04-15
In previous papers, we studied 't Hooft-Polyakov (TP) monopole configurations in U(2) gauge theory on the fuzzy 2-sphere, and showed that they have nonzero topological charges in the formalism based on the Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in the TP monopole background, which is defined in the projected space, and provides meaning of the projection operator. We also extend the index theorem to general configurations which do not satisfy the equation of motion, and show that configuration space can be classified into topological sectors. We further calculate the spectrum of the GW Dirac operator in TP monopole backgrounds, and consider the index theorem in these cases.
FFT-split-operator code for solving the Dirac equation in 2+1 dimensions
NASA Astrophysics Data System (ADS)
Mocken, Guido R.; Keitel, Christoph H.
2008-06-01
The main part of the code presented in this work represents an implementation of the split-operator method [J.A. Fleck, J.R. Morris, M.D. Feit, Appl. Phys. 10 (1976) 129-160; R. Heather, Comput. Phys. Comm. 63 (1991) 446] for calculating the time-evolution of Dirac wave functions. It allows to study the dynamics of electronic Dirac wave packets under the influence of any number of laser pulses and its interaction with any number of charged ion potentials. The initial wave function can be either a free Gaussian wave packet or an arbitrary discretized spinor function that is loaded from a file provided by the user. The latter option includes Dirac bound state wave functions. The code itself contains the necessary tools for constructing such wave functions for a single-electron ion. With the help of self-adaptive numerical grids, we are able to study the electron dynamics for various problems in 2+1 dimensions at high spatial and temporal resolutions that are otherwise unachievable. Along with the position and momentum space probability density distributions, various physical observables, such as the expectation values of position and momentum, can be recorded in a time-dependent way. The electromagnetic spectrum that is emitted by the evolving particle can also be calculated with this code. Finally, for planning and comparison purposes, both the time-evolution and the emission spectrum can also be treated in an entirely classical relativistic way. Besides the implementation of the above-mentioned algorithms, the program also contains a large C++ class library to model the geometric algebra representation of spinors that we use for representing the Dirac wave function. This is why the code is called "Dirac++". Program summaryProgram title: Dirac++ or (abbreviated) d++ Catalogue identifier: AEAS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing
Spectrum of the Dirac operator and multigrid algorithm with dynamical staggered fermions
Kalkreuter, T. Fachbereich Physik , Humboldt-Universitaet, Invalidenstrasse 110, D-10099 Berlin )
1995-02-01
Complete spectra of the staggered Dirac operator [ital ];sD are determined in quenched four-dimensional SU(2) gauge fields, and also in the presence of dynamical fermions. Periodic as well as antiperiodic boundary conditions are used. An attempt is made to relate the performance of multigrid (MG) and conjugate gradient (CG) algorithms for propagators with the distribution of the eigenvalues of [ital ];sD. The convergence of the CG algorithm is determined only by the condition number [kappa] and by the lattice size. Since [kappa]'s do not vary significantly when quarks become dynamic, CG convergence in unquenched fields can be predicted from quenched simulations. On the other hand, MG convergence is not affected by [kappa] but depends on the spectrum in a more subtle way.
Epstein, Charles L.
2006-01-01
Let X be a Spinℂ manifold with boundary, such that the Spinℂ structure is defined near the boundary by an almost complex structure, which is either strictly pseudoconvex or pseudoconcave (and hence contact). Using generalized Szegő projectors, we define modified ∂̄-Neumann boundary conditions, ℛeo, for spinors, which lead to subelliptic Fredholm boundary value problems for the Spinℂ–Dirac operator, ðeo. To study the index of these boundary value problems we introduce a generalization of Fredholm pairs to the “tame” category. In this context, we show that the index of the graph closure of (ðeo, ℛeo) equals the tame relative index, on the boundary, between ℛeo and the Calderon projector. Let X0 and X1 be strictly pseudoconvex, Spinℂ manifolds, as above. Let φ : bX1 → bX0, be a contact diffeomorphism, S0, S1 denote generalized Szegő projectors on bX0, bX1, respectively, and ℛ0eo, ℛ1eo, the subelliptic boundary conditions they define. If X1 is the manifold X1 with its orientation reversed, then the glued manifold X = X0 ∐φ X1 has a canonical Spinℂ structure and Dirac operator, ðXeo. Applying these results we obtain a formula for the relative index, R-Ind(S0, φ*S1), As a special case, this formula verifies a conjecture of Atiyah and Weinstein [(1997) RIMS Kokyuroku 1014:1–14] for the index of the quantization of a contact transformation between cosphere bundles. PMID:17032764
NASA Astrophysics Data System (ADS)
Pais, Abraham; Jacob, Maurice; Olive, David I.; Atiyah, Michael F.
1998-02-01
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.
NASA Astrophysics Data System (ADS)
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 Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators
NASA Astrophysics Data System (ADS)
Arrizabalaga, Naiara; Mas, Albert; Vega, Luis
2016-06-01
In this article we investigate spectral properties of the coupling {H + V_λ}, where {H = -iα \\cdot nabla+mβ} is the free Dirac operator in {{R}^3}, {m > 0} and {V_λ} is an electrostatic shell potential (which depends on a parameter {λ in {R}}) located on the boundary of a smooth domain in {{R}^3}. Our main result is an isoperimetric-type inequality for the admissible range of {λ}'s for which the coupling {H + V_λ} generates pure point spectrum in {(-m, m)}. That the ball is the unique optimizer of this inequality is also shown. Regarding some ingredients of the proof, we make use of the Birman-Schwinger principle adapted to our setting in order to prove some monotonicity property of the admissible {λ}'s, and we use this to relate the endpoints of the admissible range of {λ}'s to the sharp constant of a quadratic form inequality, from which the isoperimetric-type inequality is derived.
Dirac operators on the fuzzy AdS2 with the spins 1/2 and 1
NASA Astrophysics Data System (ADS)
Fakhri, H.; Lotfizadeh, M.
2011-10-01
It is shown here how the pseudo chirality and Dirac operators with the spins 1/2 and 1 on the commutative and fuzzy AdS2 should be constructed. The finite-dimensional and nonunitary representations of SU(1, 1) carrying the spin degrees of freedom 1/2 and 1 are used for the Dirac fields on commutative and fuzzy AdS2. In the fuzzy case, an explicit description of pseudo generalization of the Ginsparg-Wilson algebra is used to construct projective modules. The projector couplings left angular momentum and spin on the fuzzy AdS2 are used to produce minimum total angular momenta. They are realized by the first two and three representations of the total angular momentum for the spins 1/2 and 1, respectively. The pseudo projectors, the pseudo chirality, and Dirac operators with the spins 1/2 and 1 on the fuzzy AdS2 tend to their corresponding operators in the commutative limit.
NASA Astrophysics Data System (ADS)
Fatibene, Lorenzo; McLenaghan, Raymond G.; Rastelli, Giovanni
2015-12-01
The second-order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin manifold. It is shown that the operator is defined in terms of Killing vectors, valence two Killing tensors and scalar fields defined on the background manifold. The commuting operator that arises from a non-trivial Killing tensor is determined with respect to the associated system of Liouville coordinates and compared to the second-order operator that obtained from the unique separation scheme associated with such operators. It is shown by the study of several examples that the operators arising from these two approaches coincide.
The LHCb DIRAC-based production and data management operations systems
NASA Astrophysics Data System (ADS)
Stagni, F.; Charpentier, P.; LHCb Collaboration
2012-06-01
The LHCb computing model was designed in order to support the LHCb physics program, taking into account LHCb specificities (event sizes, processing times etc...). Within this model several key activities are defined, the most important of which are real data processing (reconstruction, stripping and streaming, group and user analysis), Monte-Carlo simulation and data replication. In this contribution we detail how these activities are managed by the LHCbDIRAC Data Transformation System. The LHCbDIRAC Data Transformation System leverages the workload and data management capabilities provided by DIRAC, a generic community grid solution, to support data-driven workflows (or DAGs). The ability to combine workload and data tasks within a single DAG allows to create highly sophisticated workflows with the individual steps linked by the availability of data. This approach also provides the advantage of a single point at which all activities can be monitored and controlled. While several interfaces are currently supported (including python API and CLI), we will present the ability to create LHCb workflows through a secure web interface, control their state in addition to creating and submitting jobs. To highlight the versatility of the system we present in more detail experience with real data of the 2010 and 2011 LHC run.
Spectral and localization properties for the one-dimensional Bernoulli discrete Dirac operator
Oliveira, Cesar R. de; Prado, Roberto A.
2005-07-01
An one-dimensional (1D) Dirac tight-binding model is considered and it is shown that its nonrelativistic limit is the 1D discrete Schroedinger model. For random Bernoulli potentials taking two values (without correlations), for typical realizations and for all values of the mass, it is shown that its spectrum is pure point, whereas the zero mass case presents dynamical delocalization for specific values of the energy. The massive case presents dynamical localization (excluding some particular values of the energy). Finally, for general potentials the dynamical moments for distinct masses are compared, especially the massless and massive Bernoulli cases.
Three dimensional Dirac semimetals
NASA Astrophysics Data System (ADS)
Zaheer, Saad
We extend the physics of graphene to three dimensional systems by showing that Dirac points can exist on the Fermi surface of realistic materials in three dimensions. Many of the exotic electronic properties of graphene can be ascribed to the pseudorelativistic behavior of its charge carriers due to two dimensional Dirac points on the Fermi surface. We show that certain nonsymmorphic spacegroups exhibit Dirac points among the irreducible representations of the appropriate little group at high symmetry points on the surface of the Brillouin zone. We provide a list of all Brillouin zone momenta in the 230 spacegroups that can host Dirac points. We describe microscopic considerations necessary to design materials in one of the candidate spacegroups such that the Dirac point appears at the Fermi energy without any additional non-Dirac-like Fermi pockets. We use density functional theory based methods to propose six new Dirac semimetals: BiO 2 and SbO2 in the beta-cristobalite lattice (spacegroup 227), and BiCaSiO4, BiMgSiO4, BiAlInO 4, and BiZnSiO4 in the distorted spinels lattice (spacegroup 74). Additionally we derive effective Dirac Hamiltonians given group representative operators as well as tight binding models incorporating spin-orbit coupling. Finally we study the Fermi surface of zincblende (spacegroup 216) HgTe which is effectively point-like at Gamma in the Brillouin zone and exhibits accidental degeneracies along a threefold rotation axis. Whereas compressive strain gaps the band structure into a topological insulator, tensile strain shifts the accidental degeneracies away from Gamma and enlarges the Fermi surface. States on the Fermi surface exhibit nontrivial spin texture marked by winding of spins around the threefold rotation axis and by spin vortices indicating a change in the winding number. This is confirmed by microscopic calculations performed in tensile strained HgTe and Hg0.5Zn 0.5 Te as well as k.p theory. We conclude with a summary of recent
NASA Astrophysics Data System (ADS)
Wu, Shuang-Qing
2009-03-01
It is shown that the Dirac equation is separable by variables in a five-dimensional rotating Kerr (anti-)de Sitter black hole with two independent angular momenta. A first-order symmetry operator that commutes with the Dirac operator is constructed in terms of a rank-3 Killing Yano tensor whose square is a second-order symmetric Stäckel Killing tensor admitted by the five-dimensional Kerr (anti-)de Sitter spacetime. We highlight the construction procedure of such a symmetry operator. In addition, the first law of black hole thermodynamics has been extended to the case that the cosmological constant can be viewed as a thermodynamical variable.
NASA Astrophysics Data System (ADS)
Milhorat, Jean-Louis
2015-04-01
It is shown that on a compact spin symmetric space with a Kähler or Quaternion-Kähler structure, the first eigenvalue of the Dirac operator is linked to a "lowest" action of the holonomy, given by the fiberwise action on spinors of the canonical forms characterized by this holonomy. The result is also verified for the symmetric space F4 /Spin9, proving that it is valid for all the "possible" holonomies in Berger's list occurring in that context. The proof is based on a characterization of the first eigenvalue of the Dirac operator given in Milhorat (2005) and Milhorat (2006). By the way, we review an incorrect statement in the proof of the first lemma in Milhorat (2005).
NASA Astrophysics Data System (ADS)
Brown, Laurie M.
Paul Dirac was a brilliant and original thinker. He used his physical intuition and his ideal of mathematical beauty to construct bridges between major areas of physics. This article discusses several such important works, including the bridge between quantum mechanics and relativity that led to his prediction of the existence of antimatter.
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.
NASA Astrophysics Data System (ADS)
Winklmeier, Monika; Yamada, Osanobu
2006-10-01
We investigate the existence of time-periodic solutions of the Dirac equation in the Kerr-Newman background metric. To this end, the solutions are expanded in a Fourier series with respect to the time variable t, and the Chandrasekhar separation ansatz is applied so that the question of existence of a time-periodic solution is reduced to the solvability of a certain coupled system of ordinary differential equations. First, we prove the already known result that there are no time-periodic solutions in the nonextreme case. Then, it is shown that in the extreme case for fixed black hole data there is a sequence of particle masses (mN)NɛN for which a time-periodic solution of the Dirac equation does exist. The period of the solution depends only on the data of the black hole described by the Kerr-Newman metric.
NASA Astrophysics Data System (ADS)
Kursunoglu, Behram N.; Wigner, Eugene Paul
1990-04-01
Portrait R. Feyman; List of contributors; A memorial to P. A. M. Dirac B. N. Kursunoglu; Preface B. N. Kursunoglu and E. P. Wigner; Chronology; Part I. Human Side: 1. Thinking of my darling Paul M. Dirac; 2. Dirac in coral gables S. A. Kursunoglu; 3. Recollections of Paul Dirac at Florida State University J. E. Lannutti; 4. My association with Professor Dirac Harish-Chandra; 5. What Paul Dirac meant in my life N. Kemmer; 6. Dirac's way R. Peierls; 7. An experimenter's view of P. A. M. Dirac A. D. Krisch; 8. Dirac at the University of Miami H. K. Stanford; 9. Remembering Paul Dirac E. P. Wigner; Part II. More Scientific Ideas: 10. Another side to Paul Dirac R. H. Dalitz; 11. Playing with equations, the Dirac way A. Pais; 12. Paul Dirac and Werner Heisenberg - a partnership in science L. M. Brown and H. Rechenberg; 13. Dirac's magnetic monopole and the fine structure constant W. J. Marciano and M. Goldhaber; 14. Magnetic monopoles and the halos of galaxies F. Hoyle; 15. The inadequacies of quantum field theory P. A. M. Dirac; 16. Dirac and the foundation of quantum mechanics P. T. Matthews; Part III. Influenced and Inspired by Association: 17. At the feet of Dirac J. C. Polkinghorne; 18. Reminiscences of Paul Dirac N. Mott; 19. From relativistic quantum theory to the human brain H. J. Lipkin; 20. Dirac in 1962, weak and gravitational radiation interactions J. Weber; 21. Schrödinger's cat W. E. Lamb, Jr.; 22. Dirac and finite field theories A. Salam; 23. Dirac's influence on unified field theory B. N. Kursunoglu; Index.
CREUTZ, M.
2006-01-26
It is popular to discuss low energy physics in lattice gauge theory ill terms of the small eigenvalues of the lattice Dirac operator. I play with some ensuing pitfalls in the interpretation of these eigenvalue spectra. In short, thinking about the eigenvalues of the Dirac operator in the presence of gauge fields can give some insight, for example the elegant Banks-Casher picture for chiral symmetry breaking. Nevertheless, care is necessary because the problem is highly non-linear. This manifests itself in the non-intuitive example of how adding flavors enhances rather than suppresses low eigenvalues. Issues involving zero mode suppression represent one facet of a set of connected unresolved issues. Are there non-perturbative ambiguities in quantities such as the topological susceptibility? How essential are rough gauge fields, i.e. gauge fields on which the winding number is ambiguous? How do these issues interplay with the quark masses? I hope the puzzles presented here will stimulate more thought along these lines.
NASA Astrophysics Data System (ADS)
Fransson, J.; Black-Schaffer, A. M.; Balatsky, A. V.
2016-08-01
We demonstrate how a Dirac-like magnon spectrum is generated for localized magnetic moments forming a two-dimensional honeycomb lattice. The Dirac crossing point is proven to be robust against magnon-magnon interactions, as these only shift the spectrum. Local defects induce impurity resonances near the Dirac point, as well as magnon Friedel oscillations. The energy of the Dirac point is controlled by the exchange coupling, and thus a two-dimensional array of magnetic dots is an experimentally feasible realization of Dirac magnons with tunable dispersion.
DIRAC distributed secure framework
NASA Astrophysics Data System (ADS)
Casajus, A.; Graciani, R.; LHCb DIRAC Team
2010-04-01
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.
Monitoring the DIRAC distributed system
NASA Astrophysics Data System (ADS)
Santinelli, R.; Seco, M.; Nandakumar, R.; LHCb DIRAC Team
2010-04-01
DIRAC, the LHCb community Grid solution, 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 both by agents and services and collected by a logging system. This allows us to ensure that the components are running properly and to collect useful information regarding their operations. The process status monitoring is displayed using the SLS sensor mechanism that also automatically allows to plot various quantities and keep a history of the system. A dedicated GridMap interface (ServiceMap) allows production shifters and experts to have an immediate, high-impact view of all LHCb critical services status while offering the possibility to refer to details of the SLS and SAM sensors. Error types and statistics provided by the logging service can be accessed via dedicated web interfaces on the DIRAC portal or programmatically via the python based API and CLI.
Photoconductivity in Dirac materials
Shao, J. M.; Yang, G. W.
2015-11-15
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.
Hopf, T.; Vassilevski, K. V. Escobedo-Cousin, E.; King, P. J.; Wright, N. G.; O'Neill, A. G.; Horsfall, A. B.; Goss, J. P.; Wells, G. H.; Hunt, M. R. C.
2014-10-21
Top-gated graphene field-effect transistors (GFETs) have been fabricated using bilayer epitaxial graphene grown on the Si-face of 4H-SiC substrates by thermal decomposition of silicon carbide in high vacuum. Graphene films were characterized by Raman spectroscopy, Atomic Force Microscopy, Scanning Tunnelling Microscopy, and Hall measurements to estimate graphene thickness, morphology, and charge transport properties. A 27 nm thick Al₂O₃ gate dielectric was grown by atomic layer deposition with an e-beam evaporated Al seed layer. Electrical characterization of the GFETs has been performed at operating temperatures up to 100 °C limited by deterioration of the gate dielectric performance at higher temperatures. Devices displayed stable operation with the gate oxide dielectric strength exceeding 4.5 MV/cm at 100 °C. Significant shifting of the charge neutrality point and an increase of the peak transconductance were observed in the GFETs as the operating temperature was elevated from room temperature to 100 °C.
Dirac equations with confining potentials
NASA Astrophysics Data System (ADS)
Noble, J. H.; Jentschura, U. D.
2015-01-01
This paper is devoted to a study of relativistic eigenstates of Dirac particles which are simultaneously bound by a static Coulomb potential and added linear confining potentials. Under certain conditions, despite the addition of radially symmetric, linear confining potentials, specific bound-state energies surprisingly preserve their exact Dirac-Coulomb values. The generality of the "preservation mechanism" is investigated. To this end, a Foldy-Wouthuysen transformation is used to calculate the corrections to the spin-orbit coupling induced by the linear confining potentials. We find that the matrix elements of the effective operators obtained from the scalar, and time-like confining potentials mutually cancel for specific ratios of the prefactors of the effective operators, which must be tailored to the preservation mechanism. The result of the Foldy-Wouthuysen transformation is used to verify that the preservation is restricted (for a given Hamiltonian) to only one reference state, rather than traceable to a more general relationship among the obtained effective low-energy operators. The results derived from the nonrelativistic effective operators are compared to the fully relativistic radial Dirac equations. Furthermore, we show that the preservation mechanism does not affect antiparticle (negative-energy) states.
Superalgebraic representation of Dirac matrices
NASA Astrophysics Data System (ADS)
Monakhov, V. V.
2016-01-01
We consider a Clifford extension of the Grassmann algebra in which operators are constructed from products of Grassmann variables and derivatives with respect to them. We show that this algebra contains a subalgebra isomorphic to a matrix algebra and that it additionally contains operators of a generalized matrix algebra that mix states with different numbers of Grassmann variables. We show that these operators are extensions of spin-tensors to the case of superspace. We construct a representation of Dirac matrices in the form of operators of a generalized matrix algebra.
On the disformal invariance of the Dirac equation
NASA Astrophysics Data System (ADS)
Bittencourt, Eduardo; Lobo, Iarley P.; Carvalho, Gabriel G.
2015-09-01
We analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field acting on the metric tensor. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric tensors, respecting the order of differentiability of the Dirac operator and satisfying the Clifford algebra in both metrics. We split the analysis in some cases according to the spinor mass and the norm of the Dirac current, exhibiting sufficient conditions to find classes of solutions which keep the Dirac operator invariant under the action of the disformal group.
Ultrarelativistic decoupling transformation for generalized Dirac equations
NASA Astrophysics Data System (ADS)
Noble, J. H.; Jentschura, U. D.
2015-07-01
The Foldy-Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schrödinger-Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.
Three Dimensional Dirac Semimetals
NASA Astrophysics Data System (ADS)
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.
On nonautonomous Dirac equation
Hovhannisyan, Gro; Liu Wen
2009-12-15
We construct the fundamental solution of time dependent linear ordinary Dirac system in terms of unknown phase functions. This construction gives approximate representation of solutions which is useful for the study of asymptotic behavior. Introducing analog of Rayleigh quotient for differential equations we generalize Hartman-Wintner asymptotic integration theorems with the error estimates for applications to the Dirac system. We also introduce the adiabatic invariants for the Dirac system, which are similar to the adiabatic invariant of Lorentz's pendulum. Using a small parameter method it is shown that the change in the adiabatic invariants approaches zero with the power speed as a small parameter approaches zero. As another application we calculate the transition probabilities for the Dirac system. We show that for the special choice of electromagnetic field, the only transition of an electron to the positron with the opposite spin orientation is possible.
Dynamical supersymmetric Dirac Hamiltonians
Ginocchio, J.N.
1986-01-01
Using the language of quantum electrodynamics, the Dirac Hamiltonian of a neutral fermion interacting with a tensor field is examined. A supersymmetry found for a general Dirac Hamiltonian of this type is discussed, followed by consideration of the special case of a harmonic electric potential. The square of the Dirac Hamiltonian of a neutral fermion interacting via an anomalous magnetic moment in an electric potential is shown to be equivalent to a three-dimensional supersymmetric Schroedinger equation. It is found that for a potential that grows as a power of r, the lowest energy of the Hamiltonian equals the rest mass of the fermion, and the Dirac eigenfunction has only an upper component which is normalizable. It is also found that the higher energy states have upper and lower components which form a supersymmetric doublet. 15 refs. (LEW)
NASA Astrophysics Data System (ADS)
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.
Euclidean supergravity in terms of Dirac eigenvalues
NASA Astrophysics Data System (ADS)
Vancea, Ion V.
1998-08-01
It has been recently shown that the eigenvalues of the Dirac operator can be considered as dynamical variables of Euclidean gravity. The purpose of this paper is to explore the possibility that the eigenvalues of the Dirac operator might play the same role in the case of supergravity. It is shown that for this purpose some primary constraints on covariant phase space as well as secondary constraints on the eigenspinors must be imposed. The validity of primary constraints under covariant transport is further analyzed. It is shown that in this case restrictions on the tangent bundle and on the spinor bundle of spacetime arise. The form of these restrictions is determined under some simplifying assumptions. It is also shown that manifolds with flat curvature of tangent bundle and spinor bundle satisfy these restrictions and thus they support the Dirac eigenvalues as global observables.
NASA Astrophysics Data System (ADS)
Mejjaoli, Hatem; Trimèche, Khalifa
2016-06-01
In this paper, we prove various mathematical aspects of the qualitative uncertainty principle, including Hardy's, Cowling-Price's theorem, Morgan's theorem, Beurling, Gelfand-Shilov, Miyachi theorems.
The Clifford algebra of physical space and Dirac theory
NASA Astrophysics Data System (ADS)
Vaz, Jayme, Jr.
2016-09-01
The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli matrices is shown to not be completely true. It is only true as long as the term β \\psi in the usual Dirac factorization of the Klein–Gordon equation is assumed to be the product of a square matrix β and a column matrix ψ. In this paper we show that there is another possibility besides this matrix product, in fact a possibility involving a matrix operation, and show that it leads to another possible expression for the Dirac equation. We show that, behind this other possible factorization is the formalism of the Clifford algebra of physical space. We exploit this fact, and discuss several different aspects of Dirac theory using this formalism. In particular, we show that there are four different possible sets of definitions for the parity, time reversal, and charge conjugation operations for the Dirac equation.
Dirac's Footsteps and Supersymmetry
NASA Astrophysics Data System (ADS)
Ramond, Pierre
One hundred years after its creator's birth, the Dirac equation stands as the cornerstone of XXth Century physics. But it is much more, as it carries the seeds of supersymmetry. Dirac also invented the light-cone, or "front form" dynamics, which plays a crucial role in string theory and in elucidating the finiteness of N=4 Yang-Mills theory. The light-cone structure of eleven-dimensional supergravity (N=8 supergravity in four dimensions) suggests a group-theoretical interpretation of its divergences. We speculate they could be compensated by an infinite number of triplets of massless higher spin fields, each obeying a Dirac-like equation associated with the coset F4/SO(9). The divergences are proportional to the trace over a non-compact structure containing the compact form of F4. Its nature is still unknown, but it could show the way to M-theory.
Dirac's Footsteps and Supersymmetry
NASA Astrophysics Data System (ADS)
Ramond, Pierre
2003-12-01
One hundred years after its creator's birth, the Dirac equation stands as the cornerstone of XXth Century physics. But it is much more, as it carries the seeds of supersymmetry. Dirac also invented the light-cone, or "front form" dynamics, which plays a crucial role in string theory and in elucidating the finiteness of N = 4 Yang-Mills theory. The light-cone structure of eleven-dimensional supergravity (N = 8 supergravity in four dimensions) suggests a group-theoretical interpretation of its divergences. We speculate they could be compensated by an infinite number of triplets of massless higher spin fields, each obeying a Dirac-like equation associated with the coset F4/S0(9). The divergences are proportional to the trace over a non-compact structure containing the compact form of F4. Its nature is still unknown, but it could show the way to M-theory.
Lagrangians for massive Dirac chiral superfields
NASA Astrophysics Data System (ADS)
Jiménez, Enrique; Vaquera-Araujo, C. A.
2016-06-01
A variant for the superspin one-half massive superparticle in 4D, N = 1, based on Dirac superfields, is offered. As opposed to the current known models that use spinor chiral superfields, the propagating fields of the supermultiplet are those of the lowest mass dimensions possible: scalar, Dirac and vector fields. Besides the supersymmetric chiral condition, the Dirac superfields are not further constrained, allowing a very straightforward implementation of the path-integral method. The corresponding superpropagators are presented. In addition, an interaction super Yukawa potential, formed by Dirac and scalar chiral superfields, is given in terms of their component fields. The model is first presented for the case of two superspin one-half superparticles related by the charged conjugation operator, but in order to treat the case of neutral superparticles, the Majorana condition on the Dirac superfields is also studied. We compare our proposal with the known models of spinor superfields for the one-half superparticle and show that it is equivalent to them.
A spin observable for a Dirac particle
NASA Astrophysics Data System (ADS)
Caban, P.; Rembieliński, J.; Włodarczyk, M.
2013-03-01
We discuss the form of the spin operator in relativistic quantum mechanics. We derive the form of the spin operator in the case when the states with negative energies are admitted. It appears that for a Dirac particle the spin operator reduces to the so called mean-spin operator introduced by Foldy and Wouthuysen. We show that the spin operator transforms under Lorentz group action according to an operator Wigner rotation, analogously as a Bloch vector describing polarization of a particle in momentum representation.
A spin observable for a Dirac particle
Caban, P. Rembielinski, J. Wlodarczyk, M.
2013-03-15
We discuss the form of the spin operator in relativistic quantum mechanics. We derive the form of the spin operator in the case when the states with negative energies are admitted. It appears that for a Dirac particle the spin operator reduces to the so called mean-spin operator introduced by Foldy and Wouthuysen. We show that the spin operator transforms under Lorentz group action according to an operator Wigner rotation, analogously as a Bloch vector describing polarization of a particle in momentum representation. - Highlights: Black-Right-Pointing-Pointer We examine the problem of a relativistic spin operator in the case of a Dirac particle. Black-Right-Pointing-Pointer We show that a proper spin operator coincides for positive energies with the operator used in quantum field theory. Black-Right-Pointing-Pointer This operator can be extended for negative energies. Black-Right-Pointing-Pointer We show that this operator is equivalent to the so called mean-spin operator introduced by Foldy and Wouthuysen. Black-Right-Pointing-Pointer The spin operator transforms under Lorentz group action according to the operator Wigner rotation.
NASA Astrophysics Data System (ADS)
Mao, Pu-Jian; Jia, Lin-Yu; Ren, Ji-Rong
We investigate the separability of massive Dirac equation in the charged AdS-Kerr-Taub-NUT black hole. It is shown that the Dirac equation can be separated by variables into purely radial and purely angular parts in this background spacetime. From the separated solutions for massive Dirac equation, a first-order symmetric operator that commutes with the Dirac operator is constructed and expressed in terms of Killing-Yano tensor admitted by the charged AdS-Kerr-Taub-NUT spacetime. Then the Hawking radiation of Dirac particles in the background of charged AdS-Kerr-Taub-NUT black hole is investigated via the Damour-Ruffini-Sannan method. It is shown that quantum thermal effect of the Dirac particles in the charged AdS-Kerr-Taub-NUT black hole has the same character with that of the scalar particles.
Dirac particle in a box, and relativistic quantum Zeno dynamics
NASA Astrophysics Data System (ADS)
Menon, Govind; Belyi, Sergey
2004-09-01
After developing a complete set of eigenfunctions for a Dirac particle restricted to a box, the quantum Zeno dynamics of a relativistic system is considered. The evolution of a continuously observed quantum mechanical system is governed by the theorem put forth by Misra and Sudarshan. One of the conditions for quantum Zeno dynamics to be manifest is that the Hamiltonian is semi-bounded. This Letter analyzes the effects of continuous observation of a particle whose time evolution is generated by the Dirac Hamiltonian. The theorem by Misra and Sudarshan is not applicable here since the Dirac operator is not semi-bounded.
Dirac Semimetals in Two Dimensions.
Young, Steve M; Kane, Charles L
2015-09-18
Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin Hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature Dirac cones at high-symmetry points that are not gapped by spin-orbit interactions and exhibit behavior distinct from both graphene and 3D Dirac semimetals. Using a two-site tight-binding model, we construct representatives of three possible distinct Dirac semimetal phases and show that single symmetry-protected Dirac points are impossible in two dimensions. An essential role is played by the presence of nonsymmorphic space group symmetries. We argue that these symmetries tune the system to the boundary between a 2D topological and trivial insulator. By breaking the symmetries we are able to access trivial and topological insulators as well as Weyl semimetal phases. PMID:26431004
Qualitative analysis of trapped Dirac fermions in graphene
Jakubský, Vít Krejčiřík, David
2014-10-15
We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac operator, we obtain sufficient and necessary conditions for confinement of the quasi-particles. The rigorous theoretical results are illustrated on the realistic examples of the three classes of traps.
An Effective Theory of Dirac Dark Matter
Harnik, Roni; Kribs, Graham D.; /Oregon U.
2010-06-11
A stable Dirac fermion with four-fermion interactions to leptons suppressed by a scale {Lambda} {approx} 1 TeV is shown to provide a viable candidate for dark matter. The thermal relic abundance matches cosmology, while nuclear recoil direct detection bounds are automatically avoided in the absence of (large) couplings to quarks. The annihilation cross section in the early Universe is the same as the annihilation in our galactic neighborhood. This allows Dirac fermion dark matter to naturally explain the positron ratio excess observed by PAMELA with a minimal boost factor, given present astrophysical uncertainties. We use the Galprop program for propagation of signal and background; we discuss in detail the uncertainties resulting from the propagation parameters and, more importantly, the injected spectra. Fermi/GLAST has an opportunity to see a feature in the gamma-ray spectrum at the mass of the Dirac fermion. The excess observed by ATIC/PPB-BETS may also be explained with Dirac dark matter that is heavy. A supersymmetric model with a Dirac bino provides a viable UV model of the effective theory. The dominance of the leptonic operators, and thus the observation of an excess in positrons and not in anti-protons, is naturally explained by the large hypercharge and low mass of sleptons as compared with squarks. Minimizing the boost factor implies the right-handed selectron is the lightest slepton, which is characteristic of our model. Selectrons (or sleptons) with mass less than a few hundred GeV are an inescapable consequence awaiting discovery at the LHC.
NASA Astrophysics Data System (ADS)
Schmidt, M.; Peano, V.; Marquardt, F.
2015-02-01
Recent progress in optomechanical systems may soon allow the realization of optomechanical arrays, i.e. periodic arrangements of interacting optical and vibrational modes. We show that photons and phonons on a honeycomb lattice will produce an optically tunable Dirac-type band structure. Transport in such a system can exhibit transmission through an optically created barrier, similar to Klein tunneling, but with interconversion between light and sound. In addition, edge states at the sample boundaries are dispersive and enable controlled propagation of photon-phonon polaritons.
Dirac's Claim and the Chemists
NASA Astrophysics Data System (ADS)
Simões, Ana
In 1929 Paul A. M. Dirac claimed that ``the underlying physical laws necessary for the mathematical theory of ... the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.'' This sentence of Dirac's is cited frequently by historians and philosophers of chemistry in the context of discussions on the hypothetical reduction of chemistry to physics. But how did chemists themselves react to Dirac's claim? Did they feel threatened by physicists who felt they could do their job better than themselves? Did they feel indifferent, or did they simply not care? Was Dirac's paper often cited by chemists? Why was it cited? In this paper, I provide answers to these questions on the basis of an analysis of citations to Dirac's 1929 paper in the Science Citation Index.
The DIRAC Data Management System and the Gaudi dataset federation
NASA Astrophysics Data System (ADS)
Haen, Christophe; Charpentier, Philippe; Frank, Markus; Tsaregorodtsev, Andrei
2015-12-01
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. This paper also focuses on the DIRAC File Catalog, for which a lot of new developments have been carried out, so that LHCb could migrate its replica catalog from the LCG File Catalog to the DFC. Finally, we will present how LHCb achieves a dataset federation without the need of an extra infrastructure.
NASA Astrophysics Data System (ADS)
Casajus, A.; Ciba, K.; Fernandez, V.; Graciani, R.; Hamar, V.; Mendez, V.; Poss, S.; Sapunov, M.; Stagni, F.; Tsaregorodtsev, A.; Ubeda, M.
2012-12-01
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.
Symmetry Breaking And The Nilpotent Dirac Equation
Rowlands, Peter
2004-08-19
A multivariate 4-vector representation for space-time and a quaternion representation for mass and the electric, strong and weak charges leads to a nilpotent form of the Dirac equation, which packages the entire physical information available about a fermion state. The nilpotent state vector breaks the symmetry between the strong, electric and weak interactions, by associating their respective charges with vector, scalar and pseudoscalar operators, leading directly to the SU(3) x SU(2)L x U(1) symmetry, and to particle structures and mass-generating states. In addition, the nilpotent Dirac equation has just three solutions for spherically-symmetric distance-dependent potentials, and these correspond once again to those that would be expected for the three interactions: linear for the strong interaction; inverse linear for the electromagnetic; and a harmonic oscillator-type solution, which can be equated with the dipolar annihilation and creation mechanisms of the weak interaction.
WKB Approxiation of the Dirac Equation with a Supersymmetric Extension
NASA Astrophysics Data System (ADS)
Markov, Yu. A.; Markova, M. A.
2015-12-01
A general scheme of the self-consistent construction of a semiclassical approximation for the Dirac equation in an external gauge field in which the standard Dirac operator is replaced by the Dirac operator with a supersymmetric extension is presented. It is shown that in contrast to the usual WKB method, here the expansion must be carried out over half-integer powers of the Planck constant ħ. The first four terms of the semiclassical expansion of the wave function are obtained in explicit form. It is shown that generalization of the initial Dirac operator leads to the appearance of new additional terms in the semiclassical equation of motion for the spin of a particle in an external field, which thus requires a modification of the Lagrangian of the spinning particle. The result so obtained is used to construct mappings between two Lagrangian descriptions of a classical color-charged spinning particle, one of which possesses local supersymmetry, and the other not. It is shown that in order for the mappings to be one-to-one it is necessary to add new additional terms to the Lagrangian without supersymmetry, obtained within the framework of the semiclassical approximation of the Dirac operator with supersymmetry.
Time Delay for the Dirac Equation
NASA Astrophysics Data System (ADS)
Naumkin, Ivan; Weder, Ricardo
2016-07-01
We consider time delay for the Dirac equation. A new method to calculate the asymptotics of the expectation values of the operator {intlimits0 ^{∞}e^{iH0t}ζ(\\vert x\\vert /R) e^{-iH0t}dt} , as {R → ∞} , is presented. Here, H 0 is the free Dirac operator and {ζ(t)} is such that {ζ(t) = 1} for {0 ≤ t ≤ 1} and {ζ(t) = 0} for {t > 1} . This approach allows us to obtain the time delay operator {δ {T}(f)} for initial states f in {{H} 2^{3/2+ɛ}({R}3;{C}4)} , {ɛ > 0} , the Sobolev space of order {3/2+ɛ} and weight 2. The relation between the time delay operator {δ{T}(f)} and the Eisenbud-Wigner time delay operator is given. In addition, the relation between the averaged time delay and the spectral shift function is presented.
NASA Astrophysics Data System (ADS)
Yanagisawa, Takashi
2015-07-01
We investigate the Kondo effect in Dirac systems, where Dirac electrons interact with the localized spin via the s-d exchange coupling. The Dirac electron in solid state has the linear dispersion and is described typically by the Hamiltonian such as Hk = vk · σ for the wave number k where σj are Pauli matrices. We derived the formula of the Kondo temperature TK by means of the Green's function theory for small J. The TK is determined from a singularity of Green's functions in the form T{K} ≃ bar{D}exp ( - {const}{.}/ρ |J|) when the exchange coupling |J| is small where bar{D} = D/√{1 + D2/(2μ )2} for a cutoff D and ρ is the density of states at the Fermi surface. When |μ| ≪ D, TK is proportional to |μ|: TK ≃ |μ| exp(-const./ρ|J|). The Kondo screening will, however, disappear when the Fermi surface shrinks to a point called the Dirac point, that is, TK vanishes when the chemical potential μ is just at the Dirac point. The resistivity and the specific heat exhibit a log-T singularity in the range TK < T ≪ |μ|/kB. Instead, for T ˜ O(|μ|) or T > |μ|, they never show log-T.
Reconstruction of symmetric Dirac-Maxwell equations using nonassociative algebra
NASA Astrophysics Data System (ADS)
Kalauni, Pushpa; Barata, J. C. A.
2015-01-01
In the presence of sources, the usual Maxwell equations are neither symmetric nor invariant with respect to the duality transformation between electric and magnetic fields. Dirac proposed the existence of magnetic monopoles for symmetrizing the Maxwell equations. In the present work, we obtain the fully symmetric Dirac-Maxwell's equations (i.e. with electric and magnetic charges and currents) as a single equation by using 4 × 4 matrix presentation of fields and derivative operators. This matrix representation has been derived with the help of the algebraic properties of quaternions and octonions. Such description gives a compact representation of electric and magnetic counterparts of the field in a single equation.
Polyakov loop fluctuations in the Dirac eigenmode expansion
NASA Astrophysics Data System (ADS)
Doi, Takahiro M.; Redlich, Krzysztof; Sasaki, Chihiro; Suganuma, Hideo
2015-11-01
We investigate correlations of the Polyakov loop fluctuations with eigenmodes of the lattice Dirac operator. Their analytic relations are derived on the temporally odd-number size lattice with the normal nontwisted periodic boundary condition for the link variables. We find that the low-lying Dirac modes yield negligible contributions to the Polyakov loop fluctuations. This property is confirmed to be valid in confined and deconfined phases by numerical simulations in SU(3) quenched QCD. These results indicate that there is no direct, one-to-one correspondence between confinement and chiral symmetry breaking in QCD in the context of different properties of the Polyakov loop fluctuation ratios.
Scalable implementation of spectral methods for the Dirac equation
Wells, J.C.
1998-10-01
The author discusses the implementation and performance on massively parallel, distributed-memory computers of a message-passing program to solve the time-dependent dirac equation in three Cartesian coordinates. Luses pseudo-spectral methods to obtain a discrete representation of the dirac spinor wavefunction and all coordinate-space operators. Algorithms for the solution of the discrete equations are iterative and depend critically on the dirac hamiltonian-wavefunction product, which he implements as a series of parallel matrix products using MPI. He investigated two communication algorithms, a ring algorithm and a collective-communication algorithm, and present performance results for each on a Paragon-MP (1024 nodes) and a Cray T3E-900 (512 nodes). The ring algorithm achieves very good performance, scaling up to the maximum number of nodes on each machine. However, the collective-communication algorithm scales effectively only on the Paragon.
Homogeneous spaces of Dirac groupoids
NASA Astrophysics Data System (ADS)
Jotz Lean, Madeleine
2016-06-01
A Poisson structure on a homogeneous space of a Poisson groupoid is homogeneous if the action of the Lie groupoid on the homogeneous space is compatible with the Poisson structures. According to a result of Liu, Weinstein and Xu, Poisson homogeneous spaces of a Poisson groupoid are in correspondence with suitable Dirac structures in the Courant algebroid defined by the Lie bialgebroid of the Poisson groupoid. We show that this correspondence result fits into a more natural context: the one of Dirac groupoids, which are objects generalizing Poisson groupoids and multiplicative closed 2-forms on groupoids.
Realization of Dirac Cones in Few Bilayer Sb(111) Films by Surface Modification.
Pan, Hui; Wang, Xue-Sen
2015-12-01
We report the first-principle study on the recovery and linearization of Dirac cones in the electronic band structures of a few bilayer Sb(111) films (n-BL Sb) by surface modification. Due to the interaction between the surface states on the two surfaces of a free-standing film, the distorted Dirac cone in n-BL Sb(111) (n < 5) disappears. We demonstrate that the Dirac cone can be restored by functionalizing one surface with certain atoms including H, Ag, and Au, to reduce the inter-surface interaction. We further show that an ideal Dirac cone with linear dispersion of topological surface states near the zone center can be realized by functionalizing both surfaces of the film with oxygen, which enhances spin-orbital coupling. The realization of Dirac cone by surface functionalization shows promise for applications of topologic materials to spintronic devices and their operation in complicated conditions. PMID:26293493
Superconductivity in doped Dirac semimetals
NASA Astrophysics Data System (ADS)
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.
Cloud flexibility using DIRAC interware
NASA Astrophysics Data System (ADS)
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
Meissner Effect of Dirac Electrons in Superconducting State Due to Inter-Band Effect
NASA Astrophysics Data System (ADS)
Mizoguchi, Tomonari; Ogata, Masao
2015-08-01
Dirac electrons in solids show characteristic physical properties due to their linear dispersion relation and two-band nature. Although the transport phenomena of Dirac electrons in a normal state have intensively been studied, the transport phenomena in a superconducting state have not been fully understood. In particular, it is not clear whether Dirac electrons in a superconducting state show Meissner effect (ME), since a diamagnetic term of a current operator is absent as a result of the linear dispersion. We investigate the ME of three dimensional massive Dirac electrons in a superconducting state on the basis of Kubo formula, and clarify that Meissner kernel becomes finite by use of the inter-band contribution. This mechanism of the ME for Dirac electrons is completely different from that for the electrons in usual metals. Our result shows that the Meissner kernel remains finite even when the superconducting gap vanishes. This is an unavoidable problem in the Dirac electron system as reported in the previous works. Thus, we use a prescription in which we subtract the normal state contribution. In order to justify this prescription, we develop a specific model where the Meissner kernel is obtained by the prescription. We also derive the result for the electron gas by taking the non-relativistic limit of Dirac Hamiltonian, and clarify that the diamagnetic term of the Meissner kernel can be regarded as the inter-band contribution between electrons and positrons in terms of the Dirac model.
Transport experiments with Dirac electrons
NASA Astrophysics Data System (ADS)
Checkelsky, Joseph George
This thesis presents transport experiments performed on solid state systems in which the behavior of the charge carriers can be described by the Dirac equation. Unlike the massive carriers in a typical material, in these systems the carriers behave like massless fermions with a photon-like dispersion predicted to greatly modify their spin and charge transport properties. The first system studied is graphene, a crystalline monolayer of carbon arranged in a hexagonal lattice. The band structure calculated from the hexagonal lattice has the form of the massless Dirac Hamiltonian. At the charge neutral Dirac point, we find that application of a magnetic field drives a transition to an insulating state. We also study the thermoelectric properties of graphene and find that the states near the Dirac point have a unique response compared to those at higher charge density. The second system is the 3D topological insulator Bi2Se3, where a Dirac-like dispersion for states on the 2D surface of the insulating 3D crystal arises as a result of the topology of the 3D bands and time reversal symmetry. To access the transport properties of the 2D states, we suppress the remnant bulk conduction channel by chemical doping and electrostatic gating. In bulk crystals we find strong quantum corrections to transport at low temperature when the bulk conduction channel is maximally suppressed. In microscopic crystals we are able better to isolate the surface conduction channel properties. We identify in-gap conducting states that have relatively high mobility compared to the bulk and exhibit weak anti-localization, consistent with predictions for protected 2D surface states with strong spin-orbit coupling.
Dequantization of the Dirac Equation: the Semiclassical Dirac Mechanics.
NASA Astrophysics Data System (ADS)
Katz, Alan R.
1987-09-01
A relativistic Hamiltonian mechanics for a Dirac particle is derived as the semi-classical limit of the Dirac equation. The theory bears much resemblance to ordinary classical mechanics, except that some of the phase space variables are four by four matrices. This is necessary because of the spin degrees of freedom of the particle. Constraints in the theory connect the four by four matrices with observables. In finding the semi-classical limit of the Dirac equation, we first find it useful to apply a WKB type of approximation to a scalar Superfield theory. By eliminating second class constraints, we obtain the Brink and Schwarz formulation of Casalbuoni's superspace Pseudomechanics. The spin 1/2 sector is then examined to find the corresponding WKB limit of the Dirac equation, a semi-classical mechanics. We next reformulate this Dirac mechanics in terms of ast-products utilizing phase space methods, guided in interpretation by what was obtained via the WKB method. With the formalism in hand, we consider a Dirac particle in a homogeneous electromagnetic field. We are able to demonstrate that the g factor is equal to two, obtain the usual equation of motion for the position and momentum, and are able to DERIVE directly from QED the relativistic spin precession equation of Bargmann, Michel, and Telegdi; an equation originally given as just a simple relativization of the expression for non-relativistic precession. This establishes a vital link between QED theory and what is actually observed in the g - 2 experiments. With this method, we can find a spin precession equation for inhomogeneous fields which contains quantum corrections to the usual equation and we present the general method. Some of these corrections may be easily deduced from gauge invariance, but only if everything is expressed in terms of ast-products, not ordinary products. The equation of motion for any observable is always given as an explicit series in Planck's constant, thus allowing a classical
Spawning rings of exceptional points out of Dirac cones
NASA Astrophysics Data System (ADS)
Zhen, Bo; Hsu, Chia Wei; Igarashi, Yuichi; Lu, Ling; Kaminer, Ido; Pick, Adi; Chua, Song-Liang; Joannopoulos, John D.; Soljačić, Marin
2015-09-01
The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure--two conical bands touching at a single point--has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformation of the Dirac cone often reveals intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity-time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. Dirac cones and exceptional points are connected: it was theoretically suggested that certain non-Hermitian perturbations can deform a Dirac cone and spawn a ring of exceptional points. Here we experimentally demonstrate such an `exceptional ring' in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone resulting from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity-time symmetric systems. Our results indicate that the radiation existing in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.
DIRAC File Replica and Metadata Catalog
NASA Astrophysics Data System (ADS)
Tsaregorodtsev, A.; Poss, S.
2012-12-01
File replica and metadata catalogs are essential parts of any distributed data management system, which are largely determining its functionality and performance. A new File Catalog (DFC) was developed in the framework of the DIRAC Project that combines both replica and metadata catalog functionality. The DFC design is based on the practical experience with the data management system of the LHCb Collaboration. It is optimized for the most common patterns of the catalog usage in order to achieve maximum performance from the user perspective. The DFC supports bulk operations for replica queries and allows quick analysis of the storage usage globally and for each Storage Element separately. It supports flexible ACL rules with plug-ins for various policies that can be adopted by a particular community. The DFC catalog allows to store various types of metadata associated with files and directories and to perform efficient queries for the data based on complex metadata combinations. Definition of file ancestor-descendent relation chains is also possible. The DFC catalog is implemented in the general DIRAC distributed computing framework following the standard grid security architecture. In this paper we describe the design of the DFC and its implementation details. The performance measurements are compared with other grid file catalog implementations. The experience of the DFC Catalog usage in the CLIC detector project are discussed.
Highly anisotropic Dirac fermions in square graphynes
NASA Astrophysics Data System (ADS)
Zhang, Lizhi; Wang, Zhengfei; Rao, Jiansheng; Li, Ziheng; Huang, Wulin; Wang, Zhiming; Du, Shixuan; Gao, Hongjun; Liu, Feng
Recently, there have been intense search of new 2D materials, and one especially appealing class of 2D materials is the all-carbon allotropes of Dirac materials. Here, we predict a new family of 2D carbon allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac Fermions, using first-principle calculations within density functional theory. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 x 105 to 7.2 x 105 m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. Our findings enrich the Dirac physics founded in other 2D Dirac systems, and offer a new design mechanism for creating Dirac band by tuning the interaction range. We envision that the highly anisotropic Dirac crescent may be exploited in all-carbon-based electronic devices for manipulating anisotropic electron propagation.
Highly anisotropic Dirac fermions in square graphynes
NASA Astrophysics Data System (ADS)
Zhang, Lizhi; Wang, Zhengfei; Rao, Jiansheng; Li, Ziheng; Huang, Wulin; Wang, Zhiming; Du, Shixuan; Gao, Hongjun; Liu, Feng
Recently, there have been intense search of new 2D materials, and one especially appealing class of 2D materials is the all-carbon allotropes of Dirac materials. Here, we predict a new family of 2D carbon allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac Fermions, using first-principle calculations within density functional theory. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 ×105 to 7.2 ×105 m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. Our findings enrich the Dirac physics founded in other 2D Dirac systems, and offer a new design mechanism for creating Dirac band by tuning the interaction range. We envision that the highly anisotropic Dirac crescent may be exploited in all-carbon-based electronic devices for manipulating anisotropic electron propagation.
Gravitational Repulsion and Dirac Antimatter
NASA Astrophysics Data System (ADS)
Kowitt, Mark E.
1996-03-01
Based on an analogy with electron and hole dynamics in semiconductors, Dirac's relativistic electron equation is generalized to include a gravitational interaction using an electromagnetic-type approximation of the gravitational potential. With gravitational and inertial masses decoupled, the equation serves to extend Dirac's deduction of antimatter parameters to include the possibility of gravitational repulsion between matter and antimatter. Consequences for general relativity and related “antigravity” issues are considered, including the nature and gravitational behavior of virtual photons, virtual pairs, and negative-energy particles. Basic cosmological implications of antigravity are explored—in particular, potential contributions to inflation, expansion, and the general absence of detectable antimatter. Experimental and observational tests are noted, and new ones suggested.
DIRAC: Secure web user interface
NASA Astrophysics Data System (ADS)
Casajus Ramo, A.; Sapunov, M.
2010-04-01
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.
Local energy decay of massive Dirac fields in the 5D Myers-Perry metric
NASA Astrophysics Data System (ADS)
Daudé, Thierry; Kamran, Niky
2012-07-01
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.
Dirac fermions in nontrivial topology black hole backgrounds
Gozdz, Marek; Nakonieczny, Lukasz; Rogatko, Marek
2010-05-15
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{sup -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{sup 2} sphere pierced by a cosmic string. This factor modifies the eigenvalues of the Dirac operator acting on the transverse manifold.
Separating the variables in a massless Dirac equation in Minkowski space
Lisitsyn, Y.V.
1995-07-01
Exact integration of the Dirac equation is a classical topic in mathematical physics, which has been researched for several decades. A basic method is complete segregation of the variables. Such separation can be attained in a Dirac equation containing an external electromagnetic field in Minkowski space by means of complete sets of first-order symmetry matrix operators. The purpose of this paper is to solve an analogous case for a free massless Dirac equation. That task has a special feature because external fields are absent and the massless equation is reduced to a D`Alambert equation by squaring. Nevertheless, interest attaches to states defined by the first-order symmetry-operator matrices that cannot be obtained by setting the mass to zero in systems containing a mass Dirac equation.
Dirac cone and double zero materials
NASA Astrophysics Data System (ADS)
Chan, C. T.; Huang, Xueqin; Lai, Yun; Hang, Zhi Hong; Zheng, Huihuo
2011-10-01
Materials with zero permittivity and zero permeability (double zero) possess very interesting wave manipulation characteristics. Systems with Dirac cones in the band structure also possess amazing wave transport properties. These two classes of material are actually related to each other. We show that dielectric photonic crystals can be designed and fabricated which exhibit Dirac cones at k = 0 at a finite frequency. A subset of such materials behave as if they have zero permittivity and zero permeability at the Dirac point, as well as exhibiting properties intrinsic to a Dirac cone.
Dirac cone and double zero materials
Chan, C. T.; Huang Xueqin; Hang Zhihong; Zheng Huihuo; Lai Yun
2011-10-03
Materials with zero permittivity and zero permeability (double zero) possess very interesting wave manipulation characteristics. Systems with Dirac cones in the band structure also possess amazing wave transport properties. These two classes of material are actually related to each other. We show that dielectric photonic crystals can be designed and fabricated which exhibit Dirac cones at k = 0 at a finite frequency. A subset of such materials behave as if they have zero permittivity and zero permeability at the Dirac point, as well as exhibiting properties intrinsic to a Dirac cone.
A Short Biography of Paul A. M. Dirac and Historical Development of Dirac Delta Function
ERIC Educational Resources Information Center
Debnath, Lokenath
2013-01-01
This paper deals with a short biography of Paul Dirac, his first celebrated work on quantum mechanics, his first formal systematic use of the Dirac delta function and his famous work on quantum electrodynamics and quantum statistics. Included are his first discovery of the Dirac relativistic wave equation, existence of positron and the intrinsic…
The Dirac equation in an external electromagnetic field: symmetry algebra and exact integration
NASA Astrophysics Data System (ADS)
Breev, A. I.; Shapovalov, A. V.
2016-01-01
Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are not obtained by separation of variables for several external electromagnetic fields. We have considered an example of crossed electric and magnetic fields of a special type for which the Dirac equation admits a nonlocal symmetry operator.
NASA Astrophysics Data System (ADS)
Kononets, Y. V.
2010-05-01
An algebraic block-diagonalization of the Dirac Hamiltonian in a time-independent external field reveals a charge-index conservation law which forbids the physical phenomena of the Klein paradox type and guarantees a single-particle nature of the Dirac equation in strong external fields. Simultaneously, the method defines simpler quantum-mechanical objects—paulions and antipaulions, whose 2-component wave functions determine the Dirac electron states through exact operator relations. Based on algebraic symmetry, the presented theory leads to a new understanding of the Dirac equation physics, including new insight into the Dirac measurements and a consistent scheme of relativistic quantum mechanics of electron in the paulion representation. Along with analysis of the mathematical anatomy of the Klein paradox falsity, a complete set of paradox-free eigenfunctions for the Klein problem is obtained and investigated via stationary solutions of the Pauli-like equations with respective paulion Hamiltonians. It is shown that the physically correct Dirac states in the Klein zone are characterized by the total particle reflection from the potential step and satisfy the fundamental charge-index conservation law.
Dirac solutions for quaternionic potentials
De Leo, Stefano Giardino, Sergio
2014-02-15
The Dirac equation is solved for quaternionic potentials, i V{sub 0} + j W{sub 0} (V{sub 0}∈R , W{sub 0}∈C). The study shows two different solutions. The first one contains particle and anti-particle solutions and leads to the diffusion, tunneling, and Klein energy zones. The standard solution is recovered taking the complex limit of this solution. The second solution, which does not have a complex counterpart, can be seen as a V{sub 0}-antiparticle or |W{sub 0}|-particle solution.
Dirac's aether in curved spacetime.
Oliveira; Teixeira
2000-06-01
Proca's equations for two types of fields in a Dirac's aether with electric conductivity sigma are solved exactly. The Proca electromagnetic fields are assumed with cylindrical symmetry. The background is a static, curved spacetime whose spatial section is homogeneous and has the topology of either the three-sphere S 3 or the projective three-space P 3. Simple relations between the range of Proca field lambda, the Universe radius R, the limit of photon rest mass mgamma and the conductivity sigma are written down. PMID:10932114
Halogenated arsenenes as Dirac materials
NASA Astrophysics Data System (ADS)
Tang, Wencheng; Sun, Minglei; Ren, Qingqiang; Wang, Sake; Yu, Jin
2016-07-01
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.
Electromagnetic Klein-Gordon and Dirac Equations in Scale Relativity
NASA Astrophysics Data System (ADS)
Célérier, Marie-Noëlle; Nottale, Laurent
We present a new step in the foundation of quantum field theory with the tools of scale relativity. Previously, quantum motion equations (Schrödinger, Klein-Gordon, Dirac, Pauli) have been derived as geodesic equations written with a quantum-covariant derivative operator. Then, the nature of gauge transformations, of gauge fields and of conserved charges have been given a geometric meaning in terms of a scale-covariant derivative tool. Finally, the electromagnetic Klein-Gordon equation has been recovered with a covariant derivative constructed by combining the quantum-covariant velocity operator and the scale-covariant derivative. We show here that if one tries to derive the electromagnetic Dirac equation from the Klein-Gordon one as for the free particle motion, i.e. as a square root of the time part of the Klein-Gordon operator, one obtains an additional term which is the relativistic analog of the spin-magnetic field coupling term of the Pauli equation. However, if one first applies the quantum covariance, then implements the scale covariance through the scale-covariant derivative, one obtains the electromagnetic Dirac equation in its usual form. This method can also be applied successfully to the derivation of the electromagnetic Klein-Gordon equation. This suggests it rests on more profound roots of the theory, since it encompasses naturally the spin-charge coupling.
The modular class of a Dirac map
NASA Astrophysics Data System (ADS)
Caseiro, Raquel
2016-06-01
In this paper we study the modular classes of Dirac manifolds and of Dirac maps, and we discuss their basic properties. We apply these results to explain the relationship between the modular classes of the various structures involved in the reduction of a Poisson manifold under the action of a Poisson-Lie group.
The Dirac equation in Kerr-Newman-Ads black hole background
NASA Astrophysics Data System (ADS)
Belgiorno, Francesco; Cacciatori, Sergio L.
2010-03-01
We consider the Dirac equation on the Kerr-Newman-AdS black hole background. We first perform the variable separation for the Dirac equation and define the Hamiltonian operator Ĥ. Then we show that for a massive Dirac field with mass μ>=1/(2l), where l is linked to the cosmological constant Λ by Λ≕-3/l2, essential self-adjointness of Ĥ on C0∞((r+,∞)×S2)4 is obtained even in presence of the boundarylike behavior of infinity in an asymptotically AdS black hole background. Furthermore, qualitative spectral properties of the Hamiltonian are taken into account and in agreement with the existing results concerning the case of stationary axisymmetric asymptotically flat black holes we infer the absence of time-periodic and normalizable solutions of the Dirac equation around the black hole in the nonextremal case.
‘Parabolic’ trapped modes and steered Dirac cones in platonic crystals
McPhedran, R. C.; Movchan, A. B.; Movchan, N. V.; Brun, M.; Smith, M. J. A.
2015-01-01
This paper discusses the properties of flexural waves governed by the biharmonic operator, and propagating in a thin plate pinned at doubly periodic sets of points. The emphases are on the design of dispersion surfaces having the Dirac cone topology, and on the related topic of trapped modes in plates for a finite set (cluster) of pinned points. The Dirac cone topologies we exhibit have at least two cones touching at a point in the reciprocal lattice, augmented by another band passing through the point. We show that these Dirac cones can be steered along symmetry lines in the Brillouin zone by varying the aspect ratio of rectangular lattices of pins, and that, as the cones are moved, the involved band surfaces tilt. We link Dirac points with a parabolic profile in their neighbourhood, and the characteristic of this parabolic profile decides the direction of propagation of the trapped mode in finite clusters.
The Dirac equation in Kerr-Newman-Ads black hole background
Belgiorno, Francesco; Cacciatori, Sergio L.
2010-03-15
We consider the Dirac equation on the Kerr-Newman-AdS black hole background. We first perform the variable separation for the Dirac equation and define the Hamiltonian operator H. Then we show that for a massive Dirac field with mass {mu}{>=}1/(2l), where l is linked to the cosmological constant {lambda} by {lambda}=:-3/l{sup 2}, essential self-adjointness of H on C{sub 0}{sup {infinity}}((r{sub +},{infinity})xS{sup 2}){sup 4} is obtained even in presence of the boundarylike behavior of infinity in an asymptotically AdS black hole background. Furthermore, qualitative spectral properties of the Hamiltonian are taken into account and in agreement with the existing results concerning the case of stationary axisymmetric asymptotically flat black holes we infer the absence of time-periodic and normalizable solutions of the Dirac equation around the black hole in the nonextremal case.
Double Dirac Semimetals in Three Dimensions
NASA Astrophysics Data System (ADS)
Wieder, Benjamin J.; Kim, Youngkuk; Rappe, A. M.; Kane, C. L.
2016-05-01
We study a class of Dirac semimetals that feature an eightfold-degenerate double Dirac point. We show that 7 of the 230 space groups can host such Dirac points and argue that they all generically display linear dispersion. We introduce an explicit tight-binding model for space groups 130 and 135. Space group 135 can host an intrinsic double Dirac semimetal with no additional states at the Fermi energy. This defines a symmetry-protected topological critical point, and we show that a uniaxial compressive strain applied in different directions leads to topologically distinct insulating phases. In addition, the double Dirac semimetal can accommodate topological line defects that bind helical modes. Connections are made to theories of strongly interacting filling-enforced semimetals, and potential materials realizations are discussed.
Tunable Dirac Fermion Dynamics in Topological Insulators
NASA Astrophysics Data System (ADS)
Chen, Chaoyu; Xie, Zhuojin; Feng, Ya; Yi, Hemian; Liang, Aiji; He, Shaolong; Mou, Daixiang; He, Junfeng; Peng, Yingying; Liu, Xu; Liu, Yan; Zhao, Lin; Liu, Guodong; Dong, Xiaoli; Zhang, Jun; Yu, Li; Wang, Xiaoyang; Peng, Qinjun; Wang, Zhimin; Zhang, Shenjin; Yang, Feng; Chen, Chuangtian; Xu, Zuyan; Zhou, X. J.
2013-08-01
Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving relativistic Dirac fermions which are responsible for exotic quantum phenomena and potential applications in spintronics and quantum computations. It is essential to understand how the Dirac fermions interact with other electrons, phonons and disorders. Here we report super-high resolution angle-resolved photoemission studies on the Dirac fermion dynamics in the prototypical Bi2(Te,Se)3 topological insulators. We have directly revealed signatures of the electron-phonon coupling and found that the electron-disorder interaction dominates the scattering process. The Dirac fermion dynamics in Bi2(Te3-xSex) topological insulators can be tuned by varying the composition, x, or by controlling the charge carriers. Our findings provide crucial information in understanding and engineering the electron dynamics of the Dirac fermions for fundamental studies and potential applications.
Double Dirac Semimetals in Three Dimensions.
Wieder, Benjamin J; Kim, Youngkuk; Rappe, A M; Kane, C L
2016-05-01
We study a class of Dirac semimetals that feature an eightfold-degenerate double Dirac point. We show that 7 of the 230 space groups can host such Dirac points and argue that they all generically display linear dispersion. We introduce an explicit tight-binding model for space groups 130 and 135. Space group 135 can host an intrinsic double Dirac semimetal with no additional states at the Fermi energy. This defines a symmetry-protected topological critical point, and we show that a uniaxial compressive strain applied in different directions leads to topologically distinct insulating phases. In addition, the double Dirac semimetal can accommodate topological line defects that bind helical modes. Connections are made to theories of strongly interacting filling-enforced semimetals, and potential materials realizations are discussed. PMID:27203335
Revisiting double Dirac delta potential
NASA Astrophysics Data System (ADS)
Ahmed, Zafar; Kumar, Sachin; Sharma, Mayank; Sharma, Vibhu
2016-07-01
We study a general double Dirac delta potential to show that this is the simplest yet still versatile solvable potential to introduce double wells, avoided crossings, resonances and perfect transmission (T = 1). Perfect transmission energies turn out to be the critical property of symmetric and anti-symmetric cases wherein these discrete energies are found to correspond to the eigenvalues of a Dirac delta potential placed symmetrically between two rigid walls. For well(s) or barrier(s), perfect transmission (or zero reflectivity, R(E)) at energy E=0 is non-intuitive. However, this has been found earlier and called the ‘threshold anomaly’. Here we show that it is a critical phenomenon and we can have 0≤slant R(0)\\lt 1 when the parameters of the double delta potential satisfy an interesting condition. We also invoke a zero-energy and zero curvature eigenstate (\\psi (x)={Ax}+B) of the delta well between two symmetric rigid walls for R(0)=0. We resolve that the resonant energies and the perfect transmission energies are different and they arise differently.
On the Neuberger overlap operator
NASA Astrophysics Data System (ADS)
Boriçi, Artan
1999-04-01
We compute Neuberger's overlap operator by the Lanczos algorithm applied to the Wilson-Dirac operator. Locality of the operator for quenched QCD data and its eigenvalue spectrum in an instanton background are studied.
NASA Astrophysics Data System (ADS)
Cariglia, Marco; Krtouš, Pavel; Kubizňák, David
2011-07-01
We intrinsically characterize separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions. Namely, we explicitly demonstrate that, in such spacetimes, there exists a complete set of first-order mutually commuting operators, one of which is the Dirac operator, that allows for common eigenfunctions which can be found in a separated form and correspond precisely to the general solution of the Dirac equation found by Oota and Yasui [Phys. Lett. BPYLBAJ0370-2693 659, 688 (2008)10.1016/j.physletb.2007.11.057]. Since all the operators in the set can be generated from the principal conformal Killing-Yano tensor, this establishes the (up-to-now) missing link among the existence of hidden symmetry, presence of a complete set of commuting operators, and separability of the Dirac equation in these spacetimes.
LHCbDirac: distributed computing in LHCb
NASA Astrophysics Data System (ADS)
Stagni, F.; Charpentier, P.; Graciani, R.; Tsaregorodtsev, A.; Closier, J.; Mathe, Z.; Ubeda, M.; Zhelezov, A.; Lanciotti, E.; Romanovskiy, V.; Ciba, K. D.; Casajus, A.; Roiser, S.; Sapunov, M.; Remenska, D.; Bernardoff, V.; Santana, R.; Nandakumar, R.
2012-12-01
We present LHCbDirac, an extension of the DIRAC community Grid solution that handles 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 handling 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. Before putting in production a new release, a number of certification tests are run in a dedicated setup. This contribution highlights the versatility of the system, also presenting the experience with real data processing, data and resources management, monitoring for activities and resources.
Dirac fermions in blue-phosphorus
NASA Astrophysics Data System (ADS)
Li, Yuanchang; Chen, Xiaobin
2014-12-01
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, px, and py) and out-of-plane (pz) oribtals through the sp2 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.
NASA Astrophysics Data System (ADS)
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.
Helicity oscillations of Dirac and Majorana neutrinos
NASA Astrophysics Data System (ADS)
Dobrynina, Alexandra; Kartavtsev, Alexander; Raffelt, Georg
2016-06-01
The helicity of a Dirac neutrino with mass m evolves under the influence of a B field because it has a magnetic dipole moment proportional to m . Moreover, it was recently shown that a polarized or anisotropic medium engenders the same effect for both Dirac and Majorana neutrinos. Because a B field polarizes a background medium, it instigates helicity oscillations even for Majorana neutrinos unless the medium is symmetric between matter and antimatter. Motivated by these observations, we review the impact of a B field and of an anisotropic or polarized medium on helicity oscillations for Dirac and Majorana neutrinos from the common perspective of in-medium dispersion.
The Dirac equation and Hestenes' geometric algebra
NASA Astrophysics Data System (ADS)
Hamilton, J. Dwayne
1984-06-01
Hestenes' geometric algebra and Dirac spinors are reviewed and united into a common mathematical formalism, a unification that establishes the Dirac equation as being manifestly covariant under the Lorentz group, and one that needs no matrix representation of the Dirac algebra. New and simple methods of amplitude or ``trace'' calculations are then described. A number of problems are then considered within the context of the new approach, such as relativistic spin projections, new and covariant C and T-transformations and spinors for massless and Majorana fields.
Topological Effective Field Theories for Dirac Fermions from Index Theorem
NASA Astrophysics Data System (ADS)
Palumbo, Giandomenico; Catenacci, Roberto; Marzuoli, Annalisa
2014-01-01
Dirac fermions have a central role in high energy physics but it is well-known that they emerge also as quasiparticles in several condensed matter systems supporting topological order. We present a general method for deriving the topological effective actions of (3+1)-massless Dirac fermions living on general backgrounds and coupled with vector and axial-vector gauge fields. The first step of our strategy is standard (in the Hermitian case) and consists in connecting the determinants of Dirac operators with the corresponding analytical indices through the zeta-function regularization. Then, we introduce a suitable splitting of the heat kernel that naturally selects the purely topological part of the determinant (i.e., the topological effective action). This topological effective action is expressed in terms of gauge fields using the Atiyah-Singer index theorem which computes the analytical index in topological terms. The main new result of this paper is to provide a consistent extension of this method to the non-Hermitian case, where a well-defined determinant does not exist. Quantum systems supporting relativistic fermions can thus be topologically classified on the basis of their response to the presence of (external or emergent) gauge fields through the corresponding topological effective field theories (TEFTs).
Dirac equation on a curved surface
NASA Astrophysics Data System (ADS)
Brandt, F. T.; Sánchez-Monroy, J. A.
2016-09-01
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.
Lepton flavor violation and supersymmetric Dirac leptogenesis
Thomas, Brooks; Toharia, Manuel
2007-01-01
Dirac leptogenesis (or Dirac neutrinogenesis), in which neutrinos are purely Dirac particles, is an interesting alternative to the standard leptogenesis scenario. In its supersymmetric version, the modified form of the superpotential required for successful baryogenesis contributes new, generically nonflavor-diagonal terms to the slepton and sneutrino mass matrices. In this work, we examine how current experimental bounds on flavor-changing effects in the lepton sector (and particularly the bound on {mu}{yields}e{gamma}) constrain Dirac leptogenesis and we find that it is capable of succeeding with superpartner masses as low as {approx}100 GeV. For such light scalars and electroweakinos, upcoming experiments such as MEG are generically expected to observe signals of lepton flavor violation.
Dirac State in Giant Magnetoresistive Materials
NASA Astrophysics Data System (ADS)
Wu, Y.; Jo, N. H.; Ochi, M.; Huang, L.; Mou, D.; Kong, T.; Mun, E.; Wang, L.; Lee, Y.; Bud'Ko, S. L.; Canfield, P. C.; Trivedi, N.; Arito, R.; Kaminski, A.
We use ultrahigh resolution, tunable, vacuum ultraviolet laser-based angle-resolved photoemission spectroscopy (ARPES) to study the electronic properties of materials that recently were discovered to display titanic magnetoresistance. We find that that several of these materials have Dirac-like features in their band structure. In some materials those features are ``ordinary'' Dirac cones, while in others the linear Dirac dispersion of two crossing bands forms a linear object in 3D momentum space. Our observation poses an important question about the role of Dirac dispersion in the unusually high, non-saturating magnetoresistance of these materials. Research was supported by the US DOE, Office of Basic Energy Sciences under Contract No. DE-AC02-07CH11358; Gordon and Betty Moore Foundation EPiQS Initiative (Grant No. GBMF4411); CEM, a NSF MRSEC, under Grant No. DMR-1420451.
The Dirac equation in external fields: Variable separation in Cartesian coordinates
Shishkin, G.V.; Cabos, W.D. )
1991-11-01
The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors (J. Math. Phys. {bold 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. {bold 70}, 204 (1987)) or vector fields (J. Math. Phys. {bold 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.
The Dirac equation in external fields: Variable separation in Cartesian coordinates
NASA Astrophysics Data System (ADS)
Shishkin, German V.; Cabos, William D.
1991-11-01
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.
Dirac particle spin in strong gravitational fields
NASA Astrophysics Data System (ADS)
Obukhov, Yu. N.; Silenko, A. J.; Teryaev, O. V.
2014-01-01
Dynamics of the Dirac particle spin in general strong gravitational fields is discussed. The Hermitian Dirac Hamiltonian is derived and transformed to the Foldy-Wouthuysen (FW) representation for an arbitrary metric. The quantum mechanical equations of spin motion are found. These equations agree with corresponding classical ones. The new restriction on the anomalous gravitomagnetic moment (AGM) by the reinterpretation of Lorentz invariance tests is obtained.
Preheating in Dirac-Born-Infeld inflation
Bouatta, Nazim; Davis, Anne-Christine; Ribeiro, Raquel H.; Seery, David E-mail: A.C.Davis@damtp.cam.ac.uk E-mail: D.Seery@sussex.ac.uk
2010-09-01
We study how the universe reheats following an era of chaotic Dirac-Born-Infeld inflation, and compare the rate of particle production with that in models based on canonical kinetic terms. Particle production occurs through non-perturbative resonances whose structure is modified by the nonlinearities of the Dirac-Born-Infeld action. We investigate these modifications and show that the reheating process may be efficient. We estimate the initial temperature of the subsequent hot, radiation-dominated phase.
The degeneracy of the free Dirac equation
Gupta, V. . School of Physics Tata Inst. of Fundamental Research, Bombay ); McKellar, B.H.J. . School of Physics); Wu, D.D. . School of Physics Institute of High Energy Physics, Beijing, BJ . Electron LINAC Dept. General Atomics, San Diego, CA )
1991-08-01
Parity-mixed solutions of the free Dirac equation with the same 4-momentum are considered. The first-order EM energy has an electric dipole moment term whose value depends on the mixing angle. Further implications of this degeneracy to perturbative calculations are discussed. It is argued that the properties of the Dirac equation with the Coulomb potential can be used to decide the mixing angle, which should be zero.
Bosonic Dirac Materials in 2 dimensions
NASA Astrophysics Data System (ADS)
Banerjee, Saikat; Black-Schaffer, A. M.; Fransson, J.; Agren, H.; Balatsky, A. V.
We examine the low energy effective theory of phase oscillations in a two dimensional granular superconducting sheet where the grains are arranged in honeycomb lattice structure. Two different types of collective phase oscillations are obtained, which are analogous to the massive Leggett and massless Bogoliubov-Anderson-Gorkov modes for two-band superconductor. It is explicitly shown that the spectra of these collective Bosonic modes cross each other at K and K' points in the Brillouin zone and form a Dirac node. This Dirac node behavior in Bosonic excitations represent the case of Bosonic Dirac Materials (BDM). Dirac node is preserved in presence of an inter-grain interaction despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sub lattice symmetry by choosing different on-site potentials for the two sub lattices leads to a gap opening near the Dirac node, in analogy with Fermionic Dirac material. Supported by US DOE E304, ERC DM 321031, KAW, VR2012-3447.
NASA Astrophysics Data System (ADS)
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.
Phenomenology of Dirac Neutralino Dark Matter
Buckley, Matthew R.; Hooper, Dan; Kumar, Jason
2013-09-01
In supersymmetric models with an unbroken R-symmetry (rather than only R-parity), the neutralinos are Dirac fermions rather than Majorana. In this article, we discuss the phenomenology of neutralino dark matter in such models, including the calculation of the thermal relic abundance, and constraints and prospects for direct and indirect searches. Due to the large elastic scattering cross sections with nuclei predicted in R-symmetric models, we are forced to consider a neutralino that is predominantly bino, with very little higgsino mixing. We find a large region of parameter space in which bino-like Dirac neutralinos with masses between 10 and 380 GeV can annihilate through slepton exchange to provide a thermal relic abundance in agreement with the observed cosmological density, without relying on coannihilations or resonant annihilations. The signatures for the indirect detection of Dirac neutralinos are very different than predicted in the Majorana case, with annihilations proceeding dominately to $\\tau^+ \\tau^-$, $\\mu^+ \\mu^-$ and $e^+ e^-$ final states, without the standard chirality suppression. And unlike Majorana dark matter candidates, Dirac neutralinos experience spin-independent scattering with nuclei through vector couplings (via $Z$ and squark exchange), leading to potentially large rates at direct detection experiments. These and other characteristics make Dirac neutralinos potentially interesting within the context of recent direct and indirect detection anomalies. We also discuss the case in which the introduction of a small Majorana mass term breaks the $R$-symmetry, splitting the Dirac neutralino into a pair of nearly degenerate Majorana states.
Dynamical algebra and Dirac quantum modes in the Taub-NUT background
NASA Astrophysics Data System (ADS)
Cotaescu, Ion I.; Visinescu, Mihai
2001-09-01
The SO(4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza-Klein monopole is investigated. It is shown that the discrete quantum modes are governed by reducible representations of the o(4) dynamical algebra generated by the components of the angular momentum operator and those of the Runge-Lenz operator of the Dirac theory in the Taub-NUT background. The consequence is that there exist central and axial discrete modes whose spinors have no separated variables.
Topologically protected states in one-dimensional continuous systems and Dirac points.
Fefferman, Charles L; Lee-Thorp, James P; Weinstein, Michael I
2014-06-17
We study a class of periodic Schrödinger operators on ℝ that have Dirac points. The introduction of an "edge" via adiabatic modulation of a periodic potential by a domain wall results in the bifurcation of spatially localized "edge states," associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The bound states we construct can be realized as highly robust transverse-magnetic electromagnetic modes for a class of photonic waveguides with a phase defect. Our model captures many aspects of the phenomenon of topologically protected edge states for 2D bulk structures such as the honeycomb structure of graphene. PMID:24927571
Viability of Dirac phase leptogenesis
Anisimov, Alexey; Blanchet, Steve; Di Bari, Pasquale E-mail: blanchet@mppmu.mpg.de
2008-04-15
We discuss the conditions for a non-vanishing Dirac phase {delta} and mixing angle {theta}{sub 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 {delta}-leptogenesis, is viable when the degenerate limit for the heavy right-handed (RH) neutrino spectrum is considered. We derive an interesting joint condition on sin{theta}{sub 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 {delta}-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 sin{theta}{sub 13} and/or an account of quantum kinetic effects could completely rule out this option in the future. Therefore, {delta}-leptogenesis can be also regarded as motivation for models with degenerate heavy neutrino spectrum.
Beyond Dirac - a Unified Algebra
NASA Astrophysics Data System (ADS)
Lundberg, Wayne R.
2001-10-01
A introductory insight will be shared regarding a 'separation of variables' approach to understanding the relationship between QCD and the origins of cosmological and particle mass. The discussion will then build upon work presented at DFP 2000, focussing on the formal basis for using 3x3x3 matrix algebra as it underlies and extends Dirac notation. A set of restrictions are established which break the multiple symmetries of the 3x3x3 matrix algebra, yielding Standard Model QCD objects and interactions. It will be shown that the 3x3x3 matrix representation unifies the algebra of strong and weak (and by extension, electromagnetic) interactions. A direct correspondence to string theoretic objects is established by considering the string to be partitioned in thirds. Rubik's cube is used as a graphical means of handling algebraic manipulation of 3x3x3 algebra. Further, its potential utility for advancing pedagogical methods through active engagement is discussed. A simulated classroom exercize will be conducted.
NASA Astrophysics Data System (ADS)
Takane, Yositake
2016-01-01
An unbounded massless Dirac model with two nondegenerate Dirac cones is the simplest model for Weyl semimetals, which show the anomalous electromagnetic response of chiral magnetic effect (CME) and anomalous Hall effect (AHE). However, if this model is naively used to analyze the electromagnetic response within a linear response theory, it gives the result apparently inconsistent with the persuasive prediction based on a lattice model. We show that this serious difficulty is related to the breaking of current conservation in the Dirac model due to quantum anomaly and can be removed if current and charge operators are redefined to include the contribution from the anomaly. We demonstrate that the CME as well as the AHE can be properly described using newly defined operators, and clarify that the CME is determined by the competition between the contribution from the anomaly and that from low-energy electrons.
Uniqueness and self-conjugacy of Dirac Hamiltonians in arbitrary gravitational fields
Gorbatenko, M. V.; Neznamov, V. P.
2011-05-15
Proofs of two statements are provided in this paper. First, the authors prove that the formalism of the pseudo-Hermitian quantum mechanics allows for describing the Dirac particles motion in arbitrary stationary gravitational fields. Second, it is proved that using the Parker weight operator and the subsequent transition to the {eta} representation gives the transformation of the Schroedinger equation for the nonstationary metric, when the evolution operator becomes self-conjugate. The scalar products in the {eta} representation are flat, which makes possible the use of a standard apparatus for the Hermitian quantum mechanics. Based on the results of this paper the authors draw a conclusion about solution of the problem of uniqueness and self-conjugacy of Dirac Hamiltonians in arbitrary gravitational fields including those dependent on time. The general approach is illustrated by the example of Dirac Hamiltonians for several stationary metrics, as well as for the cosmologically flat and the open Friedmann models.
NASA Astrophysics Data System (ADS)
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
Strain engineering of Dirac cones in graphyne
Wang, Gaoxue; Kumar, Ashok; Pandey, Ravindra; Si, Mingsu
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.
Gravitationally coupled Dirac equation for antimatter
NASA Astrophysics Data System (ADS)
Jentschura, U. D.
2013-03-01
The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences (“surprises”) related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously by Brill and Wheeler [Rev. Mod. Phys.RMPHAT0034-686110.1103/RevModPhys.29.465 29, 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion of the curved-space Dirac equation from the so-called “East-Coast” to the “West-Coast” convention, in order to bring the gravitationally coupled Dirac equation to a form where it can easily be unified with the electromagnetic coupling as it is commonly used in modern particle physics calculations. The Dirac equation describes antiparticles as negative-energy states. We find a symmetry of the gravitationally coupled Dirac equation, which connects particle and antiparticle solutions for a general space-time metric of the Schwarzschild type and implies that particles and antiparticles experience the same coupling to the gravitational field, including all relativistic quantum corrections of motion. Our results demonstrate the consistency of quantum mechanics with general relativity and imply that a conceivable difference of gravitational interaction of hydrogen and antihydrogen should directly be attributed to a a “fifth force” (“quintessence”).
Discrete symmetries and mixing of Dirac neutrinos
NASA Astrophysics Data System (ADS)
Esmaili, Arman; Smirnov, Alexei Yu.
2015-11-01
We study the mixing of the Dirac neutrinos in the residual symmetries approach. The key difference from the Majorana case is that the Dirac mass matrix may have larger symmetries: Gν=Zn with n ≥3 . The symmetry group relations have been generalized to the case of Dirac neutrinos. Using them, we have found all new relations between mixing parameters and corresponding symmetry assignments, which are in agreement with the present data. The viable relations exist only for the charged lepton residual symmetry Gℓ=Z2. The relations involve elements of the rows of the Pontecorvo-Maki-Nakagawa-Sakata matrix and lead to precise predictions of the 2-3 mixing angle and certain ranges of the C P violation phase. For larger symmetries Gℓ, an agreement with the data can be achieved if ˜10 % corrections related to breaking of Gℓ and Gν are included.
Bulk Dirac Points in Distorted Spinels
NASA Astrophysics Data System (ADS)
Steinberg, Julia; Young, Steve; Zaheer, Saad; Kane, Charles; Mele, Eugene; Rappe, Andrew
2014-03-01
A Dirac point is characterized by four degenerate states that disperse linearly with momentum around a single point bk in the Brillouin zone. The resulting low energy theory is pseudorelativistic. A well-known example in two dimensions is graphene, which has a Fermi surface consisting exclusively of Dirac points that are responsible for many of its exotic properties. We report on an analogous Dirac-like Fermi surface in three-dimensional bulk materials in a distorted spinel structure on the basis of density functional theory (DFT) as well as tight-binding theory. The four examples we provide in this paper are BiZnSiO4, BiCaSiO4, BiMgSiO4, and BiAlInO4. A necessary characteristic of these structures is that they contain a Bi lattice which forms a hierarchy of chain-like substructures, with consequences for both fundamental understanding and materials design.
NASA Technical Reports Server (NTRS)
Turner, Michael S.
1991-01-01
Previous work has shown that the cooling of SN 1987A excludes a Dirac-neutrino mass greater than theta(20 keV) for nu(sub e), nu(sub mu), or nu(sub tau). The emission of wrong-helicity, Dirac neutrinos from SN 1987A, is re-examined. It is concluded that the effect of a Dirac neutrino on the cooling of SN 1987A has been underestimated due to neutrino degeneracy and additional emission processes. The limit that follows from the cooling of SN 1987A is believed to be greater (probably much greater) than 10 keV. This result is significant in light of the recent evidence for a 17 keV mass eigenstate that mixes with the electron neutrino.
White dwarfs, the Galaxy and Dirac's cosmology
NASA Technical Reports Server (NTRS)
Stothers, R.
1976-01-01
The additive and multiplicative versions of Dirac's cosmological hypothesis relating the gravitational constant variation with elapsed time and number of particles populating the universe is invoked to account for the deficiency or absence of white dwarfs fainter than about 0.0001 solar luminosity. An estimate is made of white dwarf luminosity in accordance with the two evolutionary models, and it is conjectured that some old white dwarfs with high space velocities may be on the verge of gravitational collapse. Lack of a special mechanism to produce the vast numbers of black holes or other dead stars accounting for 'missing matter' in the vicinity of the sun and in the galactic halo is noted in Dirac's multiplicative model. Results indicate that either Dirac's theory is untenable, or that radiation and heating are of some unknown nature, or that the process of creation of new matter requires a corresponding input of energy.
Phase transitions of Dirac electrons in bismuth.
Li, Lu; Checkelsky, J G; Hor, Y S; Uher, C; Hebard, A F; Cava, R J; Ong, N P
2008-07-25
The Dirac Hamiltonian, which successfully describes relativistic fermions, applies equally well to electrons in solids with linear energy dispersion, for example, in bismuth and graphene. A characteristic of these materials is that a magnetic field less than 10 tesla suffices to force the Dirac electrons into the lowest Landau level, with resultant strong enhancement of the Coulomb interaction energy. Moreover, the Dirac electrons usually come with multiple flavors or valley degeneracy. These ingredients favor transitions to a collective state with novel quantum properties in large field. By using torque magnetometry, we have investigated the magnetization of bismuth to fields of 31 tesla. We report the observation of sharp field-induced phase transitions into a state with striking magnetic anisotropy, consistent with the breaking of the threefold valley degeneracy. PMID:18653888
Asymptotic formula for eigenvalues of one dimensional Dirac system
NASA Astrophysics Data System (ADS)
Ulusoy, Ismail; Penahlı, Etibar
2016-06-01
In this paper, we study the spectral problem for one dimensional Dirac system with Dirichlet boundary conditions. By using Counting lemma, we give an asymptotic formulas of eigenvalues of Dirac system.
Nonrelativistic approximation of the Dirac equation for slow fermions in static metric spacetimes
NASA Astrophysics Data System (ADS)
Ivanov, A. N.; Pitschmann, M.
2014-08-01
We analyze the nonrelativistic approximation of the Dirac equation for slow fermions, having small kinetic energies compared to their rest energy m and moving in spacetimes with a static metric, caused by the weak gravitational field of the Earth and a chameleon field, and derive the most general effective gravitational potential to order 1/m, induced by a static metric of spacetime excluding possible rotations of the coordinate frame. The derivation of the nonrelativistic Hamilton operator of the Dirac equation is carried out by using a standard Foldy-Wouthuysen transformation. We discuss the chameleon field as source of a torsion field and torsion-matter interactions.
NASA Astrophysics Data System (ADS)
Barbaroux, Jean-Marie; Mehringer, Josef; Stockmeyer, Edgardo; Taarabt, Amal
2016-04-01
We consider two-dimensional massless Dirac operators in a radially symmetric electromagnetic field. In this case the fields may be described by one-dimensional electric and magnetic potentials V and A. We show dynamical localization in the regime when lim r → ∞ | V | / | A | < 1, where dense point spectrum occurs.
Neznamov, V. P.; Silenko, A. J.
2009-12-15
The block diagonalization of the Hamiltonian is not sufficient for the transformation to the Foldy-Wouthuysen (FW) representation. The conditions enabling the transition from the Dirac representation to the FW one are formulated and proven. The connection between wave functions in the two representations is derived. The results obtained allow calculating expectation values of operators corresponding to main classical quantities.
NASA Astrophysics Data System (ADS)
Borzdov, G. N.
2016-06-01
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency. Each standing wave consists of two eigenwaves with different complex amplitudes and opposite directions of propagation. The fundamental solution is obtained in the form of the projection operator defining the subspace of solutions to the Dirac equation. It is illustrated by the analysis of the ground state and the spin precession of the Dirac electron in the field of two counterpropagating plane waves with left and right circular polarizations. Interrelations between the fundamental solution and approximate partial solutions is discussed and a criterion for evaluating the accuracy of approximate solutions is suggested.
Spin eigen-states of Dirac equation for quasi-two-dimensional electrons
Eremko, Alexander; Brizhik, Larissa; Loktev, Vadim
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.
Search for Heavy Pointlike Dirac Monopoles
NASA Astrophysics Data System (ADS)
Abbott, B.; Abolins, M.; Acharya, B. S.; Adam, I.; Adams, D. L.; Adams, M.; Ahn, S.; Aihara, H.; Alves, G. A.; Amos, N.; Anderson, E. W.; Astur, R.; Baarmand, M. M.; Babukhadia, L.; Baden, A.; Balamurali, V.; Balderston, J.; Baldin, B.; Banerjee, S.; Bantly, J.; Barberis, E.; Bartlett, J. F.; Belyaev, A.; Beri, S. B.; Bertram, I.; Bezzubov, V. A.; Bhat, P. C.; Bhatnagar, V.; Bhattacharjee, M.; Biswas, N.; Blazey, G.; Blessing, S.; Bloom, P.; Boehnlein, A.; Bojko, N. I.; Borcherding, F.; Boswell, C.; Brandt, A.; Brock, R.; Bross, A.; Buchholz, D.; Burtovoi, V. S.; Butler, J. M.; Carvalho, W.; Casey, D.; Casilum, Z.; Castilla-Valdez, H.; Chakraborty, D.; Chang, S.-M.; Chekulaev, S. V.; Chen, L.-P.; Chen, W.; Choi, S.; Chopra, S.; Choudhary, B. C.; Christenson, J. H.; Chung, M.; Claes, D.; Clark, A. R.; Cobau, W. G.; Cochran, J.; Coney, L.; Cooper, W. E.; Cretsinger, C.; Cullen-Vidal, D.; Cummings, M. A.; Cutts, D.; Dahl, O. I.; Davis, K.; de, K.; del Signore, K.; Demarteau, M.; Denisov, D.; Denisov, S. P.; Diehl, H. T.; Diesburg, M.; di Loreto, G.; Draper, P.; Ducros, Y.; Dudko, L. V.; Dugad, S. R.; Edmunds, D.; Ellison, J.; Elvira, V. D.; Engelmann, R.; Eno, S.; Eppley, G.; Ermolov, P.; Eroshin, O. V.; Evdokimov, V. N.; Fahland, T.; Fatyga, M. K.; Feher, S.; Fein, D.; Ferbel, T.; Finocchiaro, G.; Fisk, H. E.; Fisyak, Y.; Flattum, E.; Forden, G. E.; Fortner, M.; Frame, K. C.; Fuess, S.; Gallas, E.; Galyaev, A. N.; Gartung, P.; Gavrilov, V.; Geld, T. L.; Genik, R. J.; Genser, K.; Gerber, C. E.; Gershtein, Y.; Gibbard, B.; Glenn, S.; Gobbi, B.; Goldschmidt, A.; Gómez, B.; Gómez, G.; Goncharov, P. I.; González Solís, J. L.; Gordon, H.; Goss, L. T.; Gounder, K.; Goussiou, A.; Graf, N.; Grannis, P. D.; Green, D. R.; Greenlee, H.; Grinstein, S.; Grudberg, P.; Grünendahl, S.; Guglielmo, G.; Guida, J. A.; Guida, J. M.; Gupta, A.; Gurzhiev, S. N.; Gutierrez, G.; Gutierrez, P.; Hadley, N. J.; Haggerty, H.; Hagopian, S.; Hagopian, V.; Hahn, K. S.; Hall, R. E.; Hanlet, P.; Hansen, S.; Hauptman, J. M.; Hedin, D.; Heinson, A. P.; Heintz, U.; Hernández-Montoya, R.; Heuring, T.; Hirosky, R.; Hobbs, J. D.; Hoeneisen, B.; Hoftun, J. S.; Hsieh, F.; Hu, Ting; Hu, Tong; Huehn, T.; Ito, A. S.; James, E.; Jaques, J.; Jerger, S. A.; Jesik, R.; Jiang, J. Z.-Y.; Joffe-Minor, T.; Johns, K.; Johnson, M.; Jonckheere, A.; Jones, M.; Jöstlein, H.; Jun, S. Y.; Jung, C. K.; Kahn, S.; Kalbfleisch, G.; Kang, J. S.; Karmanov, D.; Karmgard, D.; Kehoe, R.; Kelly, M. L.; Kim, C. L.; Kim, S. K.; Klima, B.; Klopfenstein, C.; Kohli, J. M.; Koltick, D.; Kostritskiy, A. V.; Kotcher, J.; Kotwal, A. V.; Kourlas, J.; Kozelov, A. V.; Kozlovsky, E. A.; Krane, J.; Krishnaswamy, M. R.; Krzywdzinski, S.; Kuleshov, S.; Kunori, S.; Landry, F.; Landsberg, G.; Lauer, B.; Leflat, A.; Li, H.; Li, J.; Li-Demarteau, Q. Z.; Lima, J. G.; Lincoln, D.; Linn, S. L.; Linnemann, J.; Lipton, R.; Liu, Y. C.; Lobkowicz, F.; Loken, S. C.; Lökös, S.; Lueking, L.; Lyon, A. L.; Maciel, A. K.; Madaras, R. J.; Madden, R.; Magaña-Mendoza, L.; Manankov, V.; Mani, S.; Mao, H. S.; Markeloff, R.; Marshall, T.; Martin, M. I.; Mauritz, K. M.; May, B.; Mayorov, A. A.; McCarthy, R.; McDonald, J.; McKibben, T.; McKinley, J.; McMahon, T.; Melanson, H. L.; Merkin, M.; Merritt, K. W.; Miettinen, H.; Mincer, A.; Mishra, C. S.; Mokhov, N.; Mondal, N. K.; Montgomery, H. E.; Mooney, P.; da Motta, H.; Murphy, C.; Nang, F.; Narain, M.; Narasimham, V. S.; Narayanan, A.; Neal, H. A.; Negret, J. P.; Nemethy, P.; Norman, D.; Oesch, L.; Oguri, V.; Oliveira, E.; Oltman, E.; Oshima, N.; Owen, D.; Padley, P.; Para, A.; Park, Y. M.; Partridge, R.; Parua, N.; Paterno, M.; Pawlik, B.; Perkins, J.; Peters, M.; Piegaia, R.; Piekarz, H.; Pischalnikov, Y.; Pope, B. G.; Prosper, H. B.; Protopopescu, S.; Qian, J.; Quintas, P. Z.; Raja, R.; Rajagopalan, S.; Ramirez, O.; Rasmussen, L.; Reucroft, S.; Rijssenbeek, M.; Rockwell, T.; Roco, M.; Rubinov, P.; Ruchti, R.; Rutherfoord, J.; Sánchez-Hernández, A.; Santoro, A.; Sawyer, L.; Schamberger, R. D.; Schellman, H.; Sculli, J.; Shabalina, E.; Shaffer, C.; Shankar, H. C.; Shivpuri, R. K.; Shupe, M.; Singh, H.; Singh, J. B.; Sirotenko, V.; Smart, W.; Smith, E.; Smith, R. P.; Snihur, R.; Snow, G. R.; Snow, J.; Snyder, S.; Solomon, J.; Sosebee, M.; Sotnikova, N.; Souza, M.; Spadafora, A. L.; Steinbrück, G.; Stephens, R. W.; Stevenson, M. L.; Stewart, D.; Stichelbaut, F.; Stoker, D.; Stolin, V.; Stoyanova, D. A.; Strauss, M.; Streets, K.; Strovink, M.; Sznajder, A.; Tamburello, P.; Tarazi, J.; Tartaglia, M.; Thomas, T. L.; Thompson, J.; Trippe, T. G.; Tuts, P. M.; Varelas, N.; Varnes, E. W.; Vititoe, D.; Volkov, A. A.; Vorobiev, A. P.; Wahl, H. D.; Wang, G.; Warchol, J.; Watts, G.; Wayne, M.; Weerts, H.; White, A.; White, J. T.; Wightman, J. A.; Willis, S.; Wimpenny, S. J.; Wirjawan, J. V.; Womersley, J.; Won, E.; Wood, D. R.; Xu, H.; Yamada, R.; Yamin, P.; Yang, J.; Yasuda, T.; Yepes, P.; Yoshikawa, C.; Youssef, S.; Yu, J.; Yu, Y.; Zhou, Z.; Zhu, Z. H.; Zieminska, D.; Zieminski, A.; Zverev, E. G.; Zylberstejn, A.
1998-07-01
We have searched for central production of a pair of photons with high transverse energies in pp¯ collisions at s = 1.8 TeV using 70 pb-1 of data collected with the D0 detector at the Fermilab Tevatron in 1994-1996. If they exist, virtual heavy pointlike Dirac monopoles could rescatter pairs of nearly real photons into this final state via a box diagram. We observe no excess of events above background, and set lower 95% C.L. limits of 610, 870, or 1580 GeV/c2 on the mass of a spin 0, 1/2, or 1 Dirac monopole.
Massive Dirac neutrinos and SN 1987A
NASA Technical Reports Server (NTRS)
Burrows, Adam; Gandhi, Raj; Turner, Michael S.
1992-01-01
The wrong-helicity states of a Dirac neutrino can provide an important cooling mechanism for young neutron stars. Based on numerical models of the early cooling of the neutron star associated with SN 1987A which self-consistently incorporate wrong-helicity neutrino emission, it is argued that a Dirac neutrino of mass greater than 30 keV (25 keV if it is degenerate) leads to shortening of the neutrino burst that is inconsistent with the Irvine-Michigan-Brookhaven and Kamiokande II data. If pions are as abundant as nucleons in the cores of neutron stars, the present limit improves to 15 keV.
On the Dirac Structure of Confinement
Adam P. Szczepaniak; Eric S. Swanson
1997-04-01
The Dirac structure of confinement is shown to be of time like-vector nature in the heavy quark limit of QCD. This stands in contradiction with the phenomenological success of the Dirac scalar confining potential. A resolution is achieved through the demonstration that an effective scalar interaction is dynamically generated by nonperturbative mixing between ordinary and hybrid Q {bar Q} states. The resolution depends crucially on the collective nature of the gluonic degrees of freedom. This implies that dynamical gluonic effects are vital when attempting to incorporate fine structure in models of the Q {bar Q} interaction.
Universality of Plasmon Excitations in Dirac Semimetals
NASA Astrophysics Data System (ADS)
Kharzeev, Dmitri E.; Pisarski, Robert D.; Yee, Ho-Ung
2015-12-01
We investigate the properties of the collective plasmon excitations in Dirac semimetals by using the methods of relativistic field theory. We find a strong and narrow plasmon excitation whose frequency is in the terahertz (THz) range which may be important for practical applications. The properties of the plasmon appear universal for all Dirac semimetals, due to the large degeneracy of the quasiparticles and the small Fermi velocity, vF≪c . This universality is closely analogous to the phenomenon of "dimensional transmutation" that is responsible for the emergence of dimensionful scales in relativistic field theories such as quantum chromodynamics.
Universality of Plasmon Excitations in Dirac Semimetals.
Kharzeev, Dmitri E; Pisarski, Robert D; Yee, Ho-Ung
2015-12-01
We investigate the properties of the collective plasmon excitations in Dirac semimetals by using the methods of relativistic field theory. We find a strong and narrow plasmon excitation whose frequency is in the terahertz (THz) range which may be important for practical applications. The properties of the plasmon appear universal for all Dirac semimetals, due to the large degeneracy of the quasiparticles and the small Fermi velocity, v_{F}≪c. This universality is closely analogous to the phenomenon of "dimensional transmutation" that is responsible for the emergence of dimensionful scales in relativistic field theories such as quantum chromodynamics. PMID:26684129
Geometric superalgebra and the Dirac equation
NASA Astrophysics Data System (ADS)
Keller, Jaime; Rodríguez, Adán
1992-01-01
A unified mathematical approach to spinors and multivectors or superalgebra is constructed in a form useful to study the mathematical description of matter and its interaction fields. The formalism then encompasses both points of view: multivectors for the description of (space-time) geometry and the description of the integer spin, interaction fields, and spinor representations suitable for the description of half odd integer, matter fields. An application is made to study the change of the Dirac equation under the spinors to multivectors (to scalars) mapping. The physical and geometric content of the multivector solutions of the Dirac-Hestenes equation is clearly shown.
Tuning Dirac points by strain in MoX2 nanoribbons (X = S, Se, Te) with a 1T' structure.
Sung, Ha-Jun; Choe, Duk-Hyun; Chang, K J
2016-06-28
For practical applications of two-dimensional topological insulators, large band gaps and Dirac states within the band gap are desirable because they allow for device operation at room temperature and quantum transport without dissipation. Based on first-principles density functional calculations, we report the tunability of the electronic structure by strain engineering in quasi-one-dimensional nanoribbons of transition metal dichalcogenides with a 1T' structure, MoX2 with X = (S, Se, Te). We find that both the band gaps and Dirac points in 1T'-MoX2 can be engineered by applying an external strain, thereby leading to a single Dirac cone within the bulk band gap. Considering the gap size and the location of the Dirac point, we suggest that, among 1T'-MoX2 nanoribbons, MoSe2 is the most suitable candidate for quantum spin Hall (QSH) devices. PMID:27257641
A short biography of Paul A. M. Dirac and historical development of Dirac delta function
NASA Astrophysics Data System (ADS)
Debnath, Lokenath
2013-12-01
This paper deals with a short biography of Paul Dirac, his first celebrated work on quantum mechanics, his first formal systematic use of the Dirac delta function and his famous work on quantum electrodynamics and quantum statistics. Included are his first discovery of the Dirac relativistic wave equation, existence of positron and the intrinsic spin and helicity of electrons. Special attention is given to Dirac's original visionary work on the existence of the magnetic monopole, and on his Large Number Hypothesis that led to the conclusion that physical quantities universally considered as constant of nature are not really constants, but they vary with cosmological time. Some concluding remarks with personal reminiscence are added in the end of the paper.
On the solution of the Dirac equation in de Sitter space
NASA Astrophysics Data System (ADS)
Klishevich, V. V.; Tyumentsev, V. A.
2005-10-01
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.
Applications of Dirac's Delta Function in Statistics
ERIC Educational Resources Information Center
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…
Paul Dirac:. Building Bridges of the Mind
NASA Astrophysics Data System (ADS)
Brown, Laurie M.
2003-12-01
Paul Dirac was a brilliant and original thinker. He used his physical intuition and his ideal of mathematical beauty to construct bridges between major areas of physics. This article discusses several such important works, including the bridge between quantum mechanics and relativity that led to his prediction of the existence of antimatter.
Duality between coordinates and Dirac field
NASA Astrophysics Data System (ADS)
Abdalla, M. C. B.; Gadelha, A. L.; Vancea, I. V.
2000-07-01
The duality between the Cartesian coordinates on the Minkowski space-time and the Dirac field is investigated. Two distinct possibilities to define this duality are shown to exist. In both cases, the equations satisfied by prepotentials are of second order.
On solvable Dirac equation with polynomial potentials
Stachowiak, Tomasz
2011-01-15
One-dimensional Dirac equation is analyzed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the linear potentials the equation in question is not solvable.
Understanding Quaternions and the Dirac Belt Trick
ERIC Educational Resources Information Center
Staley, Mark
2010-01-01
The Dirac belt trick is often employed in physics classrooms to show that a 2n rotation is not topologically equivalent to the absence of rotation whereas a 4n rotation is, mirroring a key property of quaternions and their isomorphic cousins, spinors. The belt trick can leave the student wondering if a real understanding of quaternions and spinors…
Analytic representation of the Dirac equation
NASA Astrophysics Data System (ADS)
Gill, Tepper L.; Zachary, W. W.; Alfred, Marcus
2005-08-01
In this paper, we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the wavefunctions, as is done by the Foldy-Wouthuysen method, and reveals the nonlocal time behaviour of the particle-antiparticle relationship. We then show explicitly that the Pauli equation is not completely valid for the study of the Dirac hydrogen atom problem in s-states (hyperfine splitting). We conclude that there are some open mathematical problems with any attempt to explicitly show that the Dirac equation is insufficient to explain the full hydrogen spectrum. If the perturbation method can be justified, our analysis suggests that the use of cut-offs in QED is already justified by the eigenvalue analysis that supports it. Using a new method, we are able to effect separation of variables for full coupling, solve the radial equation and provide graphs of the probability density function for the 2p- and 2s-states, and compare them with those of the Dirac-Coulomb case.
Theory and phenomenology of Dirac leptogenesis
NASA Astrophysics Data System (ADS)
Thomas, Brooks D.
2007-07-01
Dirac leptogenesis, in which neutrinos are purely Dirac and develop small but nonzero effective masses without the aid of the see-saw mechanism, provides an interesting alternative to the standard leptogenesis picture. Here we review the theory and phenomenology of Dirac leptogenesis and show that it is a viable theory capable of simultaneously satisfying all relevant bounds from cosmology, neutrino physics, and flavor violation. In addition, we also explore several potential extensions of the model, such as the possibility of right-handed sneutrino dark matter and the potential for relating the leptogenesis mechanism to the origin of the mu-term. Theories with a heavy gravitino and gaugino masses generated by anomaly mediation emerge as one natural context for Dirac leptogenesis. In such models the lightest neutralino is often expected to be predominately wino or Higgsino, and is a viable dark matter candidate. We conclude with an examination of the prospects for detecting the effectively monoenergetic photon signal that results from the annihilation of such a dark matter particle in the galactic halo.
Dirac Cones in Periodically Modulated Quantum Wells
NASA Astrophysics Data System (ADS)
Yao, Yuanzhao; Sakoda, Kazuaki
2016-06-01
We show by a degenerate k · p perturbation theory and group theory that Dirac cones in the Brillouin-zone center can be materialized for the electronic bands of periodically modulated quantum wells. We examine in particular the periodic modulation of the C4v and C6v symmetries. The analytical conclusions are confirmed by numerical calculations using the finite element method.
Emeritus trio scoops the 2013 Dirac Medal
NASA Astrophysics Data System (ADS)
Dacey, James
2013-09-01
The 2013 Dirac Medal has been awarded to three scientists whose wide-ranging work has brought profound advances in cosmology, astrophysics and fundamental physics. Thomas Kibble, James Peebles and Martin Rees all receive the honour, which is bestowed annually by the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, Italy.
Quantum simulation of the Dirac equation.
Gerritsma, R; Kirchmair, G; Zähringer, F; Solano, E; Blatt, R; Roos, C F
2010-01-01
The Dirac equation successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the existence of antimatter and is able to reproduce accurately the spectrum of the hydrogen atom. The realm of the Dirac equation-relativistic quantum mechanics-is considered to be the natural transition to quantum field theory. However, the Dirac equation also predicts some peculiar effects, such as Klein's paradox and 'Zitterbewegung', an unexpected quivering motion of a free relativistic quantum particle. These and other predicted phenomena are key fundamental examples for understanding relativistic quantum effects, but are difficult to observe in real particles. In recent years, there has been increased interest in simulations of relativistic quantum effects using different physical set-ups, in which parameter tunability allows access to different physical regimes. Here we perform a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle. We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, as well as the crossover from relativistic to non-relativistic dynamics. The high level of control of trapped-ion experimental parameters makes it possible to simulate textbook examples of relativistic quantum physics. PMID:20054392
Interquark potential calculation from Dirac brackets
NASA Astrophysics Data System (ADS)
Gaete, Patricio
2001-08-01
We obtain the binding energy of an infinitely heavy quark-antiquark pair from Dirac brackets by computing the expectation value of the pure QCD Hamiltonian. This procedure exploits the rich structure of the dressing around static fermions. Some subtle points related to exhibing explicitly the interquark energy are considered.
An extended Dirac equation in noncommutative spacetime
NASA Astrophysics Data System (ADS)
Mendes, R. Vilela
2016-05-01
Stabilizing, by deformation, the algebra of relativistic quantum mechanics a noncommutative spacetime geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a large mass solution. The nature of the solutions is discussed as well as the effects of coupling the two solutions.
The GridPP DIRAC project - DIRAC for non-LHC communities
NASA Astrophysics Data System (ADS)
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; Huang, Huaqing; Duan, Wenhui; Liu, Zhirong
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. PMID:24320285
Identifying Dirac cones in carbon allotropes with square symmetry
Wang, Jinying; Huang, Huaqing; Duan, Wenhui; Liu, Zhirong
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.
Dirac equation for electrodynamic model particles
NASA Astrophysics Data System (ADS)
Zheng-Johansson, J. X.
2008-08-01
We set up the Maxwell's equations and subsequently the classical wave equations for the electromagnetic waves which together with their generating source, an oscillatory charge of zero rest mass in general travelling, make up a particle travelling similarly as the source at velocity ν in the field of an external scalar and vector potentials. The direct solutions in constant external field are Doppler-displaced plane waves propagating at the velocity of light c; at the de Broglie wavelength scale and expressed in terms of the dynamically equivalent and appropriate geometric mean wave variables, these render as functions identical to the space-time functions of a corresponding Dirac spinor, and in turn identical to de Broglie phase waves previously obtained from explicit superposition. For two spin-half particles of a common set of space-time functions constrained with antisymmetric spin functions as follows the Pauli principle for same charges and as separately indirectly induced based on experiment for opposite charges, the complete wave functions are identical to the Dirac spinor. The back-substitution of the so explicitly determined complete wave functions in the corresponding classical wave equations of the two particles, subjected further to reductions appropriate for the stationary-state particle motion and to rotation invariance when in three dimensions, give a Dirac equation set; the procedure and conclusion are directly extendible to arbitrarily varying potentials by use of the Furious theorem and to particle motions in three dimensions by virtue of the characteristics of de Broglie particle motion. Through the derivation of the Dirac equation, the study hopes to lend insight into the connections between the Dirac wave functions and the electrodynamic components of simple particles under the government by the well established basic laws of electrodynamics.
NASA Astrophysics Data System (ADS)
Wu, Yun; Wang, Lin-Lin; Mun, Eundeok; Johnson, D. D.; Mou, Daixiang; Huang, Lunan; Lee, Yongbin; Bud'Ko, S. L.; Canfield, P. C.; Kaminski, Adam
2016-07-01
In topological quantum materials the conduction and valence bands are connected at points or along lines in the momentum space. A number of studies have demonstrated that several materials are indeed Dirac/Weyl semimetals. However, there is still no experimental confirmation of materials with line nodes, in which the Dirac nodes form closed loops in the momentum space. Here we report the discovery of a novel topological structure--Dirac node arcs--in the ultrahigh magnetoresistive material PtSn4 using laser-based angle-resolved photoemission spectroscopy data and density functional theory calculations. Unlike the closed loops of line nodes, the Dirac node arc structure arises owing to the surface states and resembles the Dirac dispersion in graphene that is extended along a short line in the momentum space. We propose that this reported Dirac node arc structure is a novel topological state that provides an exciting platform for studying the exotic properties of Dirac fermions.
Semiclassical limit for Dirac particles interacting with a gravitational field
NASA Astrophysics Data System (ADS)
Silenko, Alexander J.; Teryaev, Oleg V.
2005-03-01
The behavior of a spin-1/2 particle in a weak static gravitational field is considered. The Dirac Hamiltonian is diagonalized by the Foldy-Wouthuysen transformation providing also the simple form for the momentum and spin polarization operators. The operator equations of momentum and spin motion are derived for a first time. Their semiclassical limit is analyzed. The dipole spin-gravity coupling in the previously found (another) Hamiltonian does not lead to any observable effects. The general agreement between the quantum and classical approaches is established, contrary to several recent claims. The expression for the gravitational Stern-Gerlach force is derived. The helicity evolution in the gravitational field and corresponding accelerated frame coincides, being the manifestation of the equivalence principle.
SARAH 3.2: Dirac gauginos, UFO output, and more
NASA Astrophysics Data System (ADS)
Staub, Florian
2013-07-01
SARAH is a Mathematica package optimized for the fast, efficient and precise study of supersymmetric models beyond the MSSM: a new model can be defined in a short form and all vertices are derived. This allows SARAH to create model files for FeynArts/FormCalc, CalcHep/CompHep and WHIZARD/O'Mega. The newest version of SARAH now provides the possibility to create model files in the UFO format which is supported by MadGraph 5, MadAnalysis 5, GoSam, and soon by Herwig++. Furthermore, SARAH also calculates the mass matrices, RGEs and 1-loop corrections to the mass spectrum. This information is used to write source code for SPheno in order to create a precision spectrum generator for the given model. This spectrum-generator-generator functionality as well as the output of WHIZARD and CalcHep model files has seen further improvement in this version. Also models including Dirac gauginos are supported with the new version of SARAH, and additional checks for the consistency of the implementation of new models have been created. Program summaryProgram title:SARAH Catalogue identifier: AEIB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIB_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3 22 411 No. of bytes in distributed program, including test data, etc.: 3 629 206 Distribution format: tar.gz Programming language: Mathematica. Computer: All for which Mathematica is available. Operating system: All for which Mathematica is available. Classification: 11.1, 11.6. Catalogue identifier of previous version: AEIB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 182 (2011) 808 Does the new version supersede the previous version?: Yes, the new version includes all known features of the previous version but also provides the new features mentioned below
Plexciton Dirac points and topological modes
Yuen-Zhou, Joel; Saikin, Semion K.; Zhu, Tony; Onbasli, Mehmet C.; Ross, Caroline A.; Bulovic, Vladimir; Baldo, Marc A.
2016-01-01
Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. Here, we consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional band-structure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. An external magnetic field opens a gap between the Dirac cones if the plexciton system is interfaced with a magneto-optical layer. The resulting energy gap becomes populated with topologically protected one-way modes, which travel at the interface of this plexcitonic system. Our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter and for the control of energy flow at the nanoscale. PMID:27278258
Floquet-Engineered Valleytronics in Dirac Systems.
Kundu, Arijit; Fertig, H A; Seradjeh, Babak
2016-01-01
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. PMID:26799038
Floquet-Engineered Valleytronics in Dirac Systems
NASA Astrophysics Data System (ADS)
Kundu, Arijit; Fertig, H. A.; Seradjeh, Babak
2016-01-01
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.
Plexciton Dirac points and topological modes.
Yuen-Zhou, Joel; Saikin, Semion K; Zhu, Tony; Onbasli, Mehmet C; Ross, Caroline A; Bulovic, Vladimir; Baldo, Marc A
2016-01-01
Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. Here, we consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional band-structure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. An external magnetic field opens a gap between the Dirac cones if the plexciton system is interfaced with a magneto-optical layer. The resulting energy gap becomes populated with topologically protected one-way modes, which travel at the interface of this plexcitonic system. Our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter and for the control of energy flow at the nanoscale. PMID:27278258
Plexciton Dirac points and topological modes
NASA Astrophysics Data System (ADS)
Yuen-Zhou, Joel; Saikin, Semion K.; Zhu, Tony; Onbasli, Mehmet C.; Ross, Caroline A.; Bulovic, Vladimir; Baldo, Marc A.
2016-06-01
Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. Here, we consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional band-structure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. An external magnetic field opens a gap between the Dirac cones if the plexciton system is interfaced with a magneto-optical layer. The resulting energy gap becomes populated with topologically protected one-way modes, which travel at the interface of this plexcitonic system. Our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter and for the control of energy flow at the nanoscale.
Dirac gauginos in low scale supersymmetry breaking
NASA Astrophysics Data System (ADS)
Goodsell, Mark D.; Tziveloglou, Pantelis
2014-12-01
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.
Plexciton Dirac points and topological modes
Yuen-Zhou, Joel; Saikin, Semion K.; Zhu, Tony; Onbasli, Mehmet C.; Ross, Caroline A.; Bulovic, Vladimir; Baldo, Marc A.
2016-06-09
Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. Here, we consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional band-structure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. An external magnetic field opens a gap between the Dirac cones if the plexciton system is interfaced with a magneto-optical layer. The resulting energy gap becomes populated with topologically protected one-way modes, which travel at the interface ofmore » this plexcitonic system. Furthermore, our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter and for the control of energy flow at the nanoscale.« less
Classical electromagnetic radiation of the Dirac electron
NASA Technical Reports Server (NTRS)
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.
Octonion generalization of Pauli and Dirac matrices
NASA Astrophysics Data System (ADS)
Chanyal, B. C.
2015-10-01
Starting with octonion algebra and its 4 × 4 matrix representation, we have made an attempt to write the extension of Pauli's matrices in terms of division algebra (octonion). The octonion generalization of Pauli's matrices shows the counterpart of Pauli's spin and isospin matrices. In this paper, we also have obtained the relationship between Clifford algebras and the division algebras, i.e. a relation between octonion basis elements with Dirac (gamma), Weyl and Majorana representations. The division algebra structure leads to nice representations of the corresponding Clifford algebras. We have made an attempt to investigate the octonion formulation of Dirac wave equations, conserved current and weak isospin in simple, compact, consistent and manifestly covariant manner.
Pseudoclassical description of the Dirac Oscillator
NASA Technical Reports Server (NTRS)
Delsolmesa, Antonio; Martinezyromero, R. P.
1995-01-01
In this paper we discuss the Dirac Oscillator wave equation in terms of pseudoclassical language, using Grassmann variables to describe the internal degrees of freedom of the oscillator. Regarding the original wave equation as a classical constraint, we use the theory of constrained systems, to develop a reparameterization invariant lagrangian, which is the pseudoclassical equivalent of the quantum case. The consistency of the Hamiltonian formalism and the quantization procedure are also analyzed.
Two-particle Kapitza-Dirac diffraction
Sancho, Pedro
2010-09-15
We extend the study of Kapitza-Dirac diffraction to the case of two-particle systems. Due to the exchange effects the shape and visibility of the two-particle detection patterns show important differences for identical and distinguishable particles. We also identify a quantum statistics effect present in momentum space for some values of the initial particle momenta, which is associated with different numbers of photon absorptions compatible with the final momenta.
Dirac particle in a pseudoscalar potential
Moreno, Matias; Zentella-Dehesa, Arturo
1996-02-20
We study the problem of a Dirac particle with a pseudoscalar interaction in the potential approximation. It is shown how nonperturbative relativistic solutions arise. The case of the central pseudoscalar potential is explicitly worked out also in a closed form. The angular functions are worked out in general for this central case. Finally for the special case of the spherical well the radial solutions are shown to behave like Bessel-type functions.
Dirac particle in a pseudoscalar potential
Moreno, M.; Zentella-Dehesa, A.
1996-02-01
We study the problem of a Dirac particle with a pseudoscalar interaction in the potential approximation. It is shown how nonperturbative relativistic solutions arise. The case of the central pseudoscalar potential is explicitly worked out also in a closed form. The angular functions are worked out in general for this central case. Finally for the special case of the spherical well the radial solutions are shown to behave like Bessel-type functions. {copyright} {ital 1996 American Institute of Physics.}
Manipulation of Dirac Cones in Mechanical Graphene
NASA Astrophysics Data System (ADS)
Kariyado, Toshikaze; Hatsugai, Yasuhiro
2015-12-01
Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton’s law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we investigate mechanical graphene, which is a spring-mass model with the honeycomb structure as a typical mechanical model with nontrivial topological phenomena. The vibration spectrum of mechanical graphene is characterized by Dirac cones serving as sources of topological nontriviality. We find that the spectrum has dramatic dependence on the spring tension at equilibrium as a natural control parameter, i.e., creation and annihilation of the Dirac particles are realized as the tension increases. Just by rotating the system, the manipulated Dirac particles lead to topological transition, i.e., a jump of the “Chern number” occurs associated with flipping of propagating direction of chiral edge modes. This is a bulk-edge correspondence governed by the Newton’s law. A simple observation that in-gap edge modes exist only at the fixed boundary, but not at the free one, is attributed to the symmetry protection of topological phases.
Manipulation of Dirac Cones in Mechanical Graphene.
Kariyado, Toshikaze; Hatsugai, Yasuhiro
2015-01-01
Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton's law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we investigate mechanical graphene, which is a spring-mass model with the honeycomb structure as a typical mechanical model with nontrivial topological phenomena. The vibration spectrum of mechanical graphene is characterized by Dirac cones serving as sources of topological nontriviality. We find that the spectrum has dramatic dependence on the spring tension at equilibrium as a natural control parameter, i.e., creation and annihilation of the Dirac particles are realized as the tension increases. Just by rotating the system, the manipulated Dirac particles lead to topological transition, i.e., a jump of the "Chern number" occurs associated with flipping of propagating direction of chiral edge modes. This is a bulk-edge correspondence governed by the Newton's law. A simple observation that in-gap edge modes exist only at the fixed boundary, but not at the free one, is attributed to the symmetry protection of topological phases. PMID:26667580
Dirac Equation for Electrodynamic Model Particle
NASA Astrophysics Data System (ADS)
Zheng-Johansson, J. X.
2008-03-01
We set up the Maxwell's equations and subsequently the classical wave equations for the electromagnetic waves which together with their generating source, an oscillatory charge of zero rest mass, make up a particle travelling at velocity v as with the charge in the fields of an external scalar and vector potentials. The direct solutions in constant external field are Doppler-displaced plane waves propagating at the velocity of light c; at the de Broglie wavelength scale and expressed in terms of the dynamically equivalent and appropriate geometric mean wave variables, these render as functons identical to the space-time functions of the Dirac spinor, and these are identical to the de Broglie phase waves given previously from explicit superposition. For two spin-half particles of a common set of space-time functions constrained with antisymmetric spin functions as follows the Pauli principle for same charges and as separately indirectly induced based on experiment for opposite charges, the complete wave functions are identical to a Dirac spinor. The back-substitution of the so explicitly determined complete wave functions in the corresponding classical wave equations of the two particles, subjected further to reductions appropriate for the stationary- state particle motion and to rotation invariance when in three dimensions, give a Dirac equation set; the procedure and conclusion are directly extendible to arbitrarily varying potentials by use of the Furious theorem and to three dimensions (full paper: QTS5).
Quantum transport through 3D Dirac materials
Salehi, M.; Jafari, S.A.
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
NASA Astrophysics Data System (ADS)
Salehi, M.; Jafari, S. A.
2015-08-01
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.
Manipulation of Dirac Cones in Mechanical Graphene
Kariyado, Toshikaze; Hatsugai, Yasuhiro
2015-01-01
Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton’s law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we investigate mechanical graphene, which is a spring-mass model with the honeycomb structure as a typical mechanical model with nontrivial topological phenomena. The vibration spectrum of mechanical graphene is characterized by Dirac cones serving as sources of topological nontriviality. We find that the spectrum has dramatic dependence on the spring tension at equilibrium as a natural control parameter, i.e., creation and annihilation of the Dirac particles are realized as the tension increases. Just by rotating the system, the manipulated Dirac particles lead to topological transition, i.e., a jump of the “Chern number” occurs associated with flipping of propagating direction of chiral edge modes. This is a bulk-edge correspondence governed by the Newton’s law. A simple observation that in-gap edge modes exist only at the fixed boundary, but not at the free one, is attributed to the symmetry protection of topological phases. PMID:26667580
The Integration of CloudStack and OCCI/OpenNebula with DIRAC
NASA Astrophysics Data System (ADS)
Méndez Muñoz, Víctor; Fernández Albor, Víctor; Graciani Diaz, Ricardo; Casajús Ramo, Adriàn; Fernández Pena, Tomás; Merino Arévalo, Gonzalo; José Saborido Silva, Juan
2012-12-01
The increasing availability of Cloud resources is arising as a realistic alternative to the Grid as a paradigm for enabling scientific communities to access large distributed computing resources. The DIRAC framework for distributed computing is an easy way to efficiently access to resources from both systems. This paper explains the integration of DIRAC with two open-source Cloud Managers: OpenNebula (taking advantage of the OCCI standard) and CloudStack. These are computing tools to manage the complexity and heterogeneity of distributed data center infrastructures, allowing to create virtual clusters on demand, including public, private and hybrid clouds. This approach has required to develop an extension to the previous DIRAC Virtual Machine engine, which was developed for Amazon EC2, allowing the connection with these new cloud managers. In the OpenNebula case, the development has been based on the CernVM Virtual Software Appliance with appropriate contextualization, while in the case of CloudStack, the infrastructure has been kept more general, which permits other Virtual Machine sources and operating systems being used. In both cases, CernVM File System has been used to facilitate software distribution to the computing nodes. With the resulting infrastructure, the cloud resources are transparent to the users through a friendly interface, like the DIRAC Web Portal. The main purpose of this integration is to get a system that can manage cloud and grid resources at the same time. This particular feature pushes DIRAC to a new conceptual denomination as interware, integrating different middleware. Users from different communities do not need to care about the installation of the standard software that is available at the nodes, nor the operating system of the host machine which is transparent to the user. This paper presents an analysis of the overhead of the virtual layer, doing some tests to compare the proposed approach with the existing Grid solution. License
NASA Astrophysics Data System (ADS)
Skobelev, V. V.
2016-05-01
A solution of the Dirac equation for an electron in the field of a point nucleus (Ze), expressed in terms of an eigenfunction of the operator of the spin projection onto the third axis and the corresponding solution of the Schrödinger equation is derived. This solution is suitable for practical calculations. On the basis of this solution, using ordinary methods of QED and field theory, general principles for the emission of photons, axions, and neutrinos {(Ze)}^{*}to (Ze)+γ, a, voverline{v} by a hydrogen-like atom are formulated which take into account the spin state of the electron and, in the case of photons, their polarization. This range of questions pertaining to a comparative characteristic of processes of emission of massless or almost massless particles has, to this day, not been discussed from this point of view in the literature. Selection rules for γ, a,voverline{v} emission processes are also obtained, where for axions and neutrinos they coincide with the existing selection rules in the literature ∆m = 0,±1; with ∆l = ±1 pertaining to photons, but for photon emission a few of them do in fact differ from them with the hypothesis of odd values of ∆l, not established by us and additional to the usual values ∆l = ±1 of variation of the azimuthal quantum number l due to the appearance of "new" integrals over the spherical angle θ for ∆m = ±1, where for ∆m = 0, as before, ∆l = ±1. Moreover, the dependence of the amplitude of the photon emission process on the quantum numbers is in principle different than in the previously adopted approach to the problem although the lifetime in the excited state for small values of the quantum numbers coincides in order of magnitude with the accepted value 10-9 s.
Pseudo-Dirac Dark Matter Leaves a Trace
De Simone, Andrea; Sanz, Veronica; Sato, Hiromitsu Phil
2010-09-17
Pseudo-Dirac dark matter is a viable type of dark matter which originates from a new Dirac fermion whose two Weyl states get slightly split in mass by a small Majorana term. The decay of the heavier to the lighter state naturally occurs over a detectable length scale. Thus, whenever pseudo-Dirac dark matter is produced in a collider, it leaves a clear trace: a visible displaced vertex in association with missing energy. Moreover, pseudo-Dirac dark matter behaves Dirac-like for relic abundance and Majorana-like in direct detection experiments. We provide a general effective field theory treatment, specializing to a pseudo-Dirac bino. The dark matter mass and the mass splitting can be extracted from measurements of the decay length and the invariant mass of the products, even in the presence of missing energy.
Pseudo-Dirac dark matter leaves a trace.
De Simone, Andrea; Sanz, Veronica; Sato, Hiromitsu Phil
2010-09-17
Pseudo-Dirac dark matter is a viable type of dark matter which originates from a new Dirac fermion whose two Weyl states get slightly split in mass by a small Majorana term. The decay of the heavier to the lighter state naturally occurs over a detectable length scale. Thus, whenever pseudo-Dirac dark matter is produced in a collider, it leaves a clear trace: a visible displaced vertex in association with missing energy. Moreover, pseudo-Dirac dark matter behaves Dirac-like for relic abundance and Majorana-like in direct detection experiments. We provide a general effective field theory treatment, specializing to a pseudo-Dirac bino. The dark matter mass and the mass splitting can be extracted from measurements of the decay length and the invariant mass of the products, even in the presence of missing energy. PMID:20867629
Dirac Cones and Minigaps for Graphene on Ir(111)
NASA Astrophysics Data System (ADS)
Pletikosić, I.; Kralj, M.; Pervan, P.; Brako, R.; Coraux, J.; N'Diaye, A. T.; Busse, C.; Michely, T.
2009-02-01
Epitaxial graphene on Ir(111) prepared in excellent structural quality is investigated by angle-resolved photoelectron spectroscopy. It clearly displays a Dirac cone with the Dirac point shifted only slightly above the Fermi level. The moiré resulting from the overlaid graphene and Ir(111) surface lattices imposes a superperiodic potential giving rise to Dirac cone replicas and the opening of minigaps in the band structure.
The GridPP DIRAC project: Implementation of a multi-VO DIRAC service
NASA Astrophysics Data System (ADS)
Bauer, D.; Colling, D.; Currie, R.; Fayer, S.; Huffman, A.; Martyniak, J.; Rand, D.; Richards, A.
2015-12-01
The GridPP consortium provides computing support to many high energy physics projects in the UK. As part of this GridPP offers access to a large amount of highly distributed resources across the UK for multiple collaborations. The userbase supported by GridPP includes hundreds of users spanning multiple virtual organisations with many different computing requirements. In order to provide a common interface to these distributed a centralised DIRAC instance has been setup at Imperial College London. This paper describes the experiences learnt from deploying this DIRAC instance and the modifications that have made to support the GridPP use case.
Dirac point movement and topological phase transition in patterned graphene
NASA Astrophysics Data System (ADS)
Dvorak, Marc; Wu, Zhigang
2015-02-01
The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topological transition from semimetal to semiconductor when two inequivalent Dirac points merge, an idea that has attracted significant research interest. However, such movement normally requires unrealistically high lattice anisotropy. Here we show that anisotropic defects can break the C3 symmetry of graphene, leading to Dirac point drift in the Brillouin zone. Additionally, the long-range order in periodically patterned graphene can induce intervalley scattering between two inequivalent Dirac points, resulting in a semimetal-to-insulator topological phase transition. The magnitude and direction of Dirac point drift are predicted analytically, which are consistent with our first-principles electronic structure calculations. Thus, periodically patterned graphene can be used to study the fascinating physics associated with Dirac point movement and the corresponding phase transition.The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topological transition from semimetal to semiconductor when two inequivalent Dirac points merge, an idea that has attracted significant research interest. However, such movement normally requires unrealistically high lattice anisotropy. Here we show that anisotropic defects can break the C3 symmetry of graphene, leading to Dirac point drift in the Brillouin zone. Additionally, the long-range order in periodically patterned graphene can induce intervalley scattering between two inequivalent Dirac points, resulting in a semimetal-to-insulator topological phase transition. The
Physical account of Weyl anomaly from Dirac Sea
NASA Astrophysics Data System (ADS)
Habara, Yoshinobu; Nielsen, Holger B.; Ninomiya, Masao
2015-09-01
We rederive in a physical manner the Weyl anomaly in two-dimensional space-time by considering the Dirac Sea. It is regularized by some bosonic extra species which are formally negatively counted. In fact, we calculate the trace of the energy-momentum tensor in the Dirac Sea in presence of background gravitational field. It has to be regularized, since the Dirac Sea is bottomless and thus causes divergence. The new regularization method consists in adding various massive bosonic species some of which are to be counted negative in the Dirac Sea. The mass terms in the Lagrangian of the regularization fields have a dependence on the background gravitational field.
Klein tunneling and Dirac potentials in trapped ions
Casanova, J.; Garcia-Ripoll, J. J.; Gerritsma, R.; Roos, C. F.; Solano, E.
2010-08-15
We propose the quantum simulation of the Dirac equation with potentials, allowing the study of relativistic scattering and Klein tunneling. This quantum relativistic effect permits a positive-energy Dirac particle to propagate through a repulsive potential via the population transfer to negative-energy components. We show how to engineer scalar, pseudoscalar, and other potentials in the 1+1 Dirac equation by manipulating two trapped ions. The Dirac spinor is represented by the internal states of one ion, while its position and momentum are described by those of a collective motional mode. The second ion is used to build the desired potentials with high spatial resolution.
Prototype of a production system for Cherenkov Telescope Array with DIRAC
NASA Astrophysics Data System (ADS)
Arrabito, L.; Bregeon, J.; Haupt, A.; Graciani Diaz,
2015-12-01
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
The C 4F 10 Cherenkov detector for DIRAC-II
NASA Astrophysics Data System (ADS)
Horikawa, S.; Allkofer, Y.; Amsler, C.; Brekhovskikh, V.; Kuptsov, A.; Pentia, M.; Zhabitsky, M.
2008-09-01
A new threshold Cherenkov detector using C 4F 10 gas radiator was built and put into operation in the DIRAC-II experiment at CERN. Running on the C 4F 10 at room temperature and atmospheric pressure, the detector discriminates between pions and kaons in the momentum range of 4- 8 GeV/c. A compact radiator-gas recirculation system including a gas-liquid separation unit, hollow-fibre membranes and molecular sieves ensures gas purity for a long term of operation without a significant loss of the gas. The system is robust and stable and the pressure in the two detector vessels is regulated in the range of ±0.5 mbar. We report on the design and the technical aspects of the detector and its response in the DIRAC 2007 run.
Consistency of multi-time Dirac equations with general interaction potentials
NASA Astrophysics Data System (ADS)
Deckert, Dirk-André; Nickel, Lukas
2016-07-01
In 1932, Dirac proposed a formulation in terms of multi-time wave functions as candidate for relativistic many-particle quantum mechanics. A well-known consistency condition that is necessary for existence of solutions strongly restricts the possible interaction types between the particles. It was conjectured by Petrat and Tumulka that interactions described by multiplication operators are generally excluded by this condition, and they gave a proof of this claim for potentials without spin-coupling. Under suitable assumptions on the differentiability of possible solutions, we show that there are potentials which are admissible, give an explicit example, however, show that none of them fulfills the physically desirable Poincaré invariance. We conclude that in this sense, Dirac's multi-time formalism does not allow to model interaction by multiplication operators, and briefly point out several promising approaches to interacting models one can instead pursue.
ERIC Educational Resources Information Center
Wilkins, Jesse L. M.; Norton, Anderson; Boyce, Steven J.
2013-01-01
Previous research has documented schemes and operations that undergird students' understanding of fractions. This prior research was based, in large part, on small-group teaching experiments. However, written assessments are needed in order for teachers and researchers to assess students' ways of operating on a whole-class scale. In this…
The Hamiltonian structure of Dirac's equation in tensor form and its Fermi quantization
NASA Technical Reports Server (NTRS)
Reifler, Frank; Morris, Randall
1992-01-01
Currently, there is some interest in studying the tensor forms of the Dirac equation to elucidate the possibility of the constrained tensor fields admitting Fermi quantization. We demonstrate that the bispinor and tensor Hamiltonian systems have equivalent Fermi quantizations. Although the tensor Hamiltonian system is noncanonical, representing the tensor Poisson brackets as commutators for the Heisenberg operators directly leads to Fermi quantization without the use of bispinors.
Dirac oscillator interacting with a topological defect
Carvalho, J.; Furtado, C.; Moraes, F.
2011-09-15
In this work we study the interaction problem of a Dirac oscillator with gravitational fields produced by topological defects. The energy levels of the relativistic oscillator in the cosmic string and in the cosmic dislocation space-times are sensible to curvature and torsion associated to these defects and are important evidence of the influence of the topology on this system. In the presence of a localized magnetic field the energy levels acquire a term associated with the Aharonov-Bohm effect. We obtain the eigenfunctions and eigenvalues and see that in the nonrelativistic limit some results known in standard quantum mechanics are reached.
Incomplete Dirac reduction of constrained Hamiltonian systems
Chandre, C.
2015-10-15
First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.
Dirac neutrinos from a second Higgs doublet
NASA Astrophysics Data System (ADS)
Davidson, Shainen M.; Logan, Heather E.
2009-11-01
We propose a minimal extension of the standard model in which neutrinos are Dirac particles and their tiny masses are explained without requiring tiny Yukawa couplings. A second Higgs doublet with a tiny vacuum expectation value provides neutrino masses while simultaneously improving the naturalness of the model by allowing a heavier standard-model-like Higgs boson consistent with electroweak precision data. The model predicts a μ→eγ rate potentially detectable in the current round of experiments, as well as distinctive signatures in the production and decay of the charged Higgs H+ of the second doublet which can be tested at future colliders. Neutrinoless double beta decay is absent.
The Dirac Operator on Generalized Taub-NUT Spaces
NASA Astrophysics Data System (ADS)
Moroianu, Andrei; Moroianu, Sergiu
2011-08-01
We find sufficient conditions for the absence of harmonic L 2 spinors on spin manifolds constructed as cone bundles over a compact Kähler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vişinescu and the second author.
Upper-Division Student Difficulties with the Dirac Delta Function
ERIC Educational Resources Information Center
Wilcox, Bethany R.; Pollock, Steven J.
2015-01-01
The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them.…
Dirac oscillator and nonrelativistic Snyder-de Sitter algebra
Stetsko, M. M. E-mail: mykola@ktf.franko.lviv.ua
2015-01-15
Three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations give rise to appearance of minimal uncertainties in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator, supersymmetric quantum mechanics and shape invariance technique were applied.
Dirac oscillator and nonrelativistic Snyder-de Sitter algebra
NASA Astrophysics Data System (ADS)
Stetsko, M. M.
2015-01-01
Three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations give rise to appearance of minimal uncertainties in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator, supersymmetric quantum mechanics and shape invariance technique were applied.
Strong topological metal material with multiple Dirac cones
Ji, Huiwen; Valla, T.; Pletikosic, I.; Gibson, Q. D.; Sahasrabudhe, Girija; Cava, R. J.
2016-01-25
We report a new, cleavable, strong topological metal, Zr2Te2P, which has the same tetradymite-type crystal structure as the topological insulator Bi2Te2Se. Instead of being a semiconductor, however, Zr2Te2P is metallic with a pseudogap between 0.2 and 0.7 eV above the Fermi energy (EF). Inside this pseudogap, two Dirac dispersions are predicted: one is a surface-originated Dirac cone protected by time-reversal symmetry (TRS), while the other is a bulk-originated and slightly gapped Dirac cone with a largely linear dispersion over a 2 eV energy range. A third surface TRS-protected Dirac cone is predicted, and observed using angle-resolved photoemission spectroscopy, making Zr2Te2Pmore » the first system, to our knowledge, to realize TRS-protected Dirac cones at M¯ points. The high anisotropy of this Dirac cone is similar to the one in the hypothetical Dirac semimetal BiO2. As a result, we propose that if EF can be tuned into the pseudogap where the Dirac dispersions exist, it may be possible to observe ultrahigh carrier mobility and large magnetoresistance in this material.« less
Decay of Dirac hair around a dilaton black hole
Gibbons, Gary W.; Rogatko, Marek
2008-02-15
The intermediate and late-time behavior of a massive Dirac field in the background of static spherically symmetric dilaton black hole solutions is investigated. The intermediate asymptotic behavior of a massive Dirac field depends on the mass parameter as well as the wave number of the mode, while the late-time behavior has a power-law decay rate independent of both.
Generalized space-translated Dirac and Pauli equations for superintense laser-atom interactions
NASA Astrophysics Data System (ADS)
Boca, Madalina; Florescu, Viorica; Gavrila, Mihai
2012-02-01
We obtain a generalization of the nonrelativistic space-translation transformation to the Dirac equation in the case of a unidirectional laser pulse. This is achieved in a quantum-mechanical representation connected to the standard Dirac representation by a unitary operator T transforming the Foldy-Wouthuysen free-particle basis into the Volkov spinor basis. We show that a solution of the transformed Dirac equation containing initially low momenta p (p/mc≪1) will maintain this property at all times, no matter how intense the field or how rapidly it varies (within present experimental capabilities). As a consequence, the transformed four-component equation propagates independently electron and positron wave packets, and in fact the latter are propagated via two two-component Pauli equations, one for the electron, the other for the positron. These we shall denote as the Pauli low-momentum regime (LMR) equations, equivalent to the Dirac equation for the laser field. Successive levels of dynamical accuracy appear depending on how accurately the operator T is approximated. At the level of accuracy considered in this paper, the Pauli LMR equations contain no spin matrices and are in fact two-component Schrödinger equations containing generalized time-dependent potentials. The effects of spin are nevertheless included in the theory because, in the calculation of observables which are formulated in the laboratory frame, use is made of the spin-dependent transformation operator T. In addition, the nonrelativistic limit of our results reproduces known results for the laboratory frame with spin included. We show that in intense laser pulses the generalized potentials can undergo extreme distortion from their unperturbed form. The Pauli LMR equation for the electron is applicable to one-electron atoms of small nuclear charge(αZ≪1) interacting with lasers of all intensities and frequencies ω≪mc2.
Photoinduced Chern insulating states in semi-Dirac materials
NASA Astrophysics Data System (ADS)
Saha, Kush
2016-08-01
Two-dimensional (2D) semi-Dirac materials are characterized by a quadratic dispersion in one direction and a linear dispersion along the orthogonal direction. We study the topological phase transition in such 2D systems in the presence of an electromagnetic field. We show that a Chern insulating state emerges in a semi-Dirac system with two gapless Dirac nodes in the presence of light. In particular, we show that the intensity of a circularly polarized light can be used as a knob to generate topological states with nonzero Chern number. In addition, for fixed intensity and frequency of the light, a semi-Dirac system with two gapped Dirac nodes with trivial band topology can reveal the topological transition as a function of polarization of the light.
On the spring and mass of the Dirac oscillator
NASA Technical Reports Server (NTRS)
Crawford, James P.
1993-01-01
The Dirac oscillator is a relativistic generalization of the quantum harmonic oscillator. In particular, the square of the Hamiltonian for the Dirac oscillator yields the Klein-Gordon equation with a potential of the form: (ar(sub 2) + b(L x S)), where a and b are constants. To obtain the Dirac oscillator, a 'minimal substitution' is made in the Dirac equation, where the ordinary derivative is replaced with a covariant derivative. However, an unusual feature of the covariant derivative in this case is that the potential is a non-trivial element of the Clifford algebra. A theory which naturally gives rise to gage potentials which are non-trivial elements of the Clifford algebra is that based on local automorphism invariance. An exact solution of the automorphism gage field equations which reproduces both the potential term and the mass term of the Dirac oscillator is presented.
Optical analogue of relativistic Dirac solitons in binary waveguide arrays
Tran, Truong X.; Longhi, Stefano; Biancalana, Fabio
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.
Plasmon modes of a massive Dirac plasma, and their superlattices
NASA Astrophysics Data System (ADS)
Sachdeva, Rashi; Thakur, Anmol; Vignale, Giovanni; Agarwal, Amit
2015-05-01
We explore the collective density oscillations of a collection of charged massive Dirac particles, in one, two, and three dimensions, and their one-dimensional (1D) superlattice. We calculate the long-wavelength limit of the dynamical polarization function analytically, and use the random phase approximation to obtain the plasmon dispersion. The density dependence of the long-wavelength plasmon frequency in massive Dirac systems is found to be different compared to systems with parabolic and gapless Dirac dispersion. We also calculate the long-wavelength plasmon dispersion of a 1D metamaterial made from 1D and 2D massive Dirac plasma. Our analytical results will be useful for exploring the use of massive Dirac materials as electrostatically tunable plasmonic metamaterials and can be experimentally verified by infrared spectroscopy, as in the case of graphene [L. Ju et al., Nat. Nanotechnol. 6, 630 (2011), 10.1038/nnano.2011.146].
Floquet-Engineered Valleytronics in Dirac Systems
NASA Astrophysics Data System (ADS)
Seradjeh, Babak; Kundu, Arijit; Fertig, Herbert
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, such as monolayer transition-metal dichalcogenides. Simulating the system numerically, we find that the effect is robustness against moderate disorder and small deviations in optical parameters. We also study designs for coherent manipulation of valley degrees of freedom suitable for quantum information processing. This work was supported in part by the NSF through Grant Nos. DMR-1350663 and DMR-1506460, the US-Israel Binational Science Foundation, and by Indiana University.
Isospin of topological defects in Dirac systems
NASA Astrophysics Data System (ADS)
Herbut, Igor F.
2012-02-01
We study the Dirac quasiparticles in d-dimensional lattice systems of electrons in the presence of domain walls (d=1), vortices (d=2), or hedgehogs (d=3) of superconducting and/or insulating, order parameters, which appear as mass terms in the Dirac equation. Such topological defects have been known to carry nontrivial quantum numbers, such as charge and spin. Here we discuss their additional internal degree of freedom: irrespective of the dimensionality of space and the nature of orders that support the defect, an extra mass order parameter is found to emerge in their core. Six linearly independent local orders, which close two mutually commuting three-dimensional Clifford algebras, are proven to be in general possible. We show how the particle-hole symmetry restricts the defects to always carry the quantum numbers of a single effective isospin 1/2, quite independently of the values of their electric charge or true spin. Examples of this new degree of freedom in graphene and on surfaces of topological insulators are discussed.
High scale mixing unification for Dirac neutrinos
NASA Astrophysics Data System (ADS)
Abbas, Gauhar; Gupta, Saurabh; Rajasekaran, G.; Srivastava, Rahul
2015-06-01
Starting with the high scale mixing unification hypothesis, we investigate the renormalization-group evolution of mixing parameters and masses for Dirac-type neutrinos. Following this hypothesis, the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing angles and phase are taken to be identical to the Cabibbo-Kobayashi-Maskawa (CKM) ones at a unifying high scale. Then they are evolved to a low scale using renormalization-group equations. The notable feature of this hypothesis is that renormalization-group evolution with quasidegenerate mass pattern can explain largeness of leptonic mixing angles even for Dirac neutrinos. The renormalization-group evolution "naturally" results in a nonzero and small value of leptonic mixing angle θ13. One of the important predictions of this work is that the mixing angle θ23 is nonmaximal and lies only in the second octant. We also derive constraints on the allowed parameter range for the supersymmetry breaking and unification scales for which this hypothesis works. The results are novel and can be tested by present and future experiments.
Dirac particle, gravity, and inertial effects
NASA Astrophysics Data System (ADS)
Huang, Justin C.
Dirac's equation with gravity for a noninertial observer is derived using local coordinate methods. Calculations for the equation are carried out to second order in the local coordinates. For easy application to interference experiments, the Schrödinger form of the Dirac equation with a well defined Hamiltonian in the local coordinates is presented. The presence of gravitational weighting factors in the scalar product lead to hermitian and antihermitian sectors for the Hamiltonian. The antihermitian part depends directly on the curvature and vanishes for zero curvature. The hermitian part which is important for the determination of phases is studied in detail and the nonrelativistic case is obtained by the application of three successive Foldy-Wouthuysen transformations. The results also give local currents and interactions which have pure inertial, pure gravity and mixed sectors. The pure inertial terms are the ones obtained by Hehl and Ni. The pure gravity and mixed sectors have contributions which are electric, magnetic and double magnetic in character. The focus is on the curvature contributions. Some are well within reach of the anticipated accuracy of atomic interferometers currently under consideration and other terms may follow if improvements can be made.
Spin-foam fermions: PCT symmetry, Dirac determinant and correlation functions
NASA Astrophysics Data System (ADS)
Han, Muxin; Rovelli, Carlo
2013-04-01
We discuss fermion coupling in the framework of spin-foam quantum gravity. We analyze the gravity-fermion spin-foam model and its fermion correlation functions. We show that there is a spin-foam analogue of PCT symmetry for the fermion fields on a spin-foam model, which is proved for spin-foam fermion correlation functions. We compute the determinant of the Dirac operator for the fermions, where two presentations of the Dirac determinant are given in terms of diagram expansions. We compute the fermion correlation functions and show that they can be given by Feynman diagrams on the spin-foams, where the Feynman propagators can be represented by a discretized path integral of a world-line action along the edges of the underlying 2-complex.
The Dirac point electron in zero-gravity Kerr–Newman spacetime
Kiessling, M. K.-H.; Tahvildar-Zadeh, A. S.
2015-04-15
Dirac’s wave equation for a point electron in the topologically nontrivial maximal analytically extended electromagnetic Kerr–Newman spacetime is studied in a limit G → 0, where G is Newton’s constant of universal gravitation. The following results are obtained: the formal Dirac Hamiltonian on the static spacelike slices is essentially self-adjoint and the spectrum of the self-adjoint extension is symmetric about zero, featuring a continuum with a gap about zero that, under two smallness conditions, contains a point spectrum. The symmetry result extends to the Dirac operator on a generalization of the zero-G Kerr–Newman spacetime with different electric-monopole/magnetic-dipole-moment ratios.
Unconventional spin Hall effect and axial current generation in a Dirac semimetal
NASA Astrophysics Data System (ADS)
Okuma, Nobuyuki; Ogata, Masao
2016-04-01
We investigate electrical transport in a three-dimensional massless Dirac fermion model that describes a Dirac semimetal state realized in topological materials. We derive a set of interdependent diffusion equations with eight local degrees of freedom, including the electric charge density and the spin density, that respond to an external electric field. By solving the diffusion equations for a system with a boundary, we demonstrate that a spin Hall effect with spin accumulation occurs even though the conventional spin current operator is zero. The Noether current associated with chiral symmetry, known as the axial current, is also discussed. We demonstrate that the axial current flows near the boundary and that it is perpendicular to the electric current.
Single-cone real-space finite difference scheme for the time-dependent Dirac equation
NASA Astrophysics Data System (ADS)
Hammer, René; Pötz, Walter; Arnold, Anton
2014-05-01
A finite difference scheme for the numerical treatment of the (3+1)D Dirac equation is presented. Its staggered-grid intertwined discretization treats space and time coordinates on equal footing, thereby avoiding the notorious fermion doubling problem. This explicit scheme operates entirely in real space and leads to optimal linear scaling behavior for the computational effort per space-time grid-point. It allows for an easy and efficient parallelization. A functional for a norm on the grid is identified. It can be interpreted as probability density and is proved to be conserved by the scheme. The single-cone dispersion relation is shown and exact stability conditions are derived. Finally, a single-cone scheme for the two-component (2+1)D Dirac equation, its properties, and a simulation of scattering at a Klein step are presented.
NASA Astrophysics Data System (ADS)
Wu, Shuang-Qing
2009-08-01
The aim of this paper is to investigate the separability of a spin-1/2 spinor field in a five-dimensional rotating, charged black hole constructed by Cvetič and Youm in string theory, in the case when three U(1) charges are set equal. This black hole solution represents a natural generalization of the famous four-dimensional Kerr-Newman solution to five dimensions with the inclusion of a Chern-Simons term to the Maxwell equation. It is shown that the usual Dirac equation cannot be separated by variables in this general spacetime with two independent angular momenta. However if one supplements an additional counterterm into the usual Dirac operator, then the modified Dirac equation for the spin-1/2 spinor particles is separable in this rotating, charged Einstein-Maxwell-Chern-Simons black hole background geometry. A first-order symmetry operator that commutes with the modified Dirac operator has exactly the same form as that previously found in the uncharged Myers-Perry black hole case. It is expressed in terms of a rank-three totally antisymmetric tensor and its covariant derivative. This tensor obeys a generalized Killing-Yano equation and its square is a second-order symmetric Stäckel-Killing tensor admitted by the five-dimensional rotating, charged black hole spacetime.
Wu Shuangqing
2009-08-15
The aim of this paper is to investigate the separability of a spin-1/2 spinor field in a five-dimensional rotating, charged black hole constructed by Cvetic and Youm in string theory, in the case when three U(1) charges are set equal. This black hole solution represents a natural generalization of the famous four-dimensional Kerr-Newman solution to five dimensions with the inclusion of a Chern-Simons term to the Maxwell equation. It is shown that the usual Dirac equation cannot be separated by variables in this general spacetime with two independent angular momenta. However if one supplements an additional counterterm into the usual Dirac operator, then the modified Dirac equation for the spin-1/2 spinor particles is separable in this rotating, charged Einstein-Maxwell-Chern-Simons black hole background geometry. A first-order symmetry operator that commutes with the modified Dirac operator has exactly the same form as that previously found in the uncharged Myers-Perry black hole case. It is expressed in terms of a rank-three totally antisymmetric tensor and its covariant derivative. This tensor obeys a generalized Killing-Yano equation and its square is a second-order symmetric Staeckel-Killing tensor admitted by the five-dimensional rotating, charged black hole spacetime.
SARAH 3.2: Dirac gauginos, UFO output, and more
NASA Astrophysics Data System (ADS)
Staub, Florian
2013-07-01
SARAH is a Mathematica package optimized for the fast, efficient and precise study of supersymmetric models beyond the MSSM: a new model can be defined in a short form and all vertices are derived. This allows SARAH to create model files for FeynArts/FormCalc, CalcHep/CompHep and WHIZARD/O'Mega. The newest version of SARAH now provides the possibility to create model files in the UFO format which is supported by MadGraph 5, MadAnalysis 5, GoSam, and soon by Herwig++. Furthermore, SARAH also calculates the mass matrices, RGEs and 1-loop corrections to the mass spectrum. This information is used to write source code for SPheno in order to create a precision spectrum generator for the given model. This spectrum-generator-generator functionality as well as the output of WHIZARD and CalcHep model files has seen further improvement in this version. Also models including Dirac gauginos are supported with the new version of SARAH, and additional checks for the consistency of the implementation of new models have been created. Program summaryProgram title:SARAH Catalogue identifier: AEIB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIB_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3 22 411 No. of bytes in distributed program, including test data, etc.: 3 629 206 Distribution format: tar.gz Programming language: Mathematica. Computer: All for which Mathematica is available. Operating system: All for which Mathematica is available. Classification: 11.1, 11.6. Catalogue identifier of previous version: AEIB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 182 (2011) 808 Does the new version supersede the previous version?: Yes, the new version includes all known features of the previous version but also provides the new features mentioned below
Wu, Yun; Wang, Lin -Lin; Mun, Eundeok; Johnson, D. D.; Mou, Daixiang; Huang, Lunan; Lee, Yongbin; Bud’ko, S. L.; Canfield, P. C.; Kaminski, Adam
2016-04-04
In topological quantum materials1,2,3 the conduction and valence bands are connected at points or along lines in the momentum space. A number of studies have demonstrated that several materials are indeed Dirac/Weyl semimetals4,5,6,7,8. However, there is still no experimental confirmation of materials with line nodes, in which the Dirac nodes form closed loops in the momentum space2,3. Here we report the discovery of a novel topological structure—Dirac node arcs—in the ultrahigh magnetoresistive material PtSn4 using laser-based angle-resolved photoemission spectroscopy data and density functional theory calculations. Unlike the closed loops of line nodes, the Dirac node arc structure arises owing tomore » the surface states and resembles the Dirac dispersion in graphene that is extended along a short line in the momentum space. Here, we propose that this reported Dirac node arc structure is a novel topological state that provides an exciting platform for studying the exotic properties of Dirac fermions.« less
Absorbing layers for the Dirac equation
Pinaud, Olivier
2015-05-15
This work is devoted to the construction of perfectly matched layers (PML) for the Dirac equation, that not only arises in relativistic quantum mechanics but also in the dynamics of electrons in graphene or in topological insulators. While the resulting equations are stable at the continuous level, some care is necessary in order to obtain a stable scheme at the discrete level. This is related to the so-called fermion doubling problem. For this matter, we consider the numerical scheme introduced by Hammer et al. [19], and combine it with the discretized PML equations. We state some arguments for the stability of the resulting scheme, and perform simulations in two dimensions. The perfectly matched layers are shown to exhibit, in various configurations, superior absorption than the absorbing potential method and the so-called transport-like boundary conditions.
Warm Dirac-Born-Infeld inflation
Cai Yifu; Dent, James B.; Easson, Damien A.
2011-05-15
We propose a warm inflationary model in the context of relativistic D-brane inflation in a warped throat, which has Dirac-Born-Infeld (DBI) kinetic term and is coupled to radiation through a dissipation term. The perturbation freezes at the sound horizon and the power spectrum is determined by a combination of the dissipative parameter and the sound speed parameter. The thermal dissipation ameliorates the eta problem and softens theoretical constraints from the extra-dimensional volume and from observational bounds on the tensor-to-scalar ratio. The warm DBI model can lead to appreciable non-Gaussianity of the equilateral type. As a phenomenological model, ignoring compactification constraints, we show that large-field warm inflation models do not necessarily yield a large tensor-to-scalar ratio.
On regularizations of the Dirac delta distribution
NASA Astrophysics Data System (ADS)
Hosseini, Bamdad; Nigam, Nilima; Stockie, John M.
2016-01-01
In this article we consider regularizations of the Dirac delta distribution with applications to prototypical elliptic and hyperbolic partial differential equations (PDEs). We study the convergence of a sequence of distributions SH to a singular term S as a parameter H (associated with the support size of SH) shrinks to zero. We characterize this convergence in both the weak-* topology of distributions and a weighted Sobolev norm. These notions motivate a framework for constructing regularizations of the delta distribution that includes a large class of existing methods in the literature. This framework allows different regularizations to be compared. The convergence of solutions of PDEs with these regularized source terms is then studied in various topologies such as pointwise convergence on a deleted neighborhood and weighted Sobolev norms. We also examine the lack of symmetry in tensor product regularizations and effects of dissipative error in hyperbolic problems.
Massive mesons in Weyl-Dirac theory
NASA Astrophysics Data System (ADS)
Mirabotalebi, S.; Ahmadi, F.; Salehi, H.
2008-01-01
In order to study the mass generation of the vector fields in the framework of a conformal invariant gravitational model, the Weyl-Dirac theory is considered. The mass of the Weyl’s meson fields plays a principal role in this theory, it connects basically the conformal and gauge symmetries. We estimate this mass by using the large-scale characteristics of the observed universe. To do this we firstly specify a preferred conformal frame as a cosmological frame, then in this frame, we introduce an exact possible solution of the theory. We also study the dynamical effect of the massive vector meson fields on the trajectories of an elementary particle. We show that a local change of the cosmological frame leads to a Hamilton-Jacobi equation describing a particle with an adjustable mass. The dynamical effect of the massive vector meson field presents itself in the form of a correction term for the mass of the particle.
Absorbing layers for the Dirac equation
NASA Astrophysics Data System (ADS)
Pinaud, Olivier
2015-05-01
This work is devoted to the construction of perfectly matched layers (PML) for the Dirac equation, that not only arises in relativistic quantum mechanics but also in the dynamics of electrons in graphene or in topological insulators. While the resulting equations are stable at the continuous level, some care is necessary in order to obtain a stable scheme at the discrete level. This is related to the so-called fermion doubling problem. For this matter, we consider the numerical scheme introduced by Hammer et al. [19], and combine it with the discretized PML equations. We state some arguments for the stability of the resulting scheme, and perform simulations in two dimensions. The perfectly matched layers are shown to exhibit, in various configurations, superior absorption than the absorbing potential method and the so-called transport-like boundary conditions.
Negative Energies in the Dirac Equation
NASA Astrophysics Data System (ADS)
Dvoeglazov, Valeriy V.
2016-04-01
It is easy to check that both algebraic equation Det(hat p - m) = 0 and Det(hat p + m) = 0 for u- and v- 4-spinors have solutions with p0 = ± {E_p} = ± √ {{{{p}}^2} + {m^2}}. The same is true for higher-spin equations. Meanwhile, every book considers the equality p0=Ep for both u- and v- spinors of the (1/2, 0)⊕(0, 1/2) representation only, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We reconsider this possibility on the quantum field level for both s=1/2 and higher-spin particles.
New Dirac equation from the view point of particle
Ozaydin, Fatih; Altintas, Azmi Ali; Susam, Lidya Amon; Arik, Metin; Yarman, Tolga
2012-09-06
According to the classical approach, especially the Lorentz Invariant Dirac Equation, when particles are bound to each other, the interaction term appears as a quantity belonging to the 'field'. In this work, as a totally new approach, we propose to alter the rest masses of the particles due to their interaction, as much as their respective contributions to the static binding energy. Thus we re-write and solve the Dirac Equation for the hydrogen atom, and amazingly, obtain practically the same numerical results for the ground states, as those obtained from the Dirac Equation.
Massive photons and Dirac monopoles: Electric condensate and magnetic confinement
NASA Astrophysics Data System (ADS)
Guimaraes, M. S.; Rougemont, R.; Wotzasek, C.; Zarro, C. A. D.
2013-06-01
We use the generalized Julia-Toulouse approach (GJTA) for condensation of topological currents (charges or defects) to argue that massive photons can coexist consistently with Dirac monopoles. The Proca theory is obtained here via GJTA as a low energy effective theory describing an electric condensate and the mass of the vector boson is responsible for generating a Meissner effect which confines the magnetic defects in monopole-antimonopole pairs connected by physical open magnetic vortices described by Dirac brane invariants, instead of Dirac strings.
A spinor representation of Maxwell equations and Dirac equation
Vaz, J. Jr.; Rodrigues, W.A. Jr.
1993-02-01
Using the Clifford bundle formalism and starting from the free Maxwell equations dF = {delta}F = 0 we show by writing F = b{psi}{gamma}{sup 1}{gamma}{sup 2}{psi}{sup *}, where {psi} is a Dirac-Hestenes spinor field, that the Dirac-Hestenes equation (which is the representative of the standard Dirac equation in the Clifford bundle over Minkowski spacetime) is equivalent under general assumptions to those free Maxwell equations. We briefly discuss the implications of our findings for the interpretation of quantum mechanics. 15 refs.
Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS
Schoop, Leslie M.; Ali, Mazhar N.; Straßer, Carola; Topp, Andreas; Varykhalov, Andrei; Marchenko, Dmitry; Duppel, Viola; Parkin, Stuart S. P.; Lotsch, Bettina V.; Ast, Christian R.
2016-01-01
Materials harbouring exotic quasiparticles, such as massless Dirac and Weyl fermions, have garnered much attention from physics and material science communities due to their exceptional physical properties such as ultra-high mobility and extremely large magnetoresistances. Here, we show that the highly stable, non-toxic and earth-abundant material, ZrSiS, has an electronic band structure that hosts several Dirac cones that form a Fermi surface with a diamond-shaped line of Dirac nodes. We also show that the square Si lattice in ZrSiS is an excellent template for realizing new types of two-dimensional Dirac cones recently predicted by Young and Kane. Finally, we find that the energy range of the linearly dispersed bands is as high as 2 eV above and below the Fermi level; much larger than of other known Dirac materials. This makes ZrSiS a very promising candidate to study Dirac electrons, as well as the properties of lines of Dirac nodes. PMID:27241624
Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS.
Schoop, Leslie M; Ali, Mazhar N; Straßer, Carola; Topp, Andreas; Varykhalov, Andrei; Marchenko, Dmitry; Duppel, Viola; Parkin, Stuart S P; Lotsch, Bettina V; Ast, Christian R
2016-01-01
Materials harbouring exotic quasiparticles, such as massless Dirac and Weyl fermions, have garnered much attention from physics and material science communities due to their exceptional physical properties such as ultra-high mobility and extremely large magnetoresistances. Here, we show that the highly stable, non-toxic and earth-abundant material, ZrSiS, has an electronic band structure that hosts several Dirac cones that form a Fermi surface with a diamond-shaped line of Dirac nodes. We also show that the square Si lattice in ZrSiS is an excellent template for realizing new types of two-dimensional Dirac cones recently predicted by Young and Kane. Finally, we find that the energy range of the linearly dispersed bands is as high as 2 eV above and below the Fermi level; much larger than of other known Dirac materials. This makes ZrSiS a very promising candidate to study Dirac electrons, as well as the properties of lines of Dirac nodes. PMID:27241624
Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS
NASA Astrophysics Data System (ADS)
Schoop, Leslie M.; Ali, Mazhar N.; Straßer, Carola; Topp, Andreas; Varykhalov, Andrei; Marchenko, Dmitry; Duppel, Viola; Parkin, Stuart S. P.; Lotsch, Bettina V.; Ast, Christian R.
2016-05-01
Materials harbouring exotic quasiparticles, such as massless Dirac and Weyl fermions, have garnered much attention from physics and material science communities due to their exceptional physical properties such as ultra-high mobility and extremely large magnetoresistances. Here, we show that the highly stable, non-toxic and earth-abundant material, ZrSiS, has an electronic band structure that hosts several Dirac cones that form a Fermi surface with a diamond-shaped line of Dirac nodes. We also show that the square Si lattice in ZrSiS is an excellent template for realizing new types of two-dimensional Dirac cones recently predicted by Young and Kane. Finally, we find that the energy range of the linearly dispersed bands is as high as 2 eV above and below the Fermi level; much larger than of other known Dirac materials. This makes ZrSiS a very promising candidate to study Dirac electrons, as well as the properties of lines of Dirac nodes.
On Dirac equations for linear magnetoacoustic waves propagating in an isothermal atmosphere
NASA Technical Reports Server (NTRS)
Alicki, R.; Musielak, E. Z.; Sikorski, J.; Makowiec, D.
1994-01-01
A new analytical approach to study linear magnetoacoustic waves propagating in an isothermal, stratified, and uniformly magnetized atmosphere is presented. The approach is based on Dirac equations, and the theory of Sturm-Liouville operators is used to investigate spectral properties of the obtained Dirac Hamiltonians. Two cases are considered: (1) the background magnetic field is vertical, and the waves are separated into purely magnetic (transverse) and purely acoustic (longitudinal) modes; and (2) the field is tilted with respect to the vertical direction and the magnetic and acoustic modes become coupled giving magnetoacoustic waves. For the first case, the Dirac Hamiltonian possesses either a discrete spectrum, which corresponds to standing magnetic waves, or a continuous spectrum, which can be clearly identified with freely propagating acoustic waves. For the second case, the quantum mechanical perturbation calculus is used to study coupling and energy exchange between the magnetic and acoustic components of magnetoacoustic waves. It is shown that this coupling may efficiently prevent trapping of magnetoacoustic waves instellar atmospheres.
NASA Astrophysics Data System (ADS)
Cortez, Jerónimo; Elizaga Navascués, Beatriz; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.; Velhinho, José M.
2015-11-01
We present a privileged Fock quantization of a massive Dirac field in a closed Friedmann-Robertson-Walker cosmology, partially selected by the criteria of invariance of the vacuum under the symmetries of the field equations, and unitary implementation of the dynamics. When quantizing free scalar fields in homogeneous and isotropic spacetimes with compact spatial sections, these criteria have been shown to pick out a unique Fock representation (up to unitary equivalence). Here, we employ the same criteria for fermion fields and explore whether that uniqueness result can be extended to the case of the Fock quantization of fermions. For the massive Dirac field, we start by introducing a specific choice of the complex structure that determines the Fock representation. Such a structure is invariant under the symmetries of the equations of motion. We then prove that the corresponding representation of the canonical anticommutation relations admits a unitary implementation of the dynamics. Moreover, we construct a rather general class of representations that satisfy the above criteria, and we demonstrate that they are all unitarily equivalent to our previous choice. The complex structures in this class are restricted only by certain conditions on their asymptotic behavior for modes in the ultraviolet sector of the Dirac operator. We finally show that, if one assumes that these asymptotic conditions are in fact trivial once our criteria are fulfilled, then the time-dependent scaling in the definition of the fermionic annihilation and creationlike variables is essentially unique.
Quantum field theory of photon–Dirac fermion interacting system in graphene monolayer
NASA Astrophysics Data System (ADS)
Nguyen, Bich Ha; Hieu Nguyen, Van
2016-06-01
The purpose of the present work is to elaborate quantum field theory of interacting systems comprising Dirac fermion fields in a graphene monolayer and the electromagnetic field. Since the Dirac fermions are confined in a two-dimensional plane, the interaction Hamiltonian of this system contains the projection of the electromagnetic field operator onto the plane of a graphene monolayer. Following the quantization procedure in traditional quantum electrodynamics we chose to work in the gauge determined by the weak Lorentz condition imposed on the state vectors of all physical states of the system. The explicit expression of the two-point Green function of the projection onto a graphene monolayer of a free electromagnetic field is derived. This two-point Green function and the expression of the interaction Hamiltonian together with the two-point Green functions of free Dirac fermion fields established in our previous work form the basics of the perturbation theory of the above-mentioned interacting field system. As an example, the perturbation theory is applied to the study of two-point Green functions of this interacting system of quantum fields.
Solving the Dirac equation, using the large component only, in a Dirac-type Slater orbital basis set
NASA Astrophysics Data System (ADS)
van Lenthe, E.; Baerends, E. J.; Snijders, J. G.
1995-04-01
We solve the Dirac equation by solving the two-component energy-dependent equation for the large component that results from the elimination of the small component. This requires for every occupied orbital the diagonalization of a Hamiltonian. Advantages are, however, that these Hamiltonians are all bounded from below, unlike the Dirac Hamiltonian, and that only a basis set for the large component is needed. We use Dirac-type Slater orbitals, adapted from solutions to the hydrogen-like atom. This offers the perspective of performing relativistic calculations to the same accuracy as non-relativistic ones, with a comparable number of basis functions.
Pseudo-dirac neutrinos: a challenge for neutrino telescopes.
Beacom, John F; Bell, Nicole F; Hooper, Dan; Learned, John G; Pakvasa, Sandip; Weiler, Thomas J
2004-01-01
Neutrinos may be pseudo-Dirac states, such that each generation is actually composed of two maximally mixed Majorana neutrinos separated by a tiny mass difference. The usual active neutrino oscillation phenomenology would be unaltered if the pseudo-Dirac splittings are deltam(2) less, similar 10(-12) eV(2); in addition, neutrinoless double beta decay would be highly suppressed. However, it may be possible to distinguish pseudo-Dirac from Dirac neutrinos using high-energy astrophysical neutrinos. By measuring flavor ratios as a function of L/E, mass-squared differences down to deltam(2) approximately 10(-18) eV(2) can be reached. We comment on the possibility of probing cosmological parameters with neutrinos. PMID:14753977
Dirac cones in transition metal doped boron nitride
Feng, Min; Cao, Xuewei; Shao, Bin; Zuo, Xu
2015-05-07
The transition metal (TM) doped zinc blende boron nitride (c-BN) is studied by using the first principle calculation. TM atoms fill in the interstitials in c-BN and form two-dimensional honeycomb lattice. The generalized gradient approximation and projector augmented wave method are used. The calculated density of states and band structures show that d electrons of TM atoms form impurity bands in the gap of c-BN. When the TM-BN system is in ferromagnetic or non-magnetic state, Dirac cones emerge at the K point in Brillouin zone. When TM is Ti and Co, the Dirac cones are spin polarized and very close to the Fermi level, which makes them promising candidates of Dirac half-metal [H. Ishizuka and Y. Motome, Phys. Rev. Lett. 109, 237207 (2012)]. While TM is Ni and Cu, the system is non-magnetic and Dirac cones located above the Fermi level.
Higher-order Dirac solitons in binary waveguide arrays
Tran, Truong X.; Duong, Dũng C.
2015-10-15
We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range. - Highlights: • Higher-order Dirac solitons in nonlinear binary waveguide arrays are numerically demonstrated. • Amplitude profiles of higher-order Dirac solitons are periodic during propagation. • The period of higher-order Dirac solitons decreases when the soliton order increases.
Theory of Green functions of free Dirac fermions in graphene
NASA Astrophysics Data System (ADS)
Hieu Nguyen, Van; Nguyen, Bich Ha; Dung Dinh, Ngoc
2016-03-01
This work is the beginning of our research on graphene quantum electrodynamics (GQED), based on the application of the methods of traditional quantum field theory to the study of the interacting system of quantized electromagnetic field and Dirac fermions in single-layer graphene. After a brief review of the known results concerning the lattice and electronic structures of single-layer graphene we perform the construction of the quantum fields of free Dirac fermions and the establishment of the corresponding Heisenberg quantum equations of these fields. We then elaborate the theory of Green functions of Dirac fermions in a free Dirac fermion gas at vanishing absolute temperature T = 0, the theory of Matsubara temperature Green functions and the Keldysh theory of non-equilibrium Green functions.
Geometric Structures and Field Equations of Dirac Lu Space
NASA Astrophysics Data System (ADS)
Ren, Xin-An; Zhang, Li-You
2008-11-01
In this paper, a fraktur G-invariant Lorentz metric on the Dirac Lu space is given, and then the geodesic equation is investigated. Finally, we discuss the field equations and find their solutions by the method of separating variables.
Dirac Equation for Scalar, Vector and Tensor Generalized Cornell Interaction
NASA Astrophysics Data System (ADS)
Zarrinkamar, S.; Panahi, H.; Rezaei, M.; Baradaran, M.
2016-03-01
We consider spin and pseudospin symmetry limits of Dirac equation in the presence of scalar, vector and tensor generalized Cornell interaction and report the solutions via the quasi-exact analytical ansatz approach.
RKKY interaction of magnetic impurities in Dirac and Weyl semimetals
NASA Astrophysics Data System (ADS)
Chang, Hao-Ran; Zhou, Jianhui; Wang, Shi-Xiong; Shan, Wen-Yu; Xiao, Di
2015-12-01
We theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities in both Dirac and Weyl semimetals (SMs). We find that the internode process, as well as the unique three-dimensional spin-momentum locking, has significant influences on the RKKY interaction, resulting in both a Heisenberg and an Ising term, and an additional Dzyaloshinsky-Moriya term if the inversion symmetry is absent. These interactions can lead to rich spin textures and possible ferromagnetism in Dirac and time-reversal symmetry-invariant Weyl SMs. The effect of anisotropic Dirac and Weyl nodes on the RKKY interaction is also discussed. Our results provide an alternative scheme to engineer topological SMs and shed new light on the application of Dirac and Weyl SMs in spintronics.
Does the Dirac cone of germanene exist on metal substrates?
Wang, Yangyang; Li, Jingzhen; Xiong, Junhua; Pan, Yuanyuan; Ye, Meng; Guo, Ying; Zhang, Han; Quhe, Ruge; Lu, Jing
2016-07-28
Germanene, a germanium analogue of graphene and silicene, has been synthesized on metal substrates. It is predicted that the intrinsic germanene has a Dirac cone in its band structure, just like graphene and silicene. Using first-principles calculations, we investigate the geometrical structures and electronic properties of germanene on the Ag, Au, Cu, Al, Pt and Ir substrates. The Dirac cone of germanene is destroyed on the Al, Pt and Ir substrates but preserved on the Ag and Au substrates with a slight band hybridization. The upper part of the Dirac cone is destroyed for germanene on the Cu substrate while the lower part remains preserved. By contrast, the Dirac cone is always destroyed for silicene on these metal substrates because of a strong band hybridization. Our study suggests that it is possible to extract the intrinsic properties of germanene on the Ag and Au substrates although it appears impossible for silicene on these two substrates. PMID:27411084
Digital quantum simulation of Dirac equation with a trapped ion
NASA Astrophysics Data System (ADS)
Shen, Yangchao; Zhang, Xiang; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jingning; Kim, Kihwan; Department Of Physical Chemistry Collaboration
2014-05-01
Recently there has been growing interest in simulating relativistic effects in controllable physical system. We digitally simulate the Dirac equation in 3 +1 dimensions with a single trapped ion. We map four internal levels of 171Yb+ ion to the Dirac bispinor. The time evolution of the Dirac equation is implemented by trotter expansion. In the 3 +1 dimension, we can observe a helicoidal motion of a free Dirac particle which reduces to Zitterbewegung in 1 +1 dimension. This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00301, the National Natural Science Foundation of China Grant 61033001, 61061130540. KK acknowledge the support from the recruitment program of global youth experts.
The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
Contreras-Astorga, Alonso Schulze-Halberg, Axel E-mail: xbataxel@gmail.com
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)].
Topological delocalization of two-dimensional massless Dirac fermions.
Nomura, Kentaro; Koshino, Mikito; Ryu, Shinsei
2007-10-01
The beta function of a two-dimensional massless Dirac Hamiltonian subject to a random scalar potential, which, e.g., underlies theoretical descriptions of graphene, is computed numerically. Although it belongs to, from a symmetry standpoint, the two-dimensional symplectic class, the beta function monotonically increases with decreasing conductance. We also provide an argument based on the spectral flows under twisting boundary conditions, which shows that none of the states of the massless Dirac Hamiltonian can be localized. PMID:17930701
Quasi-Dirac points in one-dimensional graphene superlattices
NASA Astrophysics Data System (ADS)
Chen, C. H.; Tseng, P.; Hsueh, W. J.
2016-08-01
Quasi-Dirac points (QDPs) with energy different from the traditional Dirac points (TDPs) have been found for the first time in one-dimensional graphene superlattices. The angular-averaged conductance reaches a minimum value at the QDPs, at which the Fano factor approaches 1/3. Surprisingly, the minimum conductance at these QDPs may be lower than that at the TDPs under certain conditions. This is remarkable as the minimum conductance attainable in graphene superlattices was believed to appear at TDPs.
Dirac Field, Gravity, Inertial Effects, and Computer Algebra
NASA Astrophysics Data System (ADS)
Vulcanov, Dumitru N.; Cotăescu, Ion I.
The article presents some new results obtained for the non-relativistic approximation of the Dirac equation in a non-inertial reference frame — rotated and accelerated — and in Schwarzschild gravitational field. These results are obtained with new routines of algebraic programming in REDUCE + EXCALC language for the Dirac equation in a non-inertial reference frame and after three successive Foldy-Wouthuysen transformations.
Two-Dimensional Dirac Materials: From Graphene to Topological Insulators
NASA Astrophysics Data System (ADS)
Teweldebrhan, Desalegne Bekuretsion
2011-12-01
Silicon has been reaching physical limits as the semiconductor industry moves to smaller device feature sizes, increased integration densities and faster operation speeds. There is a strong need to engineer alternative materials, which can become foundation of new computational paradigms or lead to other applications such as efficient solid-state energy conversion. Recently discovered Dirac materials, which are characterized by the liner electron dispersion, are examples of such alternative materials. In this dissertation, I investigate two representatives of Dirac materials -- graphene and topological insulators. Specifically, I focus on the (i) effects of electron beam irradiation on graphene properties and (ii) electronic and thermal characteristics of exfoliated films of Bi2Te3-family of topological insulators. I carried out Raman investigation of changes in graphene crystal lattice induced by the low and medium energy electron-beam irradiation (5.20 keV). It was found that radiation exposures result in appearance of the disorder D band around 1345 cm-1. The dependence of the ratio of the intensities of D and G peaks, I(D)/I(G), on the irradiation dose is non-monotonic suggesting graphene.s transformation to polycrystalline and then to disordered state. By controlling the irradiation dose one can change the carrier mobility and increase the resistance at the minimum conduction point. The obtained results may lead to new methods of defect engineering of graphene properties. They also have important implications for fabrication of graphene nanodevices, which involve electron beams. Bismuth telluride and related compounds are the best thermoelectric materials known today. Recently, it was determined that they reveal the topological insulator properties. We succeeded in the first "graphene-like" exfoliation of large-area crystalline films and ribbons of Bi2Te3 with the thickness going down to a single quintuple. The presence of van der Waals gaps allowed us to
Dirac equation in low dimensions: The factorization method
Sánchez-Monroy, J.A.; Quimbay, C.J.
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.
Composite Dirac Liquids: Parent States for Symmetric Surface Topological Order
NASA Astrophysics Data System (ADS)
Mross, David F.; Essin, Andrew; Alicea, Jason
2015-01-01
We introduce exotic gapless states—"composite Dirac liquids"—that can appear at a strongly interacting surface of a three-dimensional electronic topological insulator. Composite Dirac liquids exhibit a gap to all charge excitations but nevertheless feature a single massless Dirac cone built from emergent electrically neutral fermions. These states thus comprise electrical insulators that, interestingly, retain thermal properties similar to those of the noninteracting topological insulator surface. A variety of novel fully gapped phases naturally descend from composite Dirac liquids. Most remarkably, we show that gapping the neutral fermions via Cooper pairing—which crucially does not violate charge conservation—yields symmetric non-Abelian topologically ordered surface phases captured in several recent works. Other (Abelian) topological orders emerge upon alternatively gapping the neutral Dirac cone with magnetism. We establish a hierarchical relationship between these descendant phases and expose an appealing connection to paired states of composite Fermi liquids arising in the half filled Landau level of two-dimensional electron gases. To controllably access these states we exploit a quasi-1D deformation of the original electronic Dirac cone that enables us to analytically address the fate of the strongly interacting surface. The algorithm we develop applies quite broadly and further allows the construction of symmetric surface topological orders for recently introduced bosonic topological insulators.
NASA Astrophysics Data System (ADS)
Gómez Muñoz, J. L.; Delgado, F.
2016-03-01
This paper introduces QUANTUM, a free library of commands of Wolfram Mathematica that can be used to perform calculations directly in Dirac braket and operator notation. Its development started several years ago, in order to study quantum random walks. Later, many other features were included, like operator and commutator algebra, simulation and graphing of quantum computing circuits, generation and solution of Heisenberg equations of motion, among others. To the best of our knowledge, QUANTUM remains a unique tool in its use of Dirac notation, because it is used both in the input and output of the calculations. This work depicts its usage and features in Quantum Computing and Quantum Hamilton Dynamics.
Quantum transport in Dirac materials: Signatures of tilted and anisotropic Dirac and Weyl cones
NASA Astrophysics Data System (ADS)
Trescher, Maximilian; Sbierski, Björn; Brouwer, Piet W.; Bergholtz, Emil J.
2015-03-01
We calculate conductance and noise for quantum transport at the nodal point for arbitrarily tilted and anisotropic Dirac or Weyl cones. Tilted and anisotropic dispersions are generic in the absence of certain discrete symmetries, such as particle-hole and lattice point group symmetries. Whereas anisotropy affects the conductance g , but leaves the Fano factor F (the ratio of shot noise power and current) unchanged, a tilt affects both g and F . Since F is a universal number in many other situations, this finding is remarkable. We apply our general considerations to specific lattice models of strained graphene and a pyrochlore Weyl semimetal.
Understanding quaternions and the Dirac belt trick
NASA Astrophysics Data System (ADS)
Staley, Mark
2010-05-01
The Dirac belt trick is often employed in physics classrooms to show that a 2π rotation is not topologically equivalent to the absence of rotation whereas a 4π rotation is, mirroring a key property of quaternions and their isomorphic cousins, spinors. The belt trick can leave the student wondering if a real understanding of quaternions and spinors has been achieved, or if the trick is just an amusing analogy. The goal of this paper is to demystify the belt trick and to show that it suggests an underlying four-dimensional parameter space for rotations that is simply connected. An investigation into the geometry of this four-dimensional space leads directly to the system of quaternions, and to an interpretation of three-dimensional vectors as the generators of rotations in this larger four-dimensional world. The paper also shows why quaternions are the natural extension of complex numbers to four dimensions. The level of the paper is suitable for undergraduate students of physics.
Nonlinear propagation of light in Dirac matter.
Eliasson, Bengt; Shukla, P K
2011-09-01
The nonlinear interaction between intense laser light and a quantum plasma is modeled by a collective Dirac equation coupled with the Maxwell equations. The model is used to study the nonlinear propagation of relativistically intense laser light in a quantum plasma including the electron spin-1/2 effect. The relativistic effects due to the high-intensity laser light lead, in general, to a downshift of the laser frequency, similar to a classical plasma where the relativistic mass increase leads to self-induced transparency of laser light and other associated effects. The electron spin-1/2 effects lead to a frequency upshift or downshift of the electromagnetic (EM) wave, depending on the spin state of the plasma and the polarization of the EM wave. For laboratory solid density plasmas, the spin-1/2 effects on the propagation of light are small, but they may be significant in superdense plasma in the core of white dwarf stars. We also discuss extensions of the model to include kinetic effects of a distribution of the electrons on the nonlinear propagation of EM waves in a quantum plasma. PMID:22060507
Dirac-Fock Internal Conversion Coefficients
NASA Astrophysics Data System (ADS)
Band, I. M.; Trzhaskovskaya, M. B.; Nestor, C. W.; Tikkanen, P. O.; Raman, S.
2002-05-01
Internal conversion coefficients (ICCs) obtained from relativistic self-consistent-field Dirac-Fock (DF) calculations are presented. The exchange terms of DF equations are included exactly, both for the interaction between bound electrons and for the interaction between bound and free electrons. Static and dynamic effects resulting from finite nuclear size are taken into account, the latter using the surface current model. Experimental electron-binding energies are used wherever possible. The hole in the atomic shell from which an electron was emitted is not taken into consideration because there is no compelling experimental evidence to warrant it. ICCs are given here for each Z between Z=10 and Z=126; for K, L1, L2, and L3 atomic shells; for nuclear-transition multipolarities E1… E5, M1… M5; and for nuclear-transition energies from ˜1 keV above the L1 threshold to 2000 keV. Also given are the total ICCs. Accurate (≤5%) experimental ICCs ( K and total) are known for 77 transitions with multipolarities E2, M3, E3, M4, or E5. For these transitions, the theoretical DF values are, on average, about 3% lower than the theoretical relativistic Hartree-Fock-Slater (RHFS) values. The DF values are in better agreement with experimental results than the RHFS values.
Dirac Green function for angular projection potentials.
Zeller, Rudolf
2015-11-25
The aim of this paper is twofold: first, it is shown that the angular dependence of the Dirac Green function can be described analytically for potentials with non-local dependence on the angular variables if they are chosen as projection potentials in angular momentum space. Because the local dependence on the radial variable can be treated to any precision with present computing capabilities, this means that the Green function can be calculated practically exactly. Second, it is shown that a result of this kind not only holds for a single angular projection potential but also more generally, for instance if space is divided into non-overlapping cells and a separate angular projection potential is used in each cell. This opens the way for relativistic density-functional calculations within a different perspective than the conventional one. Instead of trying to obtain the density for a given potential approximately as well as possible, the density is determined exactly for non-local potentials which can approximate arbitrary local potentials as well as desired. PMID:26523824
Conventional spin current in Dirac equation
NASA Astrophysics Data System (ADS)
Lee, Soo Yong; Lee, Hyun-Woo
2007-03-01
The spin current has been one of main concerns in the field of the spintronics. Recently Rashba [PRB 68, 241315 (2003)] pointed out that in certain nonmagnetic systems with the spin-orbit coupling, the conventional definition of the spin current leads to a rather strange prediction, namely a nonzero spin current should flow even without external biases. Though the nonvanishing equilibrium spin current does not violate the time reversal symmetry, it still led many scientists to reexamine the definition of the spin current. Recalling that the spin-orbit coupling arises due to the relativistic effects, we examine in this work properties of the conventionally-defined spin current for a Dirac electron subject to an electrostatic potential V(r). Interestingly it is found that in this fully relativistic treatment, the equilibrium spin current vanishes for a wide class of V(r) including those representing the zincblende structure and the asymmetric quantum well, which is in clear contrast with the nonvanishing equilibrium spin current obtained from some effective nonrelativistic Hamiltonians. The origin of this difference is also examined.
Two-dimensional Dirac signature of germanene
Zhang, L.; Bampoulis, P.; Houselt, A. van; Zandvliet, H. J. W.
2015-09-14
The structural and electronic properties of germanene coated Ge{sub 2}Pt clusters have been determined by scanning tunneling microscopy and spectroscopy at room temperature. The interior of the germanene sheet exhibits a buckled honeycomb structure with a lattice constant of 4.3 Å and a buckling of 0.2 Å. The zigzag edges of germanene are reconstructed and display a 4× periodicity. The differential conductivity of the interior of the germanene sheet has a V-shape, which is reminiscent of the density of states of a two-dimensional Dirac system. The minimum of the differential conductivity is located close to the Fermi level and has a non-zero value, which we ascribe to the metallic character of the underlying Ge{sub 2}Pt substrate. Near the reconstructed germanene zigzag edges the shape of the differential conductivity changes from a V-shape to a more parabolic-like shape, revealing that the reconstructed germanene zigzag edges do not exhibit a pronounced metallic edge state.
Dirac Fermions in Nanoassembled Artificial Graphene
NASA Astrophysics Data System (ADS)
Gomes, Kenjiro K.; Ko, Wonhee; Mar, Warren; Manoharan, Hari C.
2011-03-01
In condensed matter, electronic properties derive from the energy band structure created by a periodic potential formed by the atoms that constitute a particular material. The power to design unique electronic states is ultimately tied to the power to design the atomic lattice. Utilizing the technique of atomic manipulation with a scanning tunneling microscope, we create an artificial lattice potential that reshapes the band structure of a normal 2D electron gas---found in the surface states of a normal metal---into a unique and distinct 2D gas of massless Dirac fermions. We present scanning tunneling spectroscopic measurements of nanoassembled honeycomb electron lattices, and we characterize their band structure through Fourier transform analysis of impurity scattering maps. The control of every atomic position in the lattice provides unprecedented control over physical parameters elusive in natural graphene systems. These abilities include atomically sharp doping configurations and the power to embed topological singularities, resulting in unique electronic states rarely encountered in natural systems. Supported by the DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under contract DE-AC02-76SF00515.
Fermi-Dirac distributions for quark partons
NASA Astrophysics Data System (ADS)
Bourrely, C.; Buccella, F.; Miele, G.; Migliore, G.; Soffer, J.; Tibullo, V.
1994-09-01
We propose to use Fermi-Dirac distributions for quark and antiquark partons. It allows a fair description of the x-dependence of the very recent NMC data on the proton and neutron structure functions F {2/ p } (x) and F {2/ n } (x) at Q 2=4 GeV2, as well as the CCFR antiquark distributionxbar q(x). We show that one can also use a corresponding Bose-Einstein expression to describe consistently the gluon distribution. The Pauli exclusion principle, which has been identified to explain the flavor asymmetry of the light-quark sea of the proton, is advocated to guide us for making a simple construction of the polarized parton distributions. We predict the spin dependent structure functions g {1/ p } (x) and g {1/ n } (x) in good agreement with EMC and SLAC data. The quark distributions involve some parameters whose values support well the hypothesis that the violation of the quark parton model sum rules is a consequence of the Pauli principle.
Dirac Green function for angular projection potentials
NASA Astrophysics Data System (ADS)
Zeller, Rudolf
2015-11-01
The aim of this paper is twofold: first, it is shown that the angular dependence of the Dirac Green function can be described analytically for potentials with non-local dependence on the angular variables if they are chosen as projection potentials in angular momentum space. Because the local dependence on the radial variable can be treated to any precision with present computing capabilities, this means that the Green function can be calculated practically exactly. Second, it is shown that a result of this kind not only holds for a single angular projection potential but also more generally, for instance if space is divided into non-overlapping cells and a separate angular projection potential is used in each cell. This opens the way for relativistic density-functional calculations within a different perspective than the conventional one. Instead of trying to obtain the density for a given potential approximately as well as possible, the density is determined exactly for non-local potentials which can approximate arbitrary local potentials as well as desired.
Weyl, Dirac and Maxwell Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular automata (QCA) theory follows, whose relativistic limit of small wave-vector provides the free dynamics of quantum field theory. The QCA theory can be regarded as an extended quantum field theory that describes in a unified way all scales ranging from an hypothetical discrete Planck scale up to the usual Fermi scale. The present paper reviews the automaton theory for the Weyl field, and the composite automata for Dirac and Maxwell fields. We then give a simple analysis of the dynamics in the momentum space in terms of a dispersive differential equation for narrowband wave-packets. We then review the phenomenology of the free-field automaton and consider possible visible effects arising from the discreteness of the framework. We conclude introducing the consequences of the automaton dispersion relation, leading to a deformed Lorentz covariance and to possible effects on the thermodynamics of ideal gases.
Analysis as a source of geometry: a non-geometric representation of the Dirac equation
NASA Astrophysics Data System (ADS)
Fang, Yan-Long; Vassiliev, Dmitri
2015-04-01
Consider a formally self-adjoint first order linear differential operator acting on pairs (two-columns) of complex-valued scalar fields over a four-manifold without boundary. We examine the geometric content of such an operator and show that it implicitly contains a Lorentzian metric, Pauli matrices, connection coefficients for spinor fields and an electromagnetic covector potential. This observation allows us to give a simple representation of the massive Dirac equation as a system of four scalar equations involving an arbitrary two-by-two matrix operator as above and its adjugate. The point of the paper is that in order to write down the Dirac equation in the physically meaningful four-dimensional hyperbolic setting one does not need any geometric constructs. All the geometry required is contained in a single analytic object—an abstract formally self-adjoint first order linear differential operator acting on pairs of complex-valued scalar fields. Supported by EPSRC grant EP/M000079/1
Low-Lying Dirac Eigenmodes, Topological Charge Fluctuations and the Instanton Liquid Model
I. Horvath; S.J. Dong; T. Draper; F.X. Lee; H.B. Thacker; J.B. Zhang
2002-05-01
The local structure of low-lying eigenmodes of the overlap Dirac operator is studied. It is found that these modes cannot be described as linear combinations of 't Hooft ''would-be'' zeromodes associated with instanton excitations that underly the Instanton Liquid Model. This implies that the instanton liquid scenario for spontaneous chiral symmetry breaking in QCD is not accurate. More generally, our data suggests that the vacuum fluctuations of topological charge are not effectively dominated by localized lumps of unit charge with which the topological ''would-be'' zeromodes could be associated.
Determination of the chiral condensate from QCD Dirac spectrum on the lattice
Fukaya, H.; Onogi, T.; Aoki, S.; Chiu, T. W.; Hashimoto, S.; Kaneko, T.; Yamada, N.; Noaki, J.
2011-04-01
We calculate the chiral condensate of QCD with 2, 2+1, and 3 flavors of sea quarks. Lattice QCD simulations are performed employing dynamical overlap fermions with up- and down-quark masses covering a range between 3 and 100 MeV. On L{approx}1.8-1.9 fm lattices at a lattice spacing {approx}0.11 fm, we calculate the eigenvalue spectrum of the overlap-Dirac operator. By matching the lattice data with the analytical prediction from chiral perturbation theory at the next-to-leading order, the chiral condensate in the massless limit of up and down quarks is determined.
Chandrashekar, C. M.
2013-01-01
From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as position translation states we obtain three different form of Hamiltonians for evolution on one-dimensional lattice. We extend this to two- and three-dimensional lattices using different Pauli basis states as position translation states for each dimension and show that the external coin operation, which is necessary for one-dimensional walk is not a necessary requirement for a walk on higher dimensions but can serve as an additional resource to control the dynamics. The two-component Hamiltonian we present here for quantum walk on different lattices can serve as a general framework to simulate, control, and study the dynamics of quantum systems governed by Dirac-like Hamiltonian. PMID:24088731
Dirac matrices for Chern-Simons gravity
Izaurieta, Fernando; Ramirez, Ricardo; Rodriguez, Eduardo
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.
Designer Dirac fermions and topological phases in molecular graphene.
Gomes, Kenjiro K; Mar, Warren; Ko, Wonhee; Guinea, Francisco; Manoharan, Hari C
2012-03-15
The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system-molecular graphene-assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p-n and p-n-p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields, wherein Dirac electrons react to 'pseudo' electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the
Isometry generators in momentum representation of the Dirac theory on the de Sitter spacetime
NASA Astrophysics Data System (ADS)
Cotăescu, Ion I.; Băltăţeanu, Doru-Marcel
2015-11-01
In this paper, it is shown that the covariant representation (CR) transforming the Dirac field under de Sitter isometries is equivalent to a direct sum of two unitary irreducible representations (UIRs) of the Sp(2, 2) group transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down for the first time finding that these representations are equivalent to an UIR from the principal series whose canonical labels are determined by the fermion mass and spin. The properties of the conserved observables (i.e. one-particle operators) associated to the de Sitter isometries via Noether theorem and of the corresponding Pauli-Lubanski type operator are also pointed out.
Negative longitudinal magnetoresistance in Dirac and Weyl metals
NASA Astrophysics Data System (ADS)
Burkov, A. A.
2015-06-01
It has recently been found that Dirac and Weyl metals are characterized by an unusual weak-field longitudinal magnetoresistance: large, negative, and quadratic in the magnetic field. This has been shown to arise from the chiral anomaly, i.e., nonconservation of the chiral charge in the presence of external electric and magnetic fields, oriented collinearly. In this paper we report on a theory of this effect in both Dirac and Weyl metals. We demonstrate that this phenomenon contains two important ingredients. One is the magnetic-field-induced coupling between the chiral and the total (or vector, in relativistic field theory terminology) charge densities. This arises from the Berry curvature and is present in principle whenever the Berry curvature is nonzero, i.e., is nonspecific to Dirac and Weyl metals. This coupling, however, leads to a large negative quadratic magnetoresistance only when the second ingredient is present, namely when the chiral charge density is a nearly conserved quantity with a long relaxation time. This property is specific to Dirac and Weyl metals and is realized only when the Fermi energy is close to Dirac or Weyl nodes, expressing an important low-energy property of these materials, emergent chiral symmetry.
Nonsymmorphic topological photonic crystal with a single surface Dirac cone
NASA Astrophysics Data System (ADS)
Lu, Ling; Fang, Chen; Fu, Liang; Johnson, Steven; Joannopoulos, John; Soljacic, Marin; MIT Collaboration
We predict a realization of the nonsymmorphic topological crystalline phase: a three-dimensional (3D) photonic crystal with a single surface Dirac cone. A single Dirac cone on the surface is the hallmark of the 3D topological insulators, where the double degeneracy at the Dirac point is protected by time-reversal symmetry and the spin-splitting away from the point is provided by the spin-orbital coupling. In our 3D topological photonic crystal, the degeneracy at the Dirac point is protected by a nonsymmorphic glide reflection and the linear splitting away from it is enabled by breaking time-reversal symmetry. Such a gapless surface state is fully robust against random disorder of any type. This bosonic topological band structure is achieved by applying alternating magnetization to gap out the 3D ''generalized Dirac points'' discovered in the bulk of our crystal. The Z2 bulk invariant is characterized through the evolution of Wannier centers. Our proposal-readily realizable using ferrimagnetic materials at microwave frequencies-can also be regarded as the photonic analog of topological crystalline insulators, providing the first 3D bosonic symmetry-protected topological system.
Dirac-Hestenes spinor fields on Riemann-Cartan manifolds
NASA Astrophysics Data System (ADS)
Rodrigues, W. A.; de Souza, Q. A. G.; Vaz, J.; Lounesto, P.
1996-09-01
In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named the spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to Geroch's theorem concerning the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-Kähler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle, CB) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.
NASA Astrophysics Data System (ADS)
McConnell, Sean; Fritzsche, Stephan; Surzhykov, Andrey
2010-03-01
During recent years, the DIRAC package has proved to be an efficient tool for studying the structural properties and dynamic behavior of hydrogen-like ions. Originally designed as a set of MAPLE procedures, this package provides interactive access to the wave and Green's functions in the non-relativistic and relativistic frameworks and supports analytical evaluation of a large number of radial integrals that are required for the construction of transition amplitudes and interaction cross sections. We provide here a new version of the DIRAC program which is developed within the framework of MATHEMATICA (version 6.0). This new version aims to cater to a wider community of researchers that use the MATHEMATICA platform and to take advantage of the generally faster processing times therein. Moreover, the addition of new procedures, a more convenient and detailed help system, as well as source code revisions to overcome identified shortcomings should ensure expanded use of the new DIRAC program over its predecessor. New version program summaryProgram title: DIRAC Catalogue identifier: ADUQ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUQ_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 45 073 No. of bytes in distributed program, including test data, etc.: 285 828 Distribution format: tar.gz Programming language: Mathematica 6.0 or higher Computer: All computers with a license for the computer algebra package Mathematica (version 6.0 or higher) Operating system: Mathematica is O/S independent Classification: 2.1 Catalogue identifier of previous version: ADUQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 165 (2005) 139 Does the new version supersede the previous version?: Yes Nature of problem: Since the early days of quantum mechanics, the
Beauty in physics: the legacy of Paul Dirac
NASA Astrophysics Data System (ADS)
McCubbin, Norman
2004-04-01
In 2002 physicists around the world celebrated the centenary of the birth of Paul Dirac, OM, FRS, Nobel Laureate, who was one of the greatest physicists of the 20th century. He made towering contributions to the formulation of quantum mechanics and he was one of the principal creators of quantum field theory. In 1928 he combined relativity and quantum mechanics in the Dirac equation, which provides a natural description for the spin of the electron and which led to the prediction, by Dirac himself, of the existence of anti-matter. In this article I try to explain, in the simplest terms, these major contributions to physics and to give some flavour of the man himself.
P.A.M. Dirac's Impact on Physics
NASA Astrophysics Data System (ADS)
Merzbacher, Eugen
2008-10-01
Paul Dirac (1902-1984) was not as well known as the other founding fathers of quantum mechanics in the 1920's, but his contributions were equally important, and he won the Nobel Prize in 1933, at the same time as Heisenberg and Schröodinger. He spent the last fifteen years of his life in the SESAPS region, in Tallahassee, Florida. I will describe his life and his work, comment on his style, and recount how he arrived at the relativistic wave equation. I will describe one of my personal encounters with Dirac and, if I can manage not to bungle it, show a physics demonstration that is relevant to the application of group theory to quantum mechanics, a subject that Dirac and other detractors scathingly referred to as Gruppenpest.
Higgs amplitude mode in massless Dirac fermion systems
NASA Astrophysics Data System (ADS)
Lu, Ming; Liu, Haiwen; Wang, Pei; Xie, X. C.
2016-02-01
The Higgs amplitude mode in superconductors is the condensed-matter analogy of Higgs bosons in particle physics. We investigate the time evolution of Higgs amplitude mode in massless Dirac systems induced by a weak quench of an attractive interaction. We find that the Higgs amplitude mode in the half-filled honeycomb lattice has a logarithmic decaying behavior, qualitatively different from the 1 /√{t } decay in the normal superconductors. Our study is also extended to the doped cases in honeycomb lattices. As for the three-dimensional Dirac semimetal at half filling, we obtain an undamped oscillation of the amplitude mode. Our finding is not only an important supplement to the previous theoretical studies on normal fermion systems but also provides an experimental signature to characterize the superconductivity in two- or three-dimensional Dirac systems.
Birefringent breakup of Dirac fermions on a square optical lattice
Kennett, Malcolm P.; Komeilizadeh, Nazanin; Kaveh, Kamran; Smith, Peter M.
2011-05-15
We introduce a lattice model for fermions in a spatially periodic magnetic field that also has spatially periodic hopping amplitudes. We discuss how this model might be realized with cold atoms in an artificial magnetic field on a square optical lattice. When there is an average flux of half a flux quantum per plaquette, the spectrum of low-energy excitations can be described by massless Dirac fermions in which the usually doubly degenerate Dirac cones split into cones with different ''speeds of light.'' These gapless birefringent Dirac fermions arise because of broken chiral symmetry in the kinetic energy term of the effective low-energy Hamiltonian. We characterize the effects of various perturbations to the low-energy spectrum, including staggered potentials, interactions, and domain-wall topological defects.
Spin-1 Dirac-Weyl fermions protected by bipartite symmetry
NASA Astrophysics Data System (ADS)
Lin, Zeren; Liu, Zhirong
2015-12-01
We propose that bipartite symmetry allows spin-1 Dirac-Weyl points, a generalization of the spin-1/2 Dirac points in graphene, to appear as topologically protected at the Fermi level. In this spirit, we provide methodology to construct spin-1 Dirac-Weyl points of this kind in a given 2D space group and get the classification of the known spin-1 systems in the literature. We also apply the workflow to predict two new systems, P3m1-9 and P31m-15, to possess spin-1 at K/K' in the Brillouin zone of hexagonal lattice. Their stability under various strains is investigated and compared with that of T3, an extensively studied model of ultracold atoms trapped in optical lattice with spin-1 also at K/K'.
Spin-1 Dirac-Weyl fermions protected by bipartite symmetry
Lin, Zeren; Liu, Zhirong
2015-12-07
We propose that bipartite symmetry allows spin-1 Dirac-Weyl points, a generalization of the spin-1/2 Dirac points in graphene, to appear as topologically protected at the Fermi level. In this spirit, we provide methodology to construct spin-1 Dirac-Weyl points of this kind in a given 2D space group and get the classification of the known spin-1 systems in the literature. We also apply the workflow to predict two new systems, P3m1-9 and P31m-15, to possess spin-1 at K/K′ in the Brillouin zone of hexagonal lattice. Their stability under various strains is investigated and compared with that of T{sub 3}, an extensively studied model of ultracold atoms trapped in optical lattice with spin-1 also at K/K′.
Accidental degeneracy of double Dirac cones in a phononic crystal
Chen, Ze-Guo; Ni, Xu; Wu, Ying; He, Cheng; Sun, Xiao-Chen; Zheng, Li-Yang; Lu, Ming-Hui; Chen, Yan-Feng
2014-01-01
Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of the Brillouin zone in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of this quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique properties in wave propagating, such as defect-insensitive propagating character and the Talbot effect. PMID:24714512
A new way of describing the Dirac bands in graphene
NASA Astrophysics Data System (ADS)
Kissinger, Gregory; Satpathy, Sashi
We develop a new way of describing the electronic structure of graphene, by treating the honeycomb lattice as a network of one-dimensional quantum wires. The electrons travel as free particles along these quantum wires and interfere at the three-way junctions formed by the carbon atoms. The model generates the linearly dispersive Dirac cone band structure as well as the chiral nature of the pseudo-spin sublattice wave functions. When vacancies are incorporated, we find that it also reproduces the well known zero mode states. This simple approach might have advantages over other methods for some applications, such as in analyzing electronic transport through graphene nanoribbons. In addition, this finding suggests new ways of constructing Dirac band materials in the laboratory by nano-patterning for investigating Dirac fermions.
Electronic structure of a graphene superlattice with massive Dirac fermions
Lima, Jonas R. F.
2015-02-28
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{sub g} can be tuned in the range 0 ≤ E{sub 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.
Nonlinear modes of the tensor Dirac equation and CPT violation
NASA Technical Reports Server (NTRS)
Reifler, Frank J.; Morris, Randall D.
1993-01-01
Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.
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.
2008-04-29
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 Schrödinger 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.
Shot noise in systems with semi-Dirac points
NASA Astrophysics Data System (ADS)
Zhai, Feng; Wang, Juan
2014-08-01
We calculate the ballistic conductance and shot noise of electrons through a two-dimensional stripe system (width W ≫ length L) with semi-Dirac band-touching points. We find that the ratio between zero-temperature noise power and mean current (the Fano factor) is highly anisotropic. When the transport is along the linear-dispersion direction and the Fermi energy is fixed at the semi-Dirac point, the Fano factor has a universal value F = 0.179 while a minimum conductivity exists and scales with L1/2. Along the parabolic dispersion direction, the Fano factor at the semi-Dirac point has a contact-independent limit exceeding 0.9, which varies weakly with L due to the common-path interference of evanescent waves. Our findings suggest a way to discern the type of band-touching points.
Shot noise in systems with semi-Dirac points
Zhai, Feng; Wang, Juan
2014-08-14
We calculate the ballistic conductance and shot noise of electrons through a two-dimensional stripe system (width W ≫ length L) with semi-Dirac band-touching points. We find that the ratio between zero-temperature noise power and mean current (the Fano factor) is highly anisotropic. When the transport is along the linear-dispersion direction and the Fermi energy is fixed at the semi-Dirac point, the Fano factor has a universal value F = 0.179 while a minimum conductivity exists and scales with L{sup 1∕2}. Along the parabolic dispersion direction, the Fano factor at the semi-Dirac point has a contact-independent limit exceeding 0.9, which varies weakly with L due to the common-path interference of evanescent waves. Our findings suggest a way to discern the type of band-touching points.
BCS Superconductivity of Dirac Electrons in Graphene Layers
NASA Astrophysics Data System (ADS)
Kopnin, N. B.; Sonin, E. B.
2008-06-01
Possible superconductivity of electrons with the Dirac spectrum is analyzed using the BCS model. We calculate the critical temperature, the superconducting energy gap, and the supercurrent as functions of the doping level and of the pairing interaction strength. Zero doping is characterized by the existence of a quantum critical point such that the critical temperature vanishes below some finite value of the interaction strength. However, the critical temperature remains finite for any nonzero electron or hole doping level when the Fermi energy is shifted away from the Dirac point. As distinct from usual superconductors, the supercurrent density is not proportional to the number of electrons but is strongly decreased due to the presence of the Dirac point.
BCS Superconductivity of Dirac electrons in graphene layers.
Kopnin, N B; Sonin, E B
2008-06-20
Possible superconductivity of electrons with the Dirac spectrum is analyzed using the BCS model. We calculate the critical temperature, the superconducting energy gap, and the supercurrent as functions of the doping level and of the pairing interaction strength. Zero doping is characterized by the existence of a quantum critical point such that the critical temperature vanishes below some finite value of the interaction strength. However, the critical temperature remains finite for any nonzero electron or hole doping level when the Fermi energy is shifted away from the Dirac point. As distinct from usual superconductors, the supercurrent density is not proportional to the number of electrons but is strongly decreased due to the presence of the Dirac point. PMID:18643614
COMMENT: Comment on `Dirac theory in spacetime algebra'
NASA Astrophysics Data System (ADS)
Baylis, William E.
2002-06-01
In contrast to formulations of the Dirac theory by Hestenes and by the present author, the formulation recently presented by Joyce (Joyce W P 2001 J. Phys. A: Math. Gen. 34 1991-2005) is equivalent to the usual Dirac equation only in the case of vanishing mass. For nonzero mass, solutions to Joyce's equation can be solutions either of the Dirac equation in the Hestenes form or of the same equation with the sign of the mass reversed, and in general they are mixtures of the two possibilities. Because of this relationship, Joyce obtains twice as many linearly independent plane-wave solutions for a given momentum eigenvalue as exist in the conventional theory. A misconception about the symmetry of the Hestenes equation and the geometric significance of the algebraic spinors is also briefly discussed.
Dirac Cones in two-dimensional conjugated polymer networks
NASA Astrophysics Data System (ADS)
Adjizian, Jean-Joseph; Briddon, Patrick; Humbert, Bernard; Duvail, Jean-Luc; Wagner, Philipp; Adda, Coline; Ewels, Christopher
2014-12-01
Linear electronic band dispersion and the associated Dirac physics has to date been limited to special-case materials, notably graphene and the surfaces of three-dimensional (3D) topological insulators. Here we report that it is possible to create two-dimensional fully conjugated polymer networks with corresponding conical valence and conduction bands and linear energy dispersion at the Fermi level. This is possible for a wide range of polymer types and connectors, resulting in a versatile new family of experimentally realisable materials with unique tuneable electronic properties. We demonstrate their stability on substrates and possibilities for doping and Dirac cone distortion. Notably, the cones can be maintained in 3D-layered crystals. Resembling covalent organic frameworks, these materials represent a potentially exciting new field combining the unique Dirac physics of graphene with the structural flexibility and design opportunities of organic-conjugated polymer chemistry.
Fillion-Gourdeau, F; Herrmann, H J; Mendoza, M; Palpacelli, S; Succi, S
2013-10-18
We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wave function) propagates in space-time as a classical statistical process (Boltzmann distribution). PMID:24182245
PREFACE: International Workshop on Dirac Electrons in Solids 2015
NASA Astrophysics Data System (ADS)
Ogata, M.; Suzumura, Y.; Fuseya, Y.; Matsuura, H.
2015-04-01
It is our pleasure to publish the Proceedings of the International Workshop on Dirac Electrons in Solids held in University of Tokyo, Japan, for January 14-15, 2015. The workshop was organized by the entitled project which lasted from April 2012 to March 2015 with 10 theorists. It has been supported by a Grand-in-Aid for Scientific Research (A) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. The subjects discussed in the workshop include bismuth, organic conductors, graphene, topological insulators, new materials including Ca3PbO, and new directions in theory (superconductivity, orbital susceptibility, etc). The number of participants was about 70 and the papers presented in the workshop include four invited talks, 16 oral presentations, and 23 poster presentations. Dirac electron systems appear in various systems, such as graphene, quasi-two-dimensional organic conductors, bismuth, surface states in topological insulators, new materials like Ca3PbO. In these systems, characteristic transport properties caused by the linear dispersion of Dirac electrons and topological properties, have been extensively discussed. In addition to these, there are many interesting research fields such as Spin-Hall effect, orbital diamagnetism due to interband effects, Landau levels characteristic to Dirac dispersion, anomalous interlayer transport phenomena and magnetoresistance, the effects of spin-orbit interaction, and electron correlation. The workshop focused on recent developments of theory and experiment of Dirac electron systems in the above materials. We note that all papers published in this volume of Journal of Physics: Conference Series were peer reviewed. Reviews were performed by expert referees with professional knowledge and high scientific standards in this field. Editors made efforts so that the papers may satisfy the criterion of a proceedings journal published by IOP Publishing. We hope that all the participants of the workshop
Chemistry at the dirac point of graphene
NASA Astrophysics Data System (ADS)
Sarkar, Santanu
device mobility. To this end, we find that the organometallic hexahapto metal complexation chemistry of graphene, in which the graphene pi-band constructively hybridizes with the vacant d-orbitals of transition metals, allows the fabrication of field effect devices which retain a high degree of the mobility with enhanced on-off ratio. In summary, we find that the singular electronic structure of graphene at the Dirac point governs the chemical reactivity of graphene and this chemistry will play a vital role in propelling graphene to assume its role as the next generation electronic material beyond silicon.
Levinson theorem for the Dirac equation in D+1 dimensions
Gu Xiaoyan; Ma Zhongqi; Dong Shihai
2003-06-01
In terms of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation with a spherically symmetric potential in D+1 dimensions is uniformly established as a relation between the total number of bound states and the sum of the phase shifts of the scattering states at E={+-}M with a given angular momentum. The critical case, where the Dirac equation has a half bound state, is analyzed in detail. A half bound state is a zero-momentum solution if its wave function is finite but does not decay fast enough at infinity to be square integrable.
Levinson theorem for Dirac particles in n dimensions
Jiang Yu
2005-02-01
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|
Dirac Monopoles in a Bose-Einstein Condensate
NASA Astrophysics Data System (ADS)
Hall, David
2014-05-01
Over eighty years ago, Dirac established a theory of magnetic monopoles consistent with both classical electrodynamics and quantum mechanics. I will discuss Dirac's theory and a recent realization of its essential features, including a monopole, in the context of the synthetic electric and magnetic fields supported by a spinor Bose-Einstein condensate. This material is based upon work supported by the National Science Foundation under grants nos. PHY-0855475 and PHY-1205822, by the Academy of Finland through its Centres of Excellence Program (grant no. 251748) and grants nos. 135794, 272806 and 141015.
Rosenfeld, Bergmann, Dirac and the Invention of Constrained Hamiltonian Dynamics
NASA Astrophysics Data System (ADS)
Salisbury, D. C.
2008-09-01
In a paper appearing in Annalen der Physik in 1930 Leon Rosenfeld invented the first procedure for producing Hamiltonian constraints. He displayed and correctly distinguished the vanishing Hamiltonian generator of time evolution, and the vanishing generator of gauge transformations for general relativity with Dirac electron and electrodynamic field sources. Though he did not do so, had he chosen one of his tetrad fields to be normal to his spacetime foliation, he would have anticipated by almost thirty years the general relativisitic Hamiltonian first published by Paul Dirac.
Magnetotransport in Dirac semimetals: Chiral magnetic effect and quantum oscillations
NASA Astrophysics Data System (ADS)
Monteiro, Gustavo; Abanov, Alexander; Kharzeev, Dmitri
Dirac semimetals are characterized by the linear dispersion of fermionic quasiparticles, with the Dirac point hidden inside a Fermi surface. We study the magnetotransport in these materials using chiral kinetic theory to describe within the same framework both the negative magnetoresistance caused by the chiral magnetic effect and quantum oscillations in the magnetoresistance due to the existence of the Fermi surface. We also consider the role of Fermi Arcs and their contribution for the SdH modes. We discuss the relevance of obtained results to recent measurements on Cd3 As2 .
Radiative heat transfer in 2D Dirac materials
Rodriguez-López, Pablo; Tse, Wang -Kong; Dalvit, Diego A. R.
2015-05-12
We compute the radiative heat transfer between two sheets of 2D Dirac materials, including topological Chern insulators and graphene, within the framework of the local approximation for the optical response of these materials. In this approximation, which neglects spatial dispersion, we derive both numerically and analytically the short-distance asymptotic of the near-field heat transfer in these systems, and show that it scales as the inverse of the distance between the two sheets. In conclusion, we discuss the limitations to the validity of this scaling law imposed by spatial dispersion in 2D Dirac materials.
Relativistic Lagrangians for the Lorentz–Dirac equation
Deguchi, Shinichi; Nakano, Kunihiko; Suzuki, Takafumi
2015-09-15
We present two types of relativistic Lagrangians for the Lorentz–Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends on the world-line parameter. Another Lagrangian includes additional cross-terms consisting of auxiliary dynamical variables and does not depend explicitly on the world-line parameter. We demonstrate that both the Lagrangians actually yield the Lorentz–Dirac equation with a source-like term.
Dirac oscillator in perpendicular magnetic and transverse electric fields
Nath, D.; Roy, P.
2014-12-15
We study (2+1) dimensional massless Dirac oscillator in the presence of perpendicular magnetic and transverse electric fields. Exact solutions are obtained and it is shown that there exists a critical magnetic field B{sub c} such that the spectrum is different in the two regions B>B{sub c} and BDirac Oscillator with magnetic as well as electric field. • Exact solutions are found. • Critical cases have been examined.
Dirac particles tunneling from black holes with topological defects
NASA Astrophysics Data System (ADS)
Jusufi, Kimet
2016-08-01
We study Hawking radiation of Dirac particles with spin-1 / 2 as a tunneling process from Schwarzschild-de Sitter and Reissner-Nordström-de Sitter black holes in background spacetimes with a spinning cosmic string and a global monopole. Solving Dirac's equation by employing the Hamilton-Jacobi method and WKB approximation we find the corresponding tunneling probabilities and the Hawking temperature. Furthermore, we show that the Hawking temperature of those black holes remains unchanged in presence of topological defects in both cases.
Does the Dirac Cone Exist in Silicene on Metal Substrates?
Quhe, Ruge; Yuan, Yakun; Zheng, Jiaxin; Wang, Yangyang; Ni, Zeyuan; Shi, Junjie; Yu, Dapeng; Yang, Jinbo; Lu, Jing
2014-01-01
Absence of the Dirac cone due to a strong band hybridization is revealed to be a common feature for epitaxial silicene on metal substrates according to our first-principles calculations for silicene on Ir, Cu, Mg, Au, Pt, Al, and Ag substrates. The destroyed Dirac cone of silicene, however, can be effectively restored with linear or parabolic dispersion by intercalating alkali metal atoms between silicene and the metal substrates, offering an opportunity to study the intriguing properties of silicene without further transfer of silicene from the metal substrates. PMID:24969493
Transitions into the negative-energy Dirac continuum
Krekora, P.; Su, Q.; Grobe, R.
2004-11-01
We compare the predictions of the single-particle Dirac equation with quantum field theory for an electron subjected to a space and time dependent field. We demonstrate analytically and numerically that a transition into the negative-energy subspace predicted by the single-particle Dirac equation is directly associated with the degree of suppression of pair-production as described by quantum field theory. We show that the portion of the mathematical wave function that populates the negative-energy states corresponds to the difference between the positron spatial density for systems with and without an electron initially present.
Job monitoring on DIRAC for Belle II distributed computing
NASA Astrophysics Data System (ADS)
Kato, Yuji; Hayasaka, Kiyoshi; Hara, Takanori; Miyake, Hideki; Ueda, Ikuo
2015-12-01
We developed a monitoring system for Belle II distributed computing, which consists of active and passive methods. In this paper we describe the passive monitoring system, where information stored in the DIRAC database is processed and visualized. We divide the DIRAC workload management flow into steps and store characteristic variables which indicate issues. These variables are chosen carefully based on our experiences, then visualized. As a result, we are able to effectively detect issues. Finally, we discuss the future development for automating log analysis, notification of issues, and disabling problematic sites.
Colloquium: Illuminating the Kapitza-Dirac effect with electron matter optics
Batelaan, H.
2007-07-15
The observation of the Kapitza-Dirac effect raises conceptual, theoretical, and experimental questions. The Kapitza-Dirac effect is often described as diffraction of free electrons from a standing wave of light or stimulated Compton scattering. However, for the two-color Kapitza-Dirac effect these two interpretations appear to lead to paradoxical conclusions. The discussion of this paradox deepens our understanding of both of these versions of the Kapitza-Dirac effect.
Iterative solution of a Dirac equation with an inverse Hamiltonian method
Hagino, K.; Tanimura, Y.
2010-11-15
We solve a singe-particle Dirac equation with Woods-Saxon potentials using an iterative method in the coordinate space representation. By maximizing the expectation value of the inverse of the Dirac Hamiltonian, this method avoids the variational collapse in which an iterative solution dives into the Dirac sea. We demonstrate that this method works efficiently, reproducing the exact solutions of the Dirac equation.
NASA Astrophysics Data System (ADS)
Gonçalves, Bruno; Ribeiro, Baltazar J.; Pereira, Dante D.; Dias, Mário M.
2016-05-01
In this paper, we focus our attention in the inconsistency that appears when the semi-exact Foldy-Wouthuysen transformation for the Dirac field interacting with space-time torsion field is performed. In order to solve this problem, we present a new involution operator that makes possible to perform the exact transformation when torsion field is present. Such operator has a structure, well known in the literature, composed of the product of an operator that acts in the matrices space and another one that acts in the function space. We also present the bound state of this theory and discuss the possible experimental analysis.
From Rational Numbers to Dirac's Bra and Ket: Symbolic Representation of Physical Laws
NASA Astrophysics Data System (ADS)
D'Agostino, Salvo
2002-05-01
Beginning at least in the nineteenth century, symbols used by physicists in their equations interacted with their physical concepts. In the 1850s, Wilhelm Eduard Weber introduced a more rational order into symbolization by adopting an absolute system of units, and thus expressing electrodynamic laws in the form of algebraic equations instead of proportionality relationships, the formerly accepted representation of physical laws. In the 1860s, James Clerk Maxwell made a further advance by using dimensional quantities, and more complex symbolic forms such as gradient, convergence, rotor, and the like, in his electromagnetic and kinetic theories. In the twentieth century, Werner Heisenberg, Max Born, Erwin Schrödinger, and others introduced new symbols for complex numbers, operators, and matrices, thus passing from the representation of metrical properties of physical systems to higher-level mathematical objects. This process was enhanced in modern theoretical physics through the introduction of matrices, creation and destruction operators, Paul A. M. Dirac's q and c numbers, and so on. In the 1930s, Dirac radicalized this transformation of symbols, being aware of the profound modification in the method and scope of the mathematical-physical relationship it entailed.
The asymptotics of an eigenfunction-correlation determinant for Dirac-δ perturbations
NASA Astrophysics Data System (ADS)
Gebert, Martin
2015-07-01
We prove the exact asymptotics of the scalar product of the ground states of two non-interacting Fermi gases confined to a 3-dimensional ball BL of radius L in the thermodynamic limit, where the underlying one-particle operators differ by a Dirac-δ perturbation. More precisely, we show the algebraic decay of the correlation determinant |det|(< φ)j L, ψk L > j , k = 1 , … , N 2 = L - ζ ( E ) + o ( 1 ) , as N, L → ∞ and N / |B L| → ρ > 0 , where φj L and ψk L denote the lowest-energy eigenfunctions of the finite-volume one-particle Schrödinger operators. The decay exponent is given in terms of the s-wave scattering phase shift ζ ( E ) ≔ /1 π 2 δ 2 ( √{ E } ) . For an attractive Dirac-δ perturbation, we conclude that the decay exponent /1 π 2 ↑arcsin↑ |T ( E ) / 2| HS 2 found in the work of Gebert et al. [J. Spect. Theory (to be published); e-print arXiv:1407.2512] does not provide a sharp upper bound on the decay of the correlation determinant.
NASA Astrophysics Data System (ADS)
Konkowski, Deborah A.; Arndt, Valerie; Helliwell, Thomas M.
2002-04-01
Klein-Gordon, Maxwell and Dirac fields are studied in quasiregular spacetimes, spacetimes with a classical quasiregular singularity, the mildest true classical singularity [G.F.R. Ellis and B.G. Schmidt, Gen. Rel. Grav.8, 915 (1977)]. A class of static quasiregular spacetimes possessing disclinations and dislocations [R.A. Puntigam and H.H. Soleng, Class. Quantum Grav. 14, 1129 (1997)] is shown to have field operators which are not essentially self-adjoint. This class of spacetimes includes an idealized cosmic string, i.e., a four-dimensional spacetime with a conical singularity [L.H. Ford and A. Vilenkin, J. Phys. A: Math. Gen. 14, 2353 (1981)], and a Galtsov/Letelier/Tod spacetime featuring a screw dislocation [K.P. Tod, Class. Quantum Grav. 11, 1331 (1994); D.V. Galtsov and P.S. Letelier, Phys. Rev. D47, 4273 (1993)]. The definition of G. T. Horowitz and D. Marolf [Phys. Rev. D52, 5670 (1995)] for a quantum-mechanically singular spacetime as one in which the spatial-derivative operator in the Klein-Gordon equation for a massive scalar field is not essentially self-adjoint is extended in the case of quasiregular spacetimes to include Maxwell and Dirac fields. Therefore, the class of static quasiregular spacetimes under consideration is quantum-mechanically singular independent of the type of test field.
NASA Astrophysics Data System (ADS)
Roy, Bitan; Yang, Kun
2013-12-01
The effective theory for bilayer graphene (BLG), subject to parallel/in-plane magnetic fields, is derived. With a sizable magnetic field the trigonal warping becomes irrelevant, and one ends up with two Dirac points in the vicinity of each valley in the low-energy limit, similar to the twisted BLG. Combining twisting and parallel field thus gives rise to a Dirac system with tunable Fermi velocity and cutoff. If the interactions are sufficiently strong, several fully gapped states can be realized in these systems, in addition to the ones in a pristine setup. Transformations of the order parameters under various symmetry operations are analyzed. The quantum critical behavior of various phase transitions driven by the twisting and the magnetic field is reported. The effects of an additional perpendicular field and possible ways to realize the new massive phases are highlighted.
The Invertible Double of Elliptic Operators
NASA Astrophysics Data System (ADS)
Booss-Bavnbek, Bernhelm; Lesch, Matthias
2009-02-01
First, we review the Dirac operator folklore about basic analytic and geometrical properties of operators of Dirac type on compact manifolds with smooth boundary and on closed partitioned manifolds and show how these properties depend on the construction of a canonical invertible double and are related to the concept of the Calderón projection. Then we summarize a recent construction of a canonical invertible double for general first order elliptic differential operators over smooth compact manifolds with boundary. We derive a natural formula for the Calderón projection which yields a generalization of the famous Cobordism Theorem. We provide a list of assumptions to obtain a continuous variation of the Calderón projection under smooth variation of the coefficients. That yields various new spectral flow theorems. Finally, we sketch a research program for confining, respectively closing, the last remaining gaps between the geometric Dirac operator type situation and the general linear elliptic case.
Distinguishing between Dirac and Majorana neutrinos withtwo-particle interferometry
Gutierrez, Thomas D.
2006-03-02
Two-particle interferometry, a second-order interferenceeffect, is explored as another possible tool to distinguish betweenmassive Dirac and Majorana neutrinos. A simple theoretical framework isdiscussed in the context of several gedanken experiments. The method canin principle provide both the mass scale and the quantum nature of theneutrino for a certain class of incoherent left-handed sourcecurrents.
750 GeV diphotons from supersymmetry with Dirac gauginos
NASA Astrophysics Data System (ADS)
Cohen, Timothy; Kribs, Graham D.; Nelson, Ann E.; Ostdiek, Bryan
2016-07-01
Motivated by the recent excess in the diphoton invariant mass near 750 GeV, we explore a supersymmetric extension of the Standard Model that includes the minimal set of superpartners as well as additional Dirac partner chiral superfields in the adjoint representation for each gauge group. The bino partner pseudoscalar is identified as the 750 GeV resonance, while superpotential interactions between it and the gluino (wino) partners yield production via gluon fusion (decay to photon pairs) at one-loop. The gauginos and these additional adjoint superpartners are married by a Dirac mass and must also have Majorana masses. While a large wino partner Majorana mass is necessary to explain the excess, the gluino can be approximately Dirac-like, providing benefits consistent with being both "supersoft" (loop corrections to the scalar masses from Dirac gauginos are free of logarithmic enhancements) and "supersafe" (the experimental limits on the squark/gluino masses can be relaxed due to the reduced production rate). Consistency with the measured Standard Model-like Higgs boson mass is imposed, and a numerical exploration of the parameter space is provided. Models that can account for the diphoton excess are additionally characterized by having couplings that can remain perturbative up to very high scales, while remaining consistent with experimental constraints, the Higgs boson mass, and an electroweak scale which is not excessively fine-tuned.
Application of covariant analytic mechanics to gravity with Dirac field
NASA Astrophysics Data System (ADS)
Nakajima, Satoshi
2016-03-01
We applied the covariant analytic mechanics with the differential forms to the Dirac field and the gravity with the Dirac field. The covariant analytic mechanics treats space and time on an equal footing regarding the differential forms as the basis variables. A significant feature of the covariant analytic mechanics is that the canonical equations, in addition to the Euler-Lagrange equation, are not only manifestly general coordinate covariant but also gauge covariant. Combining our study and the previous works (the scalar field, the abelian and non-abelian gauge fields and the gravity without the Dirac field), the applicability of the covariant analytic mechanics was checked for all fundamental fields. We studied both the first and second order formalism of the gravitational field coupled with matters including the Dirac field. It was suggested that gravitation theories including higher order curvatures cannot be treated by the second order formalism in the covariant analytic mechanics. In addition, we showed that the covariant analytic mechanics is equivalent to corrected De Donder-Weyl theory.
Path Integral for Dirac oscillator with generalized uncertainty principle
Benzair, H.; Boudjedaa, T.; Merad, M.
2012-12-15
The propagator for Dirac oscillator in (1+1) dimension, with deformed commutation relation of the Heisenberg principle, is calculated using path integral in quadri-momentum representation. As the mass is related to momentum, we then adapt the space-time transformation method to evaluate quantum corrections and this latter is dependent from the point discretization interval.
Fermi-Dirac statistics and the number theory
NASA Astrophysics Data System (ADS)
Kubasiak, Anna; Korbicz, Jaroslaw K.; Zakrzewski, Jakub; Lewenstein, Maciej
2005-11-01
We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap to partitions of given integers into distinct parts, studied in number theory. Using methods of quantum statistical physics we derive analytic expressions for cumulants of the probability distribution of the number of different partitions.
A Bosonic Analogue of a Topological Dirac Semi-Metal
NASA Astrophysics Data System (ADS)
Lapa, Matthew; Cho, Gil Young; Hughes, Taylor
We construct a bosonic analogue of a two-dimensional topological Dirac Semi-Metal (DSM). The low-energy description of the most basic 2D DSM model consists of two Dirac cones at positions +/-k0 in momentum space. The local stability of the Dirac cones is guaranteed by a composite symmetry Z2, where is time-reversal and is inversion. This model also exhibits interesting time-reversal and inversion symmetry breaking electromagnetic responses. In this work we construct a bosonic analogue of a DSM by replacing each Dirac cone with a copy of the O (4) Nonlinear Sigma Model (NLSM) with topological theta term and theta angle θ = +/- π . One copy of this NLSM also describes the gapless surface termination of the 3D Bosonic Topological Insulator (BTI). We compute the time-reversal and inversion symmetry breaking electromagnetic responses for our model and show that they are twice the value one gets in the DSM case. We also investigate the local stability of the individual O (4) NLSM's in the BSM model. Along the way we clarify many aspects of the surface theory of the BTI including the electromagnetic response, the charges of vortex excitations, and the stability to symmetry-allowed perturbations. Nsf CAREER DMR-1351895.
Short-range Coulomb correlations render massive Dirac fermions massless
NASA Astrophysics Data System (ADS)
Ebrahimkhas, M.; Jafari, S. A.
2012-04-01
Tight-binding electrons on a honeycomb lattice are described by an effective Dirac theory at low energies. Lowering symmetry by an alternate ionic potential (Δ) generates a single-particle gap in the spectrum. We employ the dynamical mean-field theory (DMFT) technique to study the effect of on-site electron correlation (U) on massive Dirac fermions. For a fixed mass parameter Δ, we find that beyond a critical value Uc1(Δ) massive Dirac fermions become massless. Further increasing U beyond Uc2(Δ), there will be another phase transition to the Mott insulating state. Therefore, the competition between the single-particle gap parameter, Δ, and the Hubbard U restores the semi-metallic nature of the parent Hamiltonian. The width of the intermediate semi-metallic regime shrinks by increasing the ionic potential. However, at small values of Δ, there is a wide interval of U values for which the system remains semi-metal. The implication of this result for graphene is that in contrast to a single-particle picture, the on-site Coulomb repulsion makes the Dirac cone spectrum robust against small values of the symmetry breaking parameter Δ.
High energy scattering of Dirac particles on smooth potentials
NASA Astrophysics Data System (ADS)
Han, Nguyen Suan; Dung, Le Anh; Xuan, Nguyen Nhu; Thang, Vu Toan
2016-08-01
The derivation of the Glauber type representation for the high energy scattering amplitude of particles of spin 1/2 is given within the framework of the Dirac equation in the Foldy-Wouthuysen (FW) representation and two-component formalism. The differential cross-sections on the Yukawa and Gaussian potentials are also considered and discussed.
Dirac equation with some time-dependent electromagnetic terms
NASA Astrophysics Data System (ADS)
Saeedi, K.; Zarrinkamar, S.; Hassanabadi, H.
2016-07-01
We study the motion of relativistic fermions in a time-dependent electromagnetic field within the framework of Dirac equation. We consider the time-dependent scalar potential of the exponential form and the vector potential of linear form. We obtain the eigenfunctions and eigenvalues.
Dirac equation in the background of the Nutku helicoid metric
NASA Astrophysics Data System (ADS)
Birkandan, T.; Hortaçsu, M.
2007-09-01
We study the solutions of the Dirac equation in the background of the Nutku helicoid metric. This metric has curvature singularities, which necessitates imposing a boundary to exclude this point. We use the Atiyah-Patodi-Singer [Math. Proc. Cambridge Philos. Soc. 77, 43 (1975)] nonlocal spectral boundary conditions for both the four and the five dimensional manifolds.
Dirac Fermions in heterostructures for designer topological phases
NASA Astrophysics Data System (ADS)
Feng, Ji
2014-03-01
Massless Dirac Fermions are found in graphene and on the surfaces of topological insulators, which are quasiparticles moving at a constant speed independent of its energy as governed by relativistic quantum mechanics. In this talk, I will show, via interfacial orbital design of Dirac states, emergent topological phases can be engineered in artificial heterostructures. As a first example, I will show that a novel class of half semi-metallic Dirac electronic phase emerges at the interface CrO2 with TiO2 in both thin film and superlattice configurations. With four spin-polarized Dirac points in the band structure, this system with simple, non-topological oxides displays spontaneous quantum anomalous Hall effect. In a second example, I will show that the superlattice valley engineering, starting with the SnTe topological mirror insulator, leads to designer topological phases with a remarkably rich phase diagram. JF acknowledges financial support by NSFC Project 11174009, and China 973 Program Projects 2013CB921900 and 2011CBA00109.
Dirac cones in the spectrum of bond-decorated graphenes
Van den Heuvel, Willem Soncini, Alessandro
2014-06-21
We present a two-band model based on periodic Hückel theory, which is capable of predicting the existence and position of Dirac cones in the first Brillouin zone of an infinite class of two-dimensional periodic carbon networks, obtained by systematic perturbation of the graphene connectivity by bond decoration, that is by inclusion of arbitrary π-electron Hückel networks into each of the three carbon–carbon π-bonds within the graphene unit cell. The bond decoration process can fundamentally modify the graphene unit cell and honeycomb connectivity, representing a simple and general way to describe many cases of graphene chemical functionalization of experimental interest, such as graphyne, janusgraphenes, and chlorographenes. Exact mathematical conditions for the presence of Dirac cones in the spectrum of the resulting two-dimensional π-networks are formulated in terms of the spectral properties of the decorating graphs. Our method predicts the existence of Dirac cones in experimentally characterized janusgraphenes and chlorographenes, recently speculated on the basis of density functional theory calculations. For these cases, our approach provides a proof of the existence of Dirac cones, and can be carried out at the cost of a back of the envelope calculation, bypassing any diagonalization step, even within Hückel theory.
Hydrogenated arsenenes as planar magnet and Dirac material
Zhang, Shengli; Cai, Bo; Zeng, Haibo E-mail: zeng.haibo@njust.edu.cn; Hu, Yonghong; Hu, Ziyu E-mail: zeng.haibo@njust.edu.cn
2015-07-13
Arsenene and antimonene are predicted to have 2.49 and 2.28 eV band gaps, which have aroused intense interest in the two-dimensional (2D) semiconductors for nanoelectronic and optoelectronic devices. Here, the hydrogenated arsenenes are reported to be planar magnet and 2D Dirac materials based on comprehensive first-principles calculations. The semi-hydrogenated (SH) arsenene is found to be a quasi-planar magnet, while the fully hydrogenated (FH) arsenene is a planar Dirac material. The buckling height of pristine arsenene is greatly decreased by the hydrogenation, resulting in a planar and relatively low-mass-density sheet. The electronic structures of arsenene are also evidently altered after hydrogenating from wide-band-gap semiconductor to metallic material for SH arsenene, and then to Dirac material for FH arsenene. The SH arsenene has an obvious magnetism, mainly contributed by the p orbital of the unsaturated As atom. Such magnetic and Dirac materials modified by hydrogenation of arsenene may have potential applications in future optoelectronic and spintronic devices.
De-Mystifying the Dirac [delta]-Function
ERIC Educational Resources Information Center
Lutzer, Carl V.
2007-01-01
In this article, we discuss an alternative method of teaching students about the Dirac [delta]-function. The method provides students with the mechanical tools they need in order to work with the [delta]-function in practice, while also fostering a sense of cohesion in the calculus curriculum by presenting the [delta]-function as an evolution of…
Analysis of DIRAC's behavior using model checking with process algebra
NASA Astrophysics Data System (ADS)
Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Graciani Diaz, Ricardo; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof
2012-12-01
DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.
Phonon-drag thermopower in 3D Dirac semimetals.
Kubakaddi, S S
2015-11-18
A theory of low-temperature phonon-drag thermopower S(g) in three-dimensional (3D) Dirac semimetals has been developed considering screened electron-phonon deformation potential coupling. Numerical investigations of S(g), in the boundary scattering regime for phonons, are made in 3D Dirac semimetal Cd3As2, as a function of temperature T and electron concentration n e. S(g) is found to increase rapidly for about T < 1 K and nearly levels off for higher T. It is also seen that S(g) increases (decreases) with decreasing n e at lower (higher) T (<2 K). A screening effect is found to be very significant, strongly affecting T and n e dependence for about <1 K and becoming negligible at higher temperature. In the Bloch-Gruneisen (BG) regime the power laws S(g) ~ T(8) (T(4)) and S(g) ~ n(e)(-5/3)(n(e)(-1/3) with (without) screening are obtained. These laws with respect to T and n e are, respectively, characteristics of 3D phonons and Dirac 3D electrons. Comparison with diffusion thermopower S(d) shows that S (g) dominates (and is much greater than) S(d) for about T > 0.2 K. Herring's law S(g) μ p ~ T (-1), relating phonon limited mobility μ p and S(g) in the BG regime, is shown to be valid in 3D Dirac semimetals. The results obtained here are compared with those in 3D semiconductors, low-dimensional semiconductor heterojunctions and graphene. We conclude that n e-dependent measurements, rather than T-dependent ones, provide a clearer signature of the 3D Dirac semimetal phase. PMID:26490643
Dirac single particle and plasmon excitations in topological insulators
NASA Astrophysics Data System (ADS)
Lupi, Stefano
Topological Insulators (TIs), like Bi2Se3 and Bi2Te3, are one of the most intriguing issues at focus in Condensed Matter Physics. TIs exhibit a band gap in the bulk like ordinary insulators, but have intrinsic 2D conducting states on their edge and surface. This means that the topology, associated with the electronic wavefunctions of the system, changes discontinuously when passing from the bulk to the surface. The edge states arise from a strong spin-orbit coupling, and they are backscattering protected, i.e. not sensitive to disorder (except that coming from magnetic impurities). Such as graphene, TIs surface charge transport is carried out by Dirac fermions, with a very high surface carrier density (n >= 1013 cm-2) , compared to typical values on metal surfaces. Apart single particle excitations, Dirac fermions in TIs sustain exotic plasmonic (collective) modes whose properties of tunability and temperature dependence can be used for photonics applications at the nanoscale. Moreover, unlike plasmons in metals, Dirac plasmons in TIs are expected to be strongly affected by an external magnetic field B due to fact that the cyclotron frequency is comparable to the the plasmon frequency, in particular when plasmons are engineered in the terahertz region of the electromagnetic spectrum. In this talk, after a general review on the properties of Topological Insulators, I will discuss the terahertz linear response of Dirac plasmons in TIs and their behavior under a strong magnetic field up to 30 T. The appearance of strong non-linear optical effects, when the THz electric field reaches values on the order of 1 MV/cm, will be also discussed. In the second part of the talk, I will discuss the sub-ps dynamics of Dirac single-particle and collective excitations as measured by optical-pump THz-probe experiments. Both the steady state and time-resolved experiments provide a unifying picture of single particle and collective electronic excitations in Topological Insulators.
Phonon-drag thermopower in 3D Dirac semimetals
NASA Astrophysics Data System (ADS)
Kubakaddi, S. S.
2015-11-01
A theory of low-temperature phonon-drag thermopower S g in three-dimensional (3D) Dirac semimetals has been developed considering screened electron-phonon deformation potential coupling. Numerical investigations of S g, in the boundary scattering regime for phonons, are made in 3D Dirac semimetal Cd3As2, as a function of temperature T and electron concentration n e. S g is found to increase rapidly for about T < 1 K and nearly levels off for higher T. It is also seen that S g increases (decreases) with decreasing n e at lower (higher) T (<2 K). A screening effect is found to be very significant, strongly affecting T and n e dependence for about <1 K and becoming negligible at higher temperature. In the Bloch-Gruneisen (BG) regime the power laws S g ~ T 8 (T 4) and S g ~ n\\text{e}-5/3 (n\\text{e}-1/3) with (without) screening are obtained. These laws with respect to T and n e are, respectively, characteristics of 3D phonons and Dirac 3D electrons. Comparison with diffusion thermopower S d shows that S g dominates (and is much greater than) S d for about T > 0.2 K. Herring’s law S g μ p ~ T -1, relating phonon limited mobility μ p and S g in the BG regime, is shown to be valid in 3D Dirac semimetals. The results obtained here are compared with those in 3D semiconductors, low-dimensional semiconductor heterojunctions and graphene. We conclude that n e-dependent measurements, rather than T-dependent ones, provide a clearer signature of the 3D Dirac semimetal phase.
Phenomenology of a semi-Dirac semi-Weyl semimetal
NASA Astrophysics Data System (ADS)
Banerjee, S.; Pickett, W. E.
2012-08-01
We extend the semiclassical study of fermionic particle-hole symmetric semi-Dirac (more appropriately, semi-Dirac semi-Weyl) dispersion of quasiparticles, ɛK=±(kx2/2m)2+(vky)2)=±ɛ0Kx4+Ky2 in dimensionless units, discovered computationally in oxide heterostructures by Pardo and collaborators. This unique system is a highly anisotropic sister phase of both (symmetric) graphene and what has become known as a Weyl semimetal, having
NASA Astrophysics Data System (ADS)
Wang, Rui-Qiang; Sheng, L.; Yang, M.; Wang, Baigeng; Xing, D. Y.
2015-06-01
We investigate the effect of spin-inelastic scattering of Dirac electrons off a high-spin nanomagnet adsorbed on a topological insulator (TI) surface, in which transitions of the nanomagnet between its internal magnetic levels are taken into account, beyond the classic spin theory. It is found that the presence of magnetic anisotropy of nanomagnets can result in a Dirac-point resonance peak in local density of states. It can significantly modify the topologically protected Dirac surface-state spectrum at the Dirac point, quite different from previously reported low-energy resonances. Furthermore, we propose to tune electrically the appearance of the Dirac-point resonance peak and its height by use of the spin-flip torque effect. This provides an approach to engineer the Dirac cone and tune the Dirac electron properties on the TI surface in the absence of an external magnetic field.
Three-dimensional photonic Dirac points stabilized by point group symmetry
NASA Astrophysics Data System (ADS)
Wang, HaiXiao; Xu, Lin; Chen, HuanYang; Jiang, Jian-Hua
2016-06-01
We discover a pair of stable three-dimensional (3D) Dirac points, a 3D photonic analog of graphene, in all-dielectric photonic crystals using structures commensurate with nanofabrication for visible-frequency photonic applications. The Dirac points carry nontrivial Z2 topology and emerge for a large range of material parameters in hollow cylinder hexagonal photonic crystals. From Kramers theorem and group theory, we find that only the C6 symmetry leads to point group symmetry stabilized Dirac points in 3D all-dielectric photonic crystals. The Dirac points are characterized using k ⃗.P ⃗ theory for photonic bands in combination with symmetry analysis. Breaking inversion symmetry splits the Dirac points into Weyl points. The physical properties and experimental consequences of Dirac points are also studied. The Dirac points are found to be robust against parameter tuning and weak disorders.
NASA Astrophysics Data System (ADS)
Cossu, Guido; Hashimoto, Shoji
2016-06-01
We investigate the properties of the background gauge field configurations that act as disorder for the Anderson localization mechanism in the Dirac spectrum of QCD at high temperatures. We compute the eigenmodes of the Möbius domain-wall fermion operator on configurations generated for the SU(3) gauge theory with two flavors of fermions, in the temperature range [0.9, 1.9]T c . We identify the source of localization of the eigenmodes with gauge configurations that are self-dual and support negative fluctuations of the Polyakov loop P L , in the high temperature sea of P L ˜ 1. The dependence of these observations on the boundary conditions of the valence operator is studied. We also investigate the spatial overlap of the left-handed and right-handed projected eigenmodes in correlation with the localization and the corresponding eigenvalue. We discuss an interpretation of the results in terms of monopole-instanton structures.
Relativistic Definition of Spin Operators
NASA Astrophysics Data System (ADS)
Ryder, Lewis H.
2002-12-01
Some years ago Mashhoon [1] made the highly interesting suggestion that there existed a coupling of spin with rotations, just as there exists such a coupling with orbital angular momentum, as seen in the Sagnac effect, for example. Spin being essentially a quantum phenomenon, the obvious place to look for this was by studying the Dirac equation, and Hehl and Ni, in such an investigation [2], indeed found a coupling term of just the type Mashhoon had envisaged. Part of their procedure, however, was to take the nonrelativistic limit, and this was done by performing appropriate Foldy-Wouthuysen (FW) transformations. In the nonrelativistic limit, it is well-known that the spin operators for Dirac particles are in essence the Pauli matrices; but it is also well-known, and indeed was part of the motivation for Foldy and Wouthuysen's paper, that for fully-fledged Dirac particles the (4×4 generalisation of the) Pauli matrices do not yield satisfactory spin operators, since spin defined in this way would not be conserved. The question therefore presented itself: is there a relativistic spin operator for Dirac particles, such that in the relativistic, as well as the nonrelativistic, régime a Mashhoon spin-rotation coupling exists?...
NASA Astrophysics Data System (ADS)
Chen, Tsung-Wei; Chiou, Dah-Wei
2014-03-01
The classical dynamics for a charged spin particle is governed by the Lorentz force equation for orbital motion and by the Thomas-Bargmann-Michel-Telegdi (T-BMT) equation for spin precession. In static and homogeneous electromagnetic fields, it has been shown that the Foldy-Wouthuysen (FW) transform of the Dirac-Pauli Hamiltonian, which describes the relativistic quantum theory for a spin-1/2 particle, is consistent with the classical Hamiltonian (with both the orbital and spin parts) up to the order of 1/m14 (m is the particle's mass) in the low-energy and weak-field limit. In this paper, we extend this correspondence to the case of inhomogeneous fields. Regardless of the field gradient (e.g. Stern-Gerlach) force, the T-BMT equation is unaltered and thus the classical Hamiltonian remains the same, but subtleties arise and need to be clarified. For the relativistic quantum theory, we apply Eriksen's method to obtain the exact FW transformations for the two special cases, which in conjunction strongly suggest that, in the weak-field limit, the FW transformed Dirac-Pauli Hamiltonian (except for the Darwin term) is in agreement with the classical Hamiltonian in a manner that classical variables correspond to quantum operators via a specific Weyl ordering. Meanwhile, the Darwin term is shown to have no classical correspondence.
Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity.
Shao, Sihong; Quintero, Niurka R; Mertens, Franz G; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2014-09-01
We consider the nonlinear Dirac equation in 1 + 1 dimension with scalar-scalar self interaction g(2)/κ+1(̅ΨΨ)(κ+1) and with mass m. Using the exact analytic form for rest frame solitary waves of the form Ψ(x,t)=ψ(x)e(-iωt) for arbitrary κ, we discuss the validity of various approaches to understanding stability that were successful for the nonlinear Schrödinger equation. In particular we study the validity of a version of Derrick's theorem and the criterion of Bogolubsky as well as the Vakhitov-Kolokolov criterion, and find that these criteria yield inconsistent results. Therefore, we study the stability by numerical simulations using a recently developed fourth-order operator splitting integration method. For different ranges of κ we map out the stability regimes in ω. We find that all stable nonlinear Dirac solitary waves have a one-hump profile, but not all one-hump waves are stable, while all waves with two humps are unstable. We also find that the time t(c), it takes for the instability to set in, is an exponentially increasing function of ω and t(c) decreases monotonically with increasing κ. PMID:25314512
NASA Astrophysics Data System (ADS)
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.
Relativistic equations with fractional and pseudodifferential operators
Babusci, D.; Dattoli, G.; Quattromini, M.
2011-06-15
In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with noninteger exponents. We apply the method to equations resembling generalizations of the heat equations and discuss the possibility of extending the procedure to the relativistic Schroedinger and Dirac equations.
Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals.
Bradlyn, Barry; Cano, Jennifer; Wang, Zhijun; Vergniory, M G; Felser, C; Cava, R J; Bernevig, B Andrei
2016-08-01
In quantum field theory, we learn that fermions come in three varieties: Majorana, Weyl, and Dirac. Here, we show that in solid-state systems this classification is incomplete, and we find several additional types of crystal symmetry-protected free fermionic excitations. We exhaustively classify linear and quadratic three-, six-, and eight-band crossings stabilized by space group symmetries in solid-state systems with spin-orbit coupling and time-reversal symmetry. Several distinct types of fermions arise, differentiated by their degeneracies at and along high-symmetry points, lines, and surfaces. Some notable consequences of these fermions are the presence of Fermi arcs in non-Weyl systems and the existence of Dirac lines. Ab initio calculations identify a number of materials that realize these exotic fermions close to the Fermi level. PMID:27445310
Confined Dirac fermions in a constant magnetic field
Jellal, Ahmed; Alhaidari, Abdulaziz D.; Bahlouli, Hocine
2009-07-15
We obtain an exact solution of the Dirac equation in (2+1) dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. The solution space consists of positive- and negative-energy solutions, each of which splits into two disconnected subspaces depending on the sign of an azimuthal quantum number k=0,{+-}1,{+-}2,... and whether the cyclotron frequency is larger or smaller than the oscillator frequency. The spinor wave function is written in terms of the associated Laguerre polynomials. For negative k, the relativistic energy spectrum is infinitely degenerate due to the fact that it is independent of k. We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the relativistic quantum Hall effect in a confining potential.
Pairing symmetry and vortex zero mode for superconducting Dirac fermions
Lu, C.-K.; Herbut, Igor F.
2010-10-01
We study vortex zero-energy bound states in presence of pairing between low-energy Dirac fermions on the surface of a topological insulator. The pairing symmetries considered include the s-wave, p-wave, and, in particular, the mixed-parity symmetry, which arises in absence of the inversion symmetry on the surface. The zero mode is analyzed within the generalized Jackiw-Rossi-Dirac Hamiltonian that contains a momentum-dependent mass term, and includes the effects of the electromagnetic gauge field and the Zeeman coupling as well. At a finite chemical potential, as long as the spectrum without the vortex is fully gapped, the presence of a single Fermi surface with a definite helicity always leads to one Majorana zero mode, in which both electron's spin projections participate. In particular, the critical effects of the Zeeman coupling on the zero mode are discussed.
Weyl and Dirac semimetals with Z2 topological charge
NASA Astrophysics Data System (ADS)
Morimoto, Takahiro; Furusaki, Akira
2014-06-01
We study the stability of gap-closing (Weyl or Dirac) points in the three-dimensional Brillouin zone of semimetals using Clifford algebras and their representation theory. We show that a pair of Weyl points with Z2 topological charge are stable in a semimetal with time-reversal and reflection symmetries when the square of the product of the two symmetry transformations equals minus identity. We present toy models of Z2 Weyl semimetals which have surface modes forming helical Fermi arcs. We also show that Dirac points with Z2 topological charge are stable in a semimetal with time-reversal, inversion, and SU(2) spin rotation symmetries when the square of the product of time-reversal and inversion equals plus identity. Furthermore, we briefly discuss the topological stability of point nodes in superconductors using Clifford algebras.
μDirac: an autonomous instrument for halocarbon measurements
NASA Astrophysics Data System (ADS)
Gostlow, B.; Robinson, A. D.; Harris, N. R. P.; O'Brien, L. M.; Oram, D. E.; Mills, G. P.; Newton, H. M.; Pyle, J. A.
2009-09-01
We describe a new instrument (μDirac) capable of measuring halocarbons in the atmosphere. Portability, power efficiency and autonomy were critical requirements in the design, and the resulting instrument can be readily deployed unattended on a range of platforms: long duration balloon, aircraft, ship and ground based stations. The instrument is a temperature programmed gas chromatograph with electron capture detector (GC-ECD). The design requirements led to μDirac being built in-house with several novel features. It currently measures a range of halocarbons (CFCs and shorter-lived halocarbons having biogenic and anthropogenic sources) with measurement precisions ranging from ∼1% sd (CCl4) to ∼9% sd (CH3I). Since the prototype instrument was first tested in 2005 the instrument has been proved in the field on technically challenging aircraft and ground based campaigns. Results from one aircraft and two ground-based deployments are described.
μDirac: an autonomous instrument for halocarbon measurements
NASA Astrophysics Data System (ADS)
Gostlow, B.; Robinson, A. D.; Harris, N. R. P.; O'Brien, L. M.; Oram, D. E.; Mills, G. P.; Newton, H. M.; Yong, S. E.; Pyle, J. A.
2010-04-01
We describe a new instrument (μDirac) capable of measuring halocarbons in the atmosphere. Portability, power efficiency and autonomy were critical design requirements and the resulting instrument can be readily deployed unattended on a range of platforms: long duration balloon, aircraft, ship and ground-based stations. The instrument is a temperature programmed gas chromatograph with electron capture detector (GC-ECD). The design requirements led to μDirac being built in-house with several novel features. It currently measures a range of halocarbons (including short-lived tracers having biogenic and anthropogenic sources) with measurement precision relative standard deviations ranging from ± 1% (CCl4) to ± 9% (CH3I). The prototype instrument was first tested in 2005 and the instrument has been proved in the field on technically challenging aircraft and ground-based campaigns. Results from an aircraft and a ground-based deployment are described.
Torsion and noninertial effects on a nonrelativistic Dirac particle
Bakke, K.
2014-07-15
We investigate torsion and noninertial effects on a spin-1/2 quantum particle in the nonrelativistic limit of the Dirac equation. We consider the cosmic dislocation spacetime as a background and show that a rotating system of reference can be used out to distances which depend on the parameter related to the torsion of the defect. Therefore, we analyse torsion effects on the spectrum of energy of a nonrelativistic Dirac particle confined to a hard-wall potential in a Fermi–Walker reference frame. -- Highlights: •Torsion effects on a spin- 1/2 particle in a noninertial reference frame. •Fermi–Walker reference frame in the cosmic dislocation spacetime background. •Torsion and noninertial effects on the confinement to a hard-wall confining potential.
Twisted kinks, Dirac transparent systems, and Darboux transformations
NASA Astrophysics Data System (ADS)
Correa, F.; Jakubský, V.
2014-12-01
Darboux transformations are employed in construction and analysis of Dirac Hamiltonians with pseudoscalar potentials. By this method, we build a four-parameter class of reflectionless systems. Their potentials correspond to the composition of complex kinks, also known as twisted kinks, that play an important role in the 1 +1 Gross-Neveu and Nambu-Jona-Lasinio field theories. The twisted kinks turn out to be multisolitonic solutions of the integrable Ablowitz-Kaup-Newell-Segur hierarchy. Consequently, all the spectral properties of the Dirac reflectionless systems are reflected in a nontrivial conserved quantity, which can be expressed in a simple way in terms of Darboux transformations. We show that the four-parameter pseudoscalar systems reduce to well-known models for specific choices of the parameters. An associated class of transparent nonrelativistic models described by a matrix Schrödinger Hamiltonian is studied and the rich algebraic structure of their integrals of motion is discussed.
Three-dimensional periodic dielectric structures having photonic Dirac points
Bravo-Abad, Jorge; Joannopoulos, John D.; Soljacic, Marin
2015-06-02
The dielectric, three-dimensional photonic materials disclosed herein feature Dirac-like dispersion in quasi-two-dimensional systems. Embodiments include a face-centered cubic (fcc) structure formed by alternating layers of dielectric rods and dielectric slabs patterned with holes on respective triangular lattices. This fcc structure also includes a defect layer, which may comprise either dielectric rods or a dielectric slab with patterned with holes. This defect layer introduces Dirac cone dispersion into the fcc structure's photonic band structure. Examples of these fcc structures enable enhancement of the spontaneous emission coupling efficiency (the .beta.-factor) over large areas, contrary to the conventional wisdom that the .beta.-factor degrades as the system's size increases. These results enable large-area, low-threshold lasers; single-photon sources; quantum information processing devices; and energy harvesting systems.
New symmetry properties of pointlike scalar and Dirac particles
NASA Astrophysics Data System (ADS)
Silenko, Alexander J.
2015-03-01
New symmetry properties are found for pointlike scalar and Dirac particles (Higgs boson and all leptons) in Riemannian and Riemann-Cartan spacetimes in the presence of electromagnetic interactions. A Hermitian form of the Klein-Gordon equation for a pointlike scalar particle in an arbitrary n -dimensional Riemannian (or Riemann-Cartan) spacetime is obtained. New conformal symmetries of initial and Hermitian forms of this equation are ascertained. In the above spacetime, general Hamiltonians in the generalized Feshbach-Villars and Foldy-Wouthuysen representations are derived. The conformal-like transformation conserving these Hamiltonians is found. Corresponding conformal symmetries of a Dirac particle are determined. It is proven that all conformal symmetries remain unchanged by an inclusion of electromagnetic interactions.
Peccei-Quinn symmetry for Dirac seesaw and leptogenesis
NASA Astrophysics Data System (ADS)
Gu, Pei-Hong
2016-07-01
We extend the DFSZ invisible axion model to simultaneously explain small Dirac neutrino masses and cosmic matter-antimatter asymmetry. After the Peccei-Quinn and electroweak symmetry breaking, the effective Yukawa couplings of the Dirac neutrinos to the standard model Higgs scalar can be highly suppressed by the ratio of the vacuum expectation value of an iso-triplet Higgs scalar over the masses of some heavy gauge-singlet fermions, iso-doublet Higgs scalars or iso-triplet fermions. The iso-triplet fields can carry a zero or nonzero hypercharge. Through the decays of the heavy gauge-singlet fermions, iso-doublet scalars or iso-triplet fermions, we can obtain a lepton asymmetry in the left-handed leptons and an opposite lepton asymmetry in the right-handed neutrinos. Since the right-handed neutrinos do not participate in the sphaleron processes, the left-handed lepton asymmetry can be partially converted to a baryon asymmetry.
Size quantization of Dirac fermions in graphene constrictions
NASA Astrophysics Data System (ADS)
Terrés, B.; Chizhova, L. A.; Libisch, F.; Peiro, J.; Jörger, D.; Engels, S.; Girschik, A.; Watanabe, K.; Taniguchi, T.; Rotkin, S. V.; Burgdörfer, J.; Stampfer, C.
2016-05-01
Quantum point contacts are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wavelength in high-quality bulk graphene can be tuned up to hundreds of nanometres, the observation of quantum confinement of Dirac electrons in nanostructured graphene has proven surprisingly challenging. Here we show ballistic transport and quantized conductance of size-confined Dirac fermions in lithographically defined graphene constrictions. At high carrier densities, the observed conductance agrees excellently with the Landauer theory of ballistic transport without any adjustable parameter. Experimental data and simulations for the evolution of the conductance with magnetic field unambiguously confirm the identification of size quantization in the constriction. Close to the charge neutrality point, bias voltage spectroscopy reveals a renormalized Fermi velocity of ~1.5 × 106 m s-1 in our constrictions. Moreover, at low carrier density transport measurements allow probing the density of localized states at edges, thus offering a unique handle on edge physics in graphene devices.
Dirac bound states of anharmonic oscillator in external fields
Hamzavi, Majid; Ikhdair, Sameer M.; Falaye, Babatunde J.
2014-02-15
We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method. -- Highlights: • Effect of the external fields on the energy levels of Dirac particle with the anharmonic oscillator is investigated. • The solutions are discussed in view of spin and pseudospin symmetries limits. • The energy levels and wave function are presented by the Nikiforov–Uvarov method.
Phase-integral solution of the radial Dirac equation
Linnaeus, Staffan
2010-03-15
A phase-integral (WKB) solution of the radial Dirac equation is constructed, retaining perfect symmetry between the two components of the wave function and introducing no singularities except at the classical transition points. The potential is allowed to be the time component of a four-vector, a Lorentz scalar, a pseudoscalar, or any combination of these. The key point in the construction is the transformation from two coupled first-order equations constituting the radial Dirac equation to a single second-order Schroedinger-type equation. This transformation can be carried out in infinitely many ways, giving rise to different second-order equations but with the same spectrum. A unique transformation is found that produces a particularly simple second-order equation and correspondingly simple and well-behaved phase-integral solutions. The resulting phase-integral formulas are applied to unbound and bound states of the Coulomb potential. For bound states, the exact energy levels are reproduced.
Solutions of the multiconfiguration Dirac-Fock equations
NASA Astrophysics Data System (ADS)
Levitt, Antoine
2014-08-01
The multiconfiguration Dirac-Fock (MCDF) model uses a linear combination of Slater determinants to approximate the electronic N-body wave function of a relativistic molecular system, resulting in a coupled system of nonlinear eigenvalue equations, the MCDF equations. In this paper, we prove the existence of solutions of these equations in the weakly relativistic regime. First, using a new variational principle as well as the results of Lewin on the multiconfiguration non-relativistic model, and Esteban and Séré on the single-configuration relativistic model, we prove the existence of critical points for the associated energy functional, under the constraint that the occupation numbers are not too small. Then, this constraint can be removed in the weakly relativistic regime, and we obtain non-constrained critical points, i.e. solutions of the multiconfiguration Dirac-Fock equations.
Multiple Virtual Tunneling of Dirac Fermions in Granular Graphene
Pachoud, Alexandre; Jaiswal, Manu; Wang, Yu; Hong, Byung-Hee; Ahn, Jong-Hyun; Loh, Kian Ping; Özyilmaz, Barbaros
2013-01-01
Graphene charge carriers behave as massless Dirac fermions, opening the exciting possibility to observe long-range virtual tunneling of electrons in a solid. In granular metals, electron hops arising from series of virtual transitions are predicted to yield observable currents at low-enough temperatures, but to date experimental evidence is lacking. We report on electron transport in granular graphene films self-assembled by hydrogenation of suspended graphene. While the log-conductance shows a characteristic T−1/2 temperature dependence, cooling the samples below 10 K drives a triple crossover: a slope break in log-conductance, simultaneous to a substantial increase in magneto-conductance and onset of large mesoscopic conductance fluctuations. These phenomena are signatures of virtual transitions of electrons between distant localized states, and conductance statistics reveal that the high crossover-temperature is due to the Dirac nature of granular graphene charge carriers. PMID:24296942
Johnson noise thermometry reveals the Dirac fluid in graphene
NASA Astrophysics Data System (ADS)
Crossno, Jesse; Shi, Jing; Wang, Ke; Liu, Xiaomeng; Harzheim, Achim; Lucas, Andrew; Sachdev, Subir; Kim, Philip; Taniguchi, Takashi; Watanabe, Kenji; Ohki, Thomas; Fong, Kin Chung
Near the charge neutrality point in graphene, the Fermi surface vanishes leading to the formation of a strongly-interacting quasi-relativistic electron-hole plasma, known as a Dirac fluid. These non-Fermi liquids share many features with quantum critical systems including a fast electron-electron scattering rate which makes them well suited to hydrodynamic descriptions. A number of exotic properties have been predicted including a diverging thermal conductivity resulting in the breakdown of the Wiedemann-Franz (WF) law. I will discuss the experimental technique--based on Johnson noise thermometry--used to measure the electronic thermal conductivity of graphene and probe the unique transport dynamics of the Dirac fluid.
Dynamical class of a two-dimensional plasmonic Dirac system
NASA Astrophysics Data System (ADS)
Silva, Érica de Mello
2015-10-01
A current goal in plasmonic science and technology is to figure out how to manage the relaxational dynamics of surface plasmons in graphene since its damping constitutes a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, different systems are said to be dynamically equivalent if they have identical relaxation functions at all times, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.
Gate-tunable graphene quantum dot and Dirac oscillator
NASA Astrophysics Data System (ADS)
Belouad, Abdelhadi; Jellal, Ahmed; Zahidi, Youness
2016-02-01
We obtain the solution of the Dirac equation in (2 + 1) dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. We study the energy spectrum of graphene quantum dot (QD) defined by electrostatic gates. We give discussions of our results based on different physical settings, whether the cyclotron frequency is similar or larger/smaller compared to the oscillator frequency. This defines an effective magnetic field that produces the effective quantized Landau levels. We study analytically such field in gate-tunable graphene QD and show that our structure allows us to control the valley degeneracy. Finally, we compare our results with already published work and also discuss the possible applications of such QD.
Infrared regime of SU(2) with one adjoint Dirac flavor
NASA Astrophysics Data System (ADS)
Athenodorou, Andreas; Bennett, Ed; Bergner, Georg; Lucini, Biagio
2015-06-01
SU(2) gauge theory with one Dirac flavor in the adjoint representation is investigated on a lattice. Initial results for the gluonic and mesonic spectrum, static potential from Wilson and Polyakov loops, and the anomalous dimension of the fermionic condensate from the Dirac mode number are presented. The results found are not consistent with conventional confining behavior, pointing instead tentatively towards a theory lying within or very near the onset of the conformal window, with the anomalous dimension of the fermionic condensate in the range 0.9 ≲γ*≲0.95 . The implications of our work for building a viable theory of strongly interacting dynamics beyond the standard model are discussed.
An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian
NASA Technical Reports Server (NTRS)
Dyall, Kenneth G.
1994-01-01
The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.
Thermal bath of Dirac field in non-inertial frames
NASA Astrophysics Data System (ADS)
Zhang, Anwei
2016-07-01
The properties of inertial Dirac thermal bath viewed from the perspective of a uniformly accelerated observer is investigated. Using the single-mode approximation, we obtain the expression of the thermal reduced density matrix, which is constructed by the effective partition function in another way compared with the case of scalar field. We deduce the spectrum of particles and antiparticles seen by Rob and antiRob, respectively. It is found that the fermionic thermal bath will suppress the appearance of Unruh particles.
A new relativistic scheme in Dirac Kohn Sham theory
NASA Astrophysics Data System (ADS)
Nakajima, Takahito; Suzumura, Toshihisa; Hirao, Kimihiko
1999-04-01
The relativistic scheme by the elimination of small components (RESC) of the four-component Dirac equation proposed previously has been incorporated into density functional theory (DFT). RESC-DFT results in a computationally efficient and numerically stable two-component Kohn-Sham formalism, suited for molecular applications. Illustrative calculations for AgH, AuH, AgCl, and AuCl have been performed employing various exchange-correlation functionals. A good agreement with experiment is obtained.
''Superluminal'' transmission via entanglement, superoscillations, and quasi-Dirac distributions
Sokolovski, D.; Mayato, R. Sala
2010-02-15
We analyze a system in which, due to entanglement between the spin and spatial degrees of freedom, the reduced transmitted state has the shape of the freely propagating pulse translated in the complex coordinate plane. In the case an apparently ''superluminal'' advancement of the pulse, the delay amplitude distribution is found to be a peculiar approximation to the Dirac {delta} function, and the transmission coefficient exhibits a well-defined superoscillatory window. Analogies with potential tunneling and Wheeler's delayed choice experiment are highlighted.
Axial Anomaly, Dirac Sea, and the Chiral Magnetic Effect
Kharzeev, D.E.
2010-05-26
Gribov viewed the axial anomaly as a manifestation of the collective motion of Dirac fermions with arbitrarily high momenta in the vacuum. In the presence of an external magnetic field and a chirality imbalance, this collective motion becomes directly observable in the form of the electric current - this is the chiral magnetic effect (CME). I give an elementary introduction into the physics of CME, and discuss the experimental status and recent developments.
Dirac Points in Two-Dimensional Inverse Opals
NASA Astrophysics Data System (ADS)
Mahan, G. D.
2013-10-01
The electron energy states and energy bands are calculated for a two-dimensional inverse opal structure. Assume that the opal structure is closed-packed circles, the inverse opal has the honeycomb lattice. The honeycomb lattice in two dimensions has a Dirac point. Its properties can be manipulated by altering the structure of the inverse opal: the radius of the circle, and the small gap between circles.
General spin and pseudospin symmetries of the Dirac equation
NASA Astrophysics Data System (ADS)
Alberto, P.; Malheiro, M.; Frederico, T.; de Castro, A.
2015-12-01
In the 1970s Smith and Tassie [G. B. Smith and L. J. Tassie, Ann. Phys. (NY) 65, 352 (1971), 10.1016/0003-4916(71)90172-2] and Bell and Ruegg [J. S. Bell and H. Ruegg, Nucl. Phys. B 98, 151 (1975), 10.1016/0550-3213(75)90206-0; J. S. Bell and H. Ruegg, Nucl. Phys. B 104, 546 (1976), 10.1016/0550-3213(76)90035-3] independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and applied to several physical systems. Twenty years after, in 1997, the pseudospin symmetry was revealed by Ginocchio [J. N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997), 10.1103/PhysRevLett.78.436] as a relativistic symmetry of the atomic nuclei when it is described by relativistic mean-field hadronic models. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrödinger-like equations, i.e, without a matrix structure. In this paper we propose a generalization of these SU(2) symmetries for potentials in the Dirac equation with several Lorentz structures, which also allow for the suppression of the matrix structure of the second-order equation of either the upper or lower components of the Dirac spinor. We derive the general properties of those potentials and list some possible candidates, which include the usual spin-pseudospin potentials, and also two- and one-dimensional potentials. An application for a particular physical system in two dimensions, electrons in graphene, is suggested.
Hawking radiation of Dirac particles from black strings
NASA Astrophysics Data System (ADS)
Ahmed, Jamil; Saifullah, K.
2011-08-01
Hawking radiation has been studied as a phenomenon of quantum tunneling in different black holes. In this paper we extend this semi-classical approach to cylindrically symmetric black holes. Using the Hamilton-Jacobi method and WKB approximation we calculate the tunneling probabilities of incoming and outgoing Dirac particles from the event horizon and find the Hawking temperature of these black holes. We obtain results both for uncharged as well as charged particles.
The Dirac equation in Kerr-Taub-NUT spacetime
NASA Astrophysics Data System (ADS)
Cebeci, Hakan; Özdemir, Nülifer
2013-09-01
We study the Dirac equation in the Kerr-Taub-NUT spacetime. We use Boyer-Lindquist coordinates and separate the resulting equations into radial and angular parts. We obtain some exact analytical solutions of the angular equations for some special cases. We also obtain the radial wave equations with an effective potential. Finally, we discuss the potentials by plotting them as a function of radial distance in a physically acceptable region.
Kondo effect and STM spectroscopy of Dirac electrons in graphene
NASA Astrophysics Data System (ADS)
Sengupta, Krishnendu
2011-03-01
We show that graphene, whose low-energy quasiparticles display Dirac like behavior, may exhibit a two-channel Kondo effect in the presence of magnetic impurities. We present a large N analysis for a generic spin S local moment coupled to Dirac electrons in graphene and demonstrate that the corresponding Kondo temperature can be tuned by an experimentally controllable applied gate voltage. We also study the STM spectra of these Dirac electrons in the presence of such impurities and demonstrate that such spectra depend qualitatively on the position of the impurity atom in the graphene matrix. More specifically, for impurity atoms atop the hexagon center, the zero-bias tunneling conductance, as measured by a STM, shows a peak; for those atop a graphene site, it shows a dip. We provide a qualitative theoretical explanation of this phenomenon and show that this unconventional behavior is a consequence of conservation/breaking of pseudospin symmetry of the Dirac quasiparticles by the impurity. We also predict that tuning the Fermi energy to zero by a gate voltage would not lead to qualitative change in the shape of the conductance spectra when the impurity is atop the hexagon center. A similar tuning of the Fermi energy for the impurity atop a site, however, would lead to a change in the tunneling conductance from a dip to a peak via an antiresonance. We discuss some recent experiments on a doped graphene sample that seem to have qualitative agreement with our theory and suggest further experiments to test our predictions. DST, India.
Nonlinear trigonometric approximation and the Dirac delta function
NASA Astrophysics Data System (ADS)
Xu, Xiubin
2007-12-01
The nonlinear approximations based on two types of trigonometric generating functions are developed. It is shown that such nonlinear approximations to the Dirac delta function on are the corresponding Gaussian quadratures applied to some Stieltjes integrals, whose integrands contain weights and the two types of generating functions. In addition, the convergence is proved and the error terms are obtained. Some numerical tests are also shown.
Dirac fermions on an anti-de Sitter background
Ambruş, Victor E. Winstanley, Elizabeth
2014-11-24
Using an exact expression for the bi-spinor of parallel transport, we construct the Feynman propagator for Dirac fermions in the vacuum state on anti-de Sitter space-time. We compute the vacuum expectation value of the stress-energy tensor by removing coincidence-limit divergences using the Hadamard method. We then use the vacuum Feynman propagator to compute thermal expectation values at finite temperature. We end with a discussion of rigidly rotating thermal states.
Effective Dirac Hamiltonian for anisotropic honeycomb lattices: Optical properties
NASA Astrophysics Data System (ADS)
Oliva-Leyva, M.; Naumis, Gerardo G.
2016-01-01
We derive the low-energy Hamiltonian for a honeycomb lattice with anisotropy in the hopping parameters. Taking the reported Dirac Hamiltonian for the anisotropic honeycomb lattice, we obtain its optical conductivity tensor and its transmittance for normal incidence of linearly polarized light. Also, we characterize its dichroic character due to the anisotropic optical absorption. As an application of our general findings, which reproduce the previous case of uniformly strained graphene, we study the optical properties of graphene under a nonmechanical distortion.
Algebraic and Dirac-Hestenes spinors and spinor fields
NASA Astrophysics Data System (ADS)
Rodrigues, Waldyr A.
2004-07-01
Almost all presentations of Dirac theory in first or second quantization in physics (and mathematics) textbooks make use of covariant Dirac spinor fields. An exception is the presentation of that theory (first quantization) offered originally by Hestenes and now used by many authors. There, a new concept of spinor field (as a sum of nonhomogeneous even multivectors fields) is used. However, a careful analysis (detailed below) shows that the original Hestenes definition cannot be correct since it conflicts with the meaning of the Fierz identities. In this paper we start a program dedicated to the examination of the mathematical and physical basis for a comprehensive definition of the objects used by Hestenes. In order to do that we give a preliminary definition of algebraic spinor fields (ASF) and Dirac-Hestenes spinor fields (DHSF) on Minkowski space-time as some equivalence classes of pairs (Ⅺu,ψⅪu), where Ⅺu is a spinorial frame field and ψⅪu is an appropriate sum of multivectors fields (to be specified below). The necessity of our definitions are shown by a careful analysis of possible formulations of Dirac theory and the meaning of the set of Fierz identities associated with the bilinear covariants (on Minkowski space-time) made with ASF or DHSF. We believe that the present paper clarifies some misunderstandings (past and recent) appearing on the literature of the subject. It will be followed by a sequel paper where definitive definitions of ASF and DHSF are given as appropriate sections of a vector bundle called the left spin-Clifford bundle. The bundle formulation is essential in order to be possible to produce a coherent theory for the covariant derivatives of these fields on arbitrary Riemann-Cartan space-times. The present paper contains also Appendixes A-E which exhibits a truly useful collection of results concerning the theory of Clifford algebras (including many tricks of the trade) necessary for the intelligibility of the text.
Fermi-Dirac statistics plus liquid description of quark partons
NASA Astrophysics Data System (ADS)
Buccella, F.; Miele, G.; Migliore, G.; Tibullo, V.
1995-12-01
A previous approach with Fermi-Dirac distributions for fermion partons is here improved to comply with the expected low x behaviour of structure functions. We are so able to get a fair description of the unpolarized and polarized structure functions of the nucleons as well as of neutrino data. We cannot reach definite conclusions, but confirm our suspicion of a relationship between the defects in Gottfried and spin sum rules.
Torsion-gravity for Dirac fields and their effective phenomenology
NASA Astrophysics Data System (ADS)
Fabbri, Luca
2014-08-01
We will consider the torsional completion of gravity for a background filled with Dirac matter fields, studying the weak-gravitational non-relativistic approximation, in view of an assessment about their effective phenomenology: we discuss how the torsionally-induced nonlinear interactions among fermion fields in this limit are compatible with all experiments and remarks on the role of torsion to suggest new physics are given.
Berry Curvature and Chiral Plasmons in Massive Dirac Materials
NASA Astrophysics Data System (ADS)
Song, Justin; Rudner, Mark
2015-03-01
In the semiclassical model of carrier dynamics, quasiparticles are described as nearly free electrons with modified characteristics modified characteristics such as effective masses which may differ significantly from those of an electron in vacuum. In addition to being influenced by external electric and magnetic fields, the trajectories of electrons in topological materials are also affected by the presence of an interesting quantum mechanical field - the Berry curvature - which is responsible for a number of anomalous transport phenomena recently observed in Dirac materials including G/hBN, and MoS2. Here we discuss how Berry curvature can affect the collective behavior of electrons in these systems. In particular, we show that the collective electronic excitations in metallic massive Dirac materials can feature a chirality even in the absence of an applied magnetic field. The chirality of these plasmons arises from the Berry curvature of the massive Dirac bands. The corresponding dispersion is split between left- and right-handed modes. We also discuss experimental manifestations.
MPI support in the DIRAC Pilot Job Workload Management System
NASA Astrophysics Data System (ADS)
Tsaregorodtsev, A.; Hamar, V.
2012-12-01
Parallel job execution in the grid environment using MPI technology presents a number of challenges for the sites providing this support. Multiple flavors of the MPI libraries, shared working directories required by certain applications, special settings for the batch systems make the MPI support difficult for the site managers. On the other hand the workload management systems with Pilot Jobs became ubiquitous although the support for the MPI applications in the Pilot frameworks was not available. This support was recently added in the DIRAC Project in the context of the GISELA Latin American Grid Initiative. Special services for dynamic allocation of virtual computer pools on the grid sites were developed in order to deploy MPI rings corresponding to the requirements of the jobs in the central task queue of the DIRAC Workload Management System. Pilot Jobs using user space file system techniques install the required MPI software automatically. The same technique is used to emulate shared working directories for the parallel MPI processes. This makes it possible to execute MPI jobs even on the sites not supporting them officially. Reusing so constructed MPI rings for execution of a series of parallel jobs increases dramatically their efficiency and turnaround. In this contribution we describe the design and implementation of the DIRAC MPI Service as well as its support for various types of MPI libraries. Advantages of coupling the MPI support with the Pilot frameworks are outlined and examples of usage with real applications are presented.
Are the surface Fermi arcs in Dirac semimetals topologically protected?
Kargarian, Mehdi; Randeria, Mohit; Lu, Yuan-Ming
2016-08-01
Motivated by recent experiments probing anomalous surface states of Dirac semimetals (DSMs) Na3Bi and Cd3As2, we raise the question posed in the title. We find that, in marked contrast to Weyl semimetals, the gapless surface states of DSMs are not topologically protected in general, except on time-reversal-invariant planes of surface Brillouin zone. We first demonstrate this finding in a minimal four-band model with a pair of Dirac nodes at [Formula: see text] where gapless states on the side surfaces are protected only near [Formula: see text] We then validate our conclusions about the absence of a topological invariant protecting double Fermi arcs in DSMs, using a K-theory analysis for space groups of Na3Bi and Cd3As2 Generically, the arcs deform into a Fermi pocket, similar to the surface states of a topological insulator, and this pocket can merge into the projection of bulk Dirac Fermi surfaces as the chemical potential is varied. We make sharp predictions for the doping dependence of the surface states of a DSM that can be tested by angle-resolved photoemission spectroscopy and quantum oscillation experiments. PMID:27436895
Dirac Fermions without bulk backscattering in rhombohedral topological insulators
NASA Astrophysics Data System (ADS)
Mera Acosta, Carlos; Lima, Matheus; Seixas, Leandro; da Silva, Antônio; Fazzio, Adalberto
2015-03-01
The realization of a spintronic device using topological insulators is not trivial, because there are inherent difficulties in achieving the surface transport regime. The majority of 3D topological insulators materials (3DTI) despite of support helical metallic surface states on an insulating bulk, forming topological Dirac fermions protected by the time-reversal symmetry, exhibit electronic scattering channels due to the presence of residual continuous bulk states near the Dirac-point. From ab initio calculations, we studied the microscopic origin of the continuous bulk states in rhombohedral topological insulators materials with the space group D3d 5 (R 3 m) , showing that it is possible to understand the emergence of residual continuous bulk states near the Dirac-point into a six bands effective model, where the breaking of the R3 symmetry beyond the Γ point has an important role in the hybridization of the px, py and pz atomic orbitals. Within these model, the mechanisms known to eliminate the bulk scattering, for instance: the stacking faults (SF), electric field and alloy, generated the similar effect in the effective states of the 3DTI. Finally, we show how the surface electronic transport is modified by perturbations of bulk with SF. We would like to thank the financial support by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP).
Delocalization of Surface Dirac Electrons in Disordered Weak Topological Insulators
NASA Astrophysics Data System (ADS)
Takane, Yositake
2014-10-01
The spectrum of massless Dirac electrons on the side surface of a three-dimensional weak topological insulator is significantly affected by whether the number of unit atomic layers constituting the sample is even or odd; it has a finite-size energy gap in the even case while it is gapless in the odd case. The conductivity of such a two-dimensional Dirac electron system with quenched disorder is calculated when the Fermi level is located at the Dirac point. It is shown that the conductivity increases with increasing disorder and shows no clear even-odd difference when the aspect ratio of the system is appropriately fixed. From the system-size dependence of the average conductivity, the scaling function β is determined under the one-parameter scaling hypothesis. The result implies that β = 0 in the clean limit at which the conductivity is minimized, and that β > 0 otherwise. Hence, the system is a perfect metal in the thermodynamic limit except in the clean limit that should be regarded as an unstable fixed point.
Transport properties of Dirac semimetal Cd3As2
NASA Astrophysics Data System (ADS)
Liang, Tian; Gibson, Quinn; Xiong, Jun; Liu, Minhao; Hirschberger, Maximilian; Cava, Robert; Ong, Nai Phuan
2014-03-01
The semimetal Cd3As2 has emerged as an attractive candidate for a Dirac semimetal. A recent LDA calculation reveals that, at the Fermi energy, it has two bulk Dirac nodes which straddle the Γ point along the kz axis. The Dirac nodes were recently observed by ARPES. We have made extensive transport measurements of Cd3As2. Because of possible Cd vacancy disorder in the very large unit cell (160 atoms), the SdH oscillations reveal a quantum lifetime that is moderately damped. Despite the disorder, the observed resistivity ρ in some crystals displays a RRR of 1000. At 4 K, the residual resistivity is anomalously low (30 n Ω cm). We estimate that the mobility exceeds 106 cm2V-1s-1. A magnetic field H strongly increases ρ by factors of 100 to 1000 at 10 Tesla. This giant magnetoresistance (MR) is highly anisotropic. The MR is largest when H is perpendicular to the axis (110) and minimal when H is ∥(110). We will discuss possible origins of this unusual anisotropic giant MR. We also discuss the possibility of detecting an enhanced longitudinal MR associated with charge pumping between Weyl nodes (the chiral anomaly). Supported by Army Research Office (ARO W911NF-11-1-0379) and NSF-MRSEC Grant DMR 0819860.
Surface states of massive Dirac fermions with separated Weyl nodes
NASA Astrophysics Data System (ADS)
Buividovich, P. V.
2016-01-01
We derive the spectra of surface states for massive Dirac Hamiltonians with either momentum or energy separation between the left- and right-handed Weyl nodes. Momentum separation between the Weyl nodes corresponds to the explicitly broken time-reversal symmetry and the energy separation - to broken parity. Such Hamiltonians provide the simplest model description of Weyl semimetals. We find that the only effect of the energy separation between the Weyl nodes is to decrease the Fermi velocity in the linear dispersion relation of the surface states of massive Dirac Hamiltonian. In the case of broken time-reversal symmetry, the spectrum of surface states interpolates in a nontrivial way between the Fermi arc-type and the Dirac cone-type dispersion relations. In particular we find that for all values of the mass and the momentum separation between the Weyl nodes the surface states only exist in a strip of finite width in momentum space. We give also some simpler examples of surface states in order to make these notes more pedagogical.
Dirac-bracket structure in multidimensional mode conversion
NASA Astrophysics Data System (ADS)
Brizard, A. J.; Tracy, E. R.; Kaufman, A. N.; Johnston, D.; Zobin, N.
2012-05-01
The intersection of two (2 n - 1)-dimensional dispersion manifolds Da and Db in the 2 n-dimensional ray phase space P yields a (2 n - 2)-dimensional conversion manifold M≡Da∩Db that naturally possesses a Dirac-bracket structure that is inherited from the canonical Poisson bracket on ray phase space. The canonical symplectic two-form Ω ≡ Ω∥ + Ω⊥, defined on the 2 n-dimensional tangent plane TP≡TM⊕(TM)⊥, can thus be decomposed into the Dirac two-form Ω∥ on the (2 n - 2)-dimensional tangent plane TM at a conversion point z0∈M, and the symplectic two-form Ω⊥ on its orthogonal 2-dimensional complement (TM)⊥. These two symplectic two-forms are introduced in our analysis of multidimensional mode conversion, where their respective geometrical roles are defined. We note that since the Dirac-bracket structure Ω∥ vanishes identically when n = 1, it represents a new structure in multidimensional ( n > 1) mode conversion theory.
Upper-division student difficulties with the Dirac delta function
NASA Astrophysics Data System (ADS)
Wilcox, Bethany R.; Pollock, Steven J.
2015-06-01
The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them. To characterize student difficulties with the delta function at the upper-division level, we examined students' responses to traditional exam questions and a standardized conceptual assessment, and conducted think-aloud interviews. Our analysis was guided by an analytical framework that focuses on how students activate, construct, execute, and reflect on the Dirac delta function in the context of problem solving in physics. Here, we focus on student difficulties using the delta function to express charge distributions in the context of junior-level electrostatics. Common challenges included invoking the delta function spontaneously, translating a description of a charge distribution into a mathematical expression using delta functions, integrating 3D or non-Cartesian delta function expressions, and recognizing that the delta function can have units. We also briefly discuss implications of these difficulties for instruction.
Diffusive quantum criticality in three-dimensional disordered Dirac semimetals
NASA Astrophysics Data System (ADS)
Roy, Bitan; Das Sarma, S.
2014-12-01
Three-dimensional Dirac semimetals are stable against weak potential disorder, but not against strong disorder. In the language of renormalization group, such stability stems from the irrelevance of weak disorder in the vicinity of the noninteracting Gaussian fixed point. However, beyond a threshold, potential disorder can take Dirac semimetals into a compressible diffusive metallic phase through a quantum phase transition (QPT), where density of states at zero energy, quasiparticle lifetime, and metallic conductivity at T =0 are finite. Universal behavior of such unconventional QPT is described within the framework of an ɛ (=d -2 ) expansion near the lower critical dimension. Various exponents near this quantum critical point are obtained after performing a two-loop perturbative expansion in the vanishing replica limit and we demonstrate that the theory is renormalizable at least to two-loop order. We argue that such QPT is always continuous in nature and shares the same university class with a similar transition driven by odd-parity disorder. The critical exponents are independent of flavor number of Dirac fermions and thus our study can be germane to disordered Cd3As2 and Na3Bi . Scaling behaviors of various measurable quantities such as specific heat and density of states across such QPT are proposed.
Anisotropic Dirac Fermions in Novel 2D Carbon and Silicon Allotropes
NASA Astrophysics Data System (ADS)
Wang, Zhenhai; Zhao, Mingwen; Zhou, Xiang-Feng; Zhu, Qiang; Zhang, Xiaoming; Dong, Huafeng; Oganov, Artem R.; He, Shumin; Grünberg, Peter
Graphene, due to its unique Dirac cones with linear dispersion, exhibits a number of novel physics, such as high carrier mobility and quantum hall effect. Successful preparation of graphene in 2004 has inspired further searches for other 2D Dirac materials. Using systematic evolutionary structure searching, here we proposed one interesting type of 2D Dirac allotropes, which were named as `phagraphene' [Nano. Lett. 15, 6182 (2015)] and `siliconeet' respectively. Compared with the isotropic energy dispersion in graphene, the Dirac cones in these samples are direction-dependent. Further investigations proved that such anisotropic behaviors and the distorted Dirac cones are robust against external strain with tunable Fermi velocities. These predictions pave a new way to construct novel functional Dirac materials that might have potential applications in future.
Classification of stable Dirac and Weyl semimetals with reflection and rotational symmetry
NASA Astrophysics Data System (ADS)
Gao, Zihao; Hua, Meng; Zhang, Haijun; Zhang, Xiao
2016-05-01
Three-dimensional (3D) Dirac and Weyl semimetals are novel states of quantum matter. We classify stable 3D Dirac and Weyl semimetals with reflection and rotational symmetry in the presence of time reversal symmetry and spin-orbit coupling, which belong to seventeen different point groups. They have two classes of reflection symmetry, with the mirror plane parallel and perpendicular to rotation axis. In both cases two types of Dirac points, existing through accidental band crossing (ABC) or at a time reversal invariant momentum (TBC), are determined by four different reflection symmetries. We classify those two types of Dirac points with a combination of different reflection and rotational symmetries. We further classify Dirac and Weyl line nodes to show in which types of mirror plane they can exist. Finally we discuss that Weyl line nodes and Dirac points can exist at the same time taking C4 v symmetry as an example.
NASA Astrophysics Data System (ADS)
Watanabe, Masataka; Komatsu, Hisato; Tsuji, Naoto; Aoki, Hideo
2015-11-01
Massless Dirac particles on the helicoid are theoretically investigated. With its possible application being helical graphene, we explore how the peculiarities of Dirac particles appear on the curved, screw-symmetric surface. Zweibein is used to derive the massless Dirac equation on the helicoid and on general curved surfaces. We show that bound states of massless Dirac electrons on the helicoid are absent, and thus the system is fully characterized by the scattering probabilities and the phase shifts. We obtain these quantities from numerically calculated wave functions. We find the local density of states and the phase shifts behave characteristically around the axis of the helicoid. Bound states of massive Dirac electrons on the surface are also shown to be absent as an extension of the above result on massless Dirac electrons. A comparison with the nonrelativistic case is also made.
Massive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator
Chen, Y.L.; Chu, J.-H.; Analytis, J.G.; Liu, Z.K.; Igarashi, K.; Kuo, H.-H.; Qi, X.L.; Mo, S.K.; Moore, R.G.; Lu, D.H.; Hashimoto, M.; Sasagawa, T.; Zhang, S.C.; Fisher, I.R.; Hussain, Z.; Shen, Z.-X.; /SLAC
2011-05-20
Topological insulators are characterized by a massless Dirac surface state and a bulk energy gap. An insulating massive Dirac fermion state is predicted to occur if the breaking of the time reversal symmetry opens an energy gap at the Dirac point, provided that the Fermi-energy resides inside both the surface and bulk gaps. By introducing magnetic dopants into the three dimensional topological insulator Bi{sub 2}Se{sub 3} to break the time reversal symmetry, we observed the formation of a massive Dirac fermion on the surface; simultaneous magnetic and charge doping furthermore positioned the Fermi-energy inside the Dirac gap. The insulating massive Dirac Fermion state thus obtained may provide a tool for studying a range of topological phenomena relevant to both condensed matter and particle physics.
Diffusion of Dirac fermions across a topological merging transition in two dimensions
NASA Astrophysics Data System (ADS)
Adroguer, P.; Carpentier, D.; Montambaux, G.; Orignac, E.
2016-03-01
A continuous deformation of a Hamiltonian possessing at low energy two Dirac points of opposite chiralities can lead to a gap opening by merging the two Dirac points. In two dimensions, the critical Hamiltonian possesses a semi-Dirac spectrum: linear in one direction but quadratic in the other. We study the transport properties across such a transition, from a Dirac semimetal through a semi-Dirac phase toward a gapped phase. Using both a Boltzmann approach and a diagrammatic Kubo approach, we describe the conductivity tensor within the diffusive regime. In particular, we show that both the anisotropy of the Fermi surface and the Dirac nature of the eigenstates combine to give rise to anisotropic transport times, manifesting themselves through an unusual matrix self-energy.
Kappa State Solutions of Dirac-Hulthen and Dirac-Eckart Problems with Pseudospin and Spin Symmetry
Soylu, A.; Bayrak, O.; Boztosun, I.
2008-11-11
In this study, the analytical solutions of the Dirac equation have been presented for the Hulthen and Eckart potentials by applying an approximation to centrifugal-like term in the case of spin symmetry, {delta}(r) = C = constant, and pseudospin symmetry, {sigma}(r) = C = constant, for any spin-orbit quantum number {kappa}. The energy eigenvalues and corresponding spinor wave functions are obtained in the closed-forms.
Exact solutions for non-Hermitian Dirac-Pauli equation in an intensive magnetic field
NASA Astrophysics Data System (ADS)
Rodionov, V. N.
2015-04-01
We consider modified Dirac-Pauli equations that are entered using {{γ }5}-mass factorization, m\\to {{m}1}+/- {{γ }5}{{m}2}, of an ordinary Klein-Gordon operator. We also consider the interaction of fermions with an intensive uniform magnetic field, focusing on their (g-2) gyromagnetic factor. Due to effective research procedures, we derive the exact solutions of the enregy spectra of pseudo-Hermitian Hamiltonians, taking into account the spin of the fermions. The basic research methods are the elucidation of the new border areas of the unbroken PT symmetry of non-Hermitian Hamiltonians. In particular, it is shown that the reality energy spectrum of fermions at rest can be expressed by limiting the intensity of the magnetic field, H≤slant {{H}max }={{m}2}/(2Δ μ {{m}1}), where Δ μ is an anomalous magnetic moment of particles.
Consequences of the N-Body Dirac Equation: The Classical Variables of Spin
NASA Astrophysics Data System (ADS)
Smith, Felix T.
2002-05-01
The group theory of the n-body Dirac equation requires a thirteen-parameter version of the Poincaré group. It has a two separate six-parameter Lorentz-like subgroups, one for velocity boosts and one for spatial displacements, i.e., a phase-space of 12 dimensions per particle. In additional to three dimensions each of position and momentum, each particle must have six rotational dimensions, three of angular momentum and three of orientation. Three of these can be identified with the spin, which has a classical as well as a quantum existence. The three "new" coordinates of orientation are conjugate to the spin momentum; they are Euler angles of an infinitesimal test body at each particle center. Their presence is required for group-theoretic consistency. New operators can be constructed, and their possible consequences and measurability will be discussed.
Simultaneous ordinary and type A N-fold supersymmetries in Schrodinger, Pauli, and Dirac equations
Ho, C.-L. . E-mail: hcl@mail.tku.edu.tw; Tanaka, T. . E-mail: ttanaka@mail.tku.edu.tw
2006-06-15
We investigate physical models which possess simultaneous ordinary and type A N-fold supersymmetries, which we call type A (N,1)-fold supersymmetry. Inequivalent type A (N,1)-fold supersymmetric models with real-valued potentials are completely classified. Among them, we find that a trigonometric Rosen-Morse type and its elliptic version are of physical interest. We investigate various aspects of these models, namely, dynamical breaking and interrelation between ordinary and N-fold supersymmetries, shape invariance, quasi-solvability, and an associated algebra which is composed of one bosonic and four fermionic operators and dubbed type A (N,1)-fold superalgebra. As realistic physical applications, we demonstrate how these systems can be embedded into Pauli and Dirac equations in external electromagnetic fields.
Pilots 2.0: DIRAC pilots for all the skies
NASA Astrophysics Data System (ADS)
Stagni, F.; Tsaregorodtsev, A.; McNab, A.; Luzzi, C.
2015-12-01
In the last few years, new types of computing infrastructures, 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 opportunistic. Most of these new infrastructures are based on virtualization techniques. Meanwhile, some concepts, such as distributed queues, lost appeal, while still supporting a vast amount of resources. Virtual Organizations are therefore facing heterogeneity of the available resources and the use of an Interware software like DIRAC to hide the diversity of underlying resources has become essential. The DIRAC WMS is based on the concept of pilot jobs that was introduced back in 2004. A pilot is what creates the possibility to run jobs on a worker node. Within DIRAC, we developed a new generation of pilot jobs, that we dubbed Pilots 2.0. Pilots 2.0 are not tied to a specific infrastructure; rather they are generic, fully configurable and extendible pilots. A Pilot 2.0 can be sent, as a script to be run, or it can be fetched from a remote location. A pilot 2.0 can run on every computing resource, e.g.: on CREAM Computing elements, on DIRAC Computing elements, on Virtual Machines as part of the contextualization script, or IAAC resources, provided that these machines are properly configured, hiding all the details of the Worker Nodes (WNs) infrastructure. Pilots 2.0 can be generated server and client side. Pilots 2.0 are the “pilots to fly in all the skies”, aiming at easy use of computing power, in whatever form it is presented. Another aim is the unification and simplification of the monitoring infrastructure for all kinds of computing resources, by using pilots as a network of distributed sensors coordinated by a central resource monitoring system. Pilots 2.0 have been developed using the command pattern. VOs using DIRAC can tune pilots 2.0 as they need, and extend or replace each and every pilot command in an easy way. In this
Transport Experiments of Topological Insulators and Dirac Semimetals
NASA Astrophysics Data System (ADS)
Xiong, Jun
The progress in understanding the Berry phase of Bloch electrons in crystals has triggered tremendous interest in discovering novel topological phases of solids. The integration of the Berry curvature in the Brillouin zone can categorize solids into phases such as topological insulators (TI), Dirac semimetals (DSM) and Weyl semimetals (WSM). These new phases have unconventional electronic states at the boundaries, such as the spin polarized electrons on the surface of a three-dimensional TI. Under proper engineering, such edge states can carry a dissipationless current, leading to a great application potential in low-power devices and topological quantum computers. Besides TI, the newly discovered Dirac and Weyl semimetals represent another example in which electrons have a linear energy-momentum dispersion. The paired Weyl nodes have opposite chiralities, and can be regarded as positive and negative monopoles of the Berry flux. Under the time-reversal, inversion and certain crystal symmetries, as in the cases of Cd3As2 and Na3Bi, the Weyl nodes with different chiralities can coexist at the same point in the Brillouin zone and the crystal becomes a Dirac semimetal. Such semimetals provide platforms for some phenomena in high energy physics, such as the chiral anomaly effect. The above predictions lie at the heart of our experimental study of topological materials. We synthesized a topological insulator, Bi2Te2 Se, with a suppressed bulk carrier density. Analysis of the prominent Shubnikov-de Haas oscillations in Bi2Te2Se demonstrates clear evidence for the Dirac surface electrons and their pi Berry phase. We also leveraged the ionic liquid gating technique to bring the chemical potential 50% closer to the Dirac point. Additionally, we studied two types of Na3Bi, a DSM. The first type with a high chemical potential exhibits a large and linear magnetoresistance (MR), implying a transport lifetime steeply tuned by the magnetic field. In the second type of Na3Bi with a
Hidden symmetry and protection of Dirac points on the honeycomb lattice
NASA Astrophysics Data System (ADS)
Hou, Jing-Min; Chen, Wei
2015-12-01
The honeycomb lattice possesses a novel energy band structure, which is characterized by two distinct Dirac points in the Brillouin zone, dominating most of the physical properties of the honeycomb structure materials. However, up till now, the origin of the Dirac points is unclear yet. Here, we discover a hidden symmetry on the honeycomb lattice and prove that the existence of Dirac points is exactly protected by such hidden symmetry. Furthermore, the moving and merging of the Dirac points and a quantum phase transition, which have been theoretically predicted and experimentally observed on the honeycomb lattice, can also be perfectly explained by the parameter dependent evolution of the hidden symmetry.
Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material
NASA Astrophysics Data System (ADS)
Banerjee, S.; Fransson, J.; Black-Schaffer, A. M.; Ågren, H.; Balatsky, A. V.
2016-04-01
We examine the low-energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in a honeycomb lattice structure. Using the example of graphene, we present evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K' points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. We show that the Dirac node is preserved in the presence of an intergrain interaction, despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sublattice symmetry by choosing different on-site potentials for the two sublattices leads to a gap opening near the Dirac node, in analogy with fermionic Dirac materials. The Dirac node dispersion of bosonic excitations is thus expanding the discussion of the conventional Dirac cone excitations to the case of bosons. We call this case as a representative of bosonic Dirac materials (BDM), similar to the case of Fermionic Dirac materials extensively discussed in the literature.
Simple way to extract solutions and features of the Dirac equation for a noncentral potentials
NASA Astrophysics Data System (ADS)
Barakat, T.; Abdalla, M. Sebawe
2016-02-01
The main purpose of the present study is to explore the classes of the Schrödinger-like wave equations derived from Dirac equation, for which the similarity transformation and asymptotic iteration algorithms can assist in generating second-order differential equation that admit general exact solutions in the presence of nonsymmetrical potential terms. For illustration purposes, we extract the exact bound-state solutions of the Dirac equation with the noncentral Hartmann potential for the cases of exact SU(2) spin and pseudospin symmetries. Also, we have shown that both Dirac-radial and Dirac-polar parts are sensitive to the variation of the involved parameters.
Hidden symmetry and protection of Dirac points on the honeycomb lattice
Hou, Jing-Min; Chen, Wei
2015-01-01
The honeycomb lattice possesses a novel energy band structure, which is characterized by two distinct Dirac points in the Brillouin zone, dominating most of the physical properties of the honeycomb structure materials. However, up till now, the origin of the Dirac points is unclear yet. Here, we discover a hidden symmetry on the honeycomb lattice and prove that the existence of Dirac points is exactly protected by such hidden symmetry. Furthermore, the moving and merging of the Dirac points and a quantum phase transition, which have been theoretically predicted and experimentally observed on the honeycomb lattice, can also be perfectly explained by the parameter dependent evolution of the hidden symmetry. PMID:26639178
NASA Astrophysics Data System (ADS)
Rodionov, V. N.
2015-11-01
The modified Dirac-Pauli equations, which is entered by means of γ 5-mass extension of Hamiltonian operators, are considered. We also take into account the interaction of fermions with the intensive homogenous magnetic field focusing attention on (g-2) gyromagnetic factor of particles with spin 1/2. Without the use of perturbation theory in the external field the exact energy spectra are deduced with regard to spin effects of fermions. We discuss the possible proposals of experimental measuring of properties of new particles which arising in this model.
NASA Astrophysics Data System (ADS)
Wu, Shuang-Qing
2008-09-01
The Dirac equation for the electron around a five-dimensional rotating black hole with two different angular momenta is separated into purely radial and purely angular equations. The general solution is expressed as a superposition of solutions derived from these two decoupled ordinary differential equations. By separating variables for the massive Klein-Gordon equation in the same spacetime background, I derive a simple and elegant form for the Stäckel-Killing tensor, which can be easily written as the square of a rank-three Killing-Yano tensor. I have also explicitly constructed a symmetry operator that commutes with the scalar Laplacian by using the Stäckel-Killing tensor, and the one with the Dirac operator by the Killing-Yano tensor admitted by the five-dimensional Myers-Perry metric, respectively.
Wu Shuangqing
2008-09-15
The Dirac equation for the electron around a five-dimensional rotating black hole with two different angular momenta is separated into purely radial and purely angular equations. The general solution is expressed as a superposition of solutions derived from these two decoupled ordinary differential equations. By separating variables for the massive Klein-Gordon equation in the same spacetime background, I derive a simple and elegant form for the Staeckel-Killing tensor, which can be easily written as the square of a rank-three Killing-Yano tensor. I have also explicitly constructed a symmetry operator that commutes with the scalar Laplacian by using the Staeckel-Killing tensor, and the one with the Dirac operator by the Killing-Yano tensor admitted by the five-dimensional Myers-Perry metric, respectively.
Universal quantum criticality in Hubbard models with massless Dirac dispersion
NASA Astrophysics Data System (ADS)
Otsuka, Yuichi; Yunoki, Seiji; Sorella, Sandro
We investigate the metal-insulator transition of two-dimensional interacting electrons with massless Dirac-like dispersion, describe by the Hubbard models on two geometrically different lattices: honeycomb and π-flux square lattices. By performing large-scale quantum Monte Carlo simulations followed by careful finite-size scaling analyses, we find that the transition from semi-metallic to antiferromagnetic insulating phases is continuous and evaluate the critical exponents with a high degree of accuracy for the corresponding universality class, which is described in the continuous limit by the Gross-Neveu model. We furthermore discuss the fate of the quasiparticle weight and the Fermi velocity across this transition.
New scale-relativistic derivations of Pauli and Dirac equations
NASA Astrophysics Data System (ADS)
Hammad, F.
2008-02-01
In scale relativity, quantum mechanics is recovered by transcribing the classical equations of motion to fractal spaces and demanding, as dictated by the principle of scale relativity, that the form of these equations be preserved. In the framework of this theory, however, the form of the classical energy equations both in the relativistic and nonrelativistic cases are not preserved. Aiming to get full covariance, i.e., to restore to these equations their classical forms, we show that the scale-relativistic form of the Schrödinger equation yields the Pauli equation, whilst the Pissondes's scale-relativistic form of the Klein-Gordon equation gives the Dirac equation.
Derivation of the Generally Covariant Generalization of the Dirac Equation
Maker, David
2010-09-30
From the Occam's razor optimized assumption of a geometric point we derive a new generally covariant generalization of the Dirac equation. We solve that equation in domains r>r{sub H}, r{approx_equal}r{sub H}, and r
Scanning tunneling spectroscopy study of the Dirac spectrum of germanene
NASA Astrophysics Data System (ADS)
Walhout, C. J.; Acun, A.; Zhang, L.; Ezawa, M.; Zandvliet, H. J. W.
2016-07-01
The temperature dependence of the density of states of germanene, synthesized on Ge/Pt crystals, has been investigated with scanning tunneling spectroscopy. After correction for thermal broadening, a virtually perfect V-shaped density of states, which is a hallmark of a two-dimensional Dirac system, has been found. In an attempt to directly measure the energy dispersion relation via quasiparticle interference we have recorded spatial maps of the differential conductivity near the edges and defects of germanene. Unfortunately, we did not find any sign of Friedel oscillations. The absence of these Friedel oscillations hints to the occurrence of Klein tunneling.
Scaling laws for nonlinear electromagnetic responses of Dirac fermion
NASA Astrophysics Data System (ADS)
Morimoto, Takahiro; Nagaosa, Naoto
2016-03-01
We theoretically propose that the Dirac fermion in two dimensions shows the giant nonlinear responses to electromagnetic fields in the terahertz region. A scaling form is obtained for the current and magnetization as functions of the normalized electromagnetic fields E /Eω and B /Bω , where the characteristic electric (magnetic) field Eω(Bω) depends on the frequency ω as ℏ ω2/e vF(ℏ ω2/e vF2) , and is typically of the order of 80 V/cm (8 mT) in the terahertz region. Applications of the present theory to graphene and surface state of a topological insulator are discussed.
Scaling of Dirac Fermions and the WKB approximation
Sabine Jeschonnek; John Tjon; Jay Van Orden
2005-07-01
We discuss a new method for obtaining the WKB approximation to the Dirac equation with a scalar potential and a time-like vector potential. We use the WKB solutions to investigate the scaling behavior of a confining model for quark-hadron duality. In this model, a light quark is bound to a heavy di-quark by a linear scalar potential. Absorption of virtual photons promotes the quark to bound states. The analog of the parton model for this case is for a virtual photon to eject the bound, ground-state quark directly into free continuum states. We compare the scaling limits of the response functions for these two transitions.
Flat-band superconductivity in strained Dirac materials
NASA Astrophysics Data System (ADS)
Kauppila, V. J.; Aikebaier, F.; Heikkilä, T. T.
2016-06-01
We consider superconducting properties of a two-dimensional Dirac material such as graphene under strain that produces a flat-band spectrum in the normal state. We show that in the superconducting state, such a model results in a highly increased critical temperature compared to the case without the strain, inhomogeneous order parameter with two-peak shaped local density of states and yet a large and almost uniform and isotropic supercurrent. This model could be realized in strained graphene or ultracold atom systems and could be responsible for unusually strong superconductivity observed in some graphite interfaces and certain IV-VI semiconductor heterostructures.
Phase structure of a holographic double monolayer Dirac semimetal
NASA Astrophysics Data System (ADS)
Grignani, Gianluca; Marini, Andrea; Pigna, Adriano-Costantino; Semenoff, Gordon W.
2016-06-01
We study a holographic D3/probe-D5-brane model of a double monolayer Dirac semimetal in a magnetic field and in the presence of a nonzero temperature. Intra-and inter-layer exciton condensates can form by varying the balanced charge density on the layers, the spatial separation and the temperature. Constant temperature phase diagrams for a wide range of layer separations and charge densities are found. The presence of a finite temperature makes the phase diagrams extremely rich and in particular leads to the appearance of a symmetric phase which was missing at zero temperature.
Optomechanical Metamaterials: Dirac polaritons, Gauge fields, and Instabilities
NASA Astrophysics Data System (ADS)
Peano, Vittorio; Schmidt, Michael; Marquardt, Florian
2014-03-01
Freestanding photonic crystals can be used to trap both light and mechanical vibrations. These ``optomechanical crystal'' structures have already been experimentally demonstrated to yield strong coupling between a photon mode and a phonon mode, co-localized at a single defect site. Future devices may feature a regular superlattice of such defects, turning them into ``optomechanical arrays.'' We predict that tailoring the optomechanical band structure of such arrays can be used to implement Dirac physics of photons and phonons, to create a photonic gauge field via mechanical vibrations, and to observe a novel optomechanical instability. ERC Starting Grant OPTOMECH and via the DARPA program ORCHID.
Spin-rotation couplings: spinning test particles and Dirac field
NASA Astrophysics Data System (ADS)
Bini, Donato; Lusanna, Luca
2008-06-01
The hypothesis of coupling between spin and rotation introduced long ago by Mashhoon is examined in the context of “1 + 3” and “3 + 1” space-time splitting techniques, either in special or in general relativity. Its content is discussed in terms of classical (Mathisson-Papapetrou-Dixon-Souriou model) as well as quantum physics (Foldy-Wouthuysen transformation for the Dirac field in an external field), reviewing and discussing all the relevant theoretical literature concerning the existence of such effect. Some original contributions are also included.
The cylindrical δ-potential and the Dirac equation
NASA Astrophysics Data System (ADS)
Loewe, M.; Marquez, F.; Zamora, R.
2012-11-01
In this paper, we discuss the Dirac equation in the presence of an attractive cylindrical δ-shell potential V(ρ) = -aδ(ρ - ρ0), where ρ is the radial coordinate and a > 0. We present a detailed discussion on the boundary conditions the wavefunction has to satisfy when crossing the support of the potential, proceeding then to explore the dependence of the ground state on the parameter a, analyzing the occurrence of supercritical effects. We also apply the Foldy-Wouthuysen transformation, discussing the non-relativistic limit of this problem.
Scanning tunneling spectroscopy study of the Dirac spectrum of germanene.
Walhout, C J; Acun, A; Zhang, L; Ezawa, M; Zandvliet, H J W
2016-07-20
The temperature dependence of the density of states of germanene, synthesized on Ge/Pt crystals, has been investigated with scanning tunneling spectroscopy. After correction for thermal broadening, a virtually perfect V-shaped density of states, which is a hallmark of a two-dimensional Dirac system, has been found. In an attempt to directly measure the energy dispersion relation via quasiparticle interference we have recorded spatial maps of the differential conductivity near the edges and defects of germanene. Unfortunately, we did not find any sign of Friedel oscillations. The absence of these Friedel oscillations hints to the occurrence of Klein tunneling. PMID:27227390
Helical Spin Order from Topological Dirac and Weyl Semimetals
NASA Astrophysics Data System (ADS)
Sun, Xiao-Qi; Zhang, Shou-Cheng; Wang, Zhong
2015-08-01
We study dynamical mass generation and the resultant helical spin orders in topological Dirac and Weyl semimetals, including the edge states of quantum spin Hall insulators, the surface states of weak topological insulators, and the bulk materials of Weyl semimetals. In particular, the helical spin textures of Weyl semimetals manifest the spin-momentum locking of Weyl fermions in a visible manner. The spin-wave fluctuations of the helical order carry electric charge density; therefore, the spin textures can be electrically controlled in a simple and predictable manner.
Tunable Dirac points and perfect transmission in asymmetric graphene superlattices
NASA Astrophysics Data System (ADS)
Zhang, Rui-Li; Li, Jin-Jing; Zhou, Yu; Peng, Ru-Wen; Huang, Run-Sheng; Wang, Mu
2015-08-01
We investigated the electronic band structures and transport properties in asymmetric graphene superlattices (AGSLs). Their asymmetric distribution of potentials can induce extra Dirac points (DPs) that are absent in periodic and symmetric graphene superlattices. The emergence and location of the DPs in the k space can be manipulated by selecting the special structure of the AGSL. As a result, tunable perfect transmissions are obtained in the system. Moreover, the conductance and Fano factor present interesting oscillatory behaviors. These findings may be used for the design of graphene-based electronic devices.
Dirac lines in the superconducting hyper-honeycomb lattice
NASA Astrophysics Data System (ADS)
Bouhon, Adrien; Black-Schaffer, Annica
Motivated by the recent discovery of the hyper-honeycomb β-Li2IrO3 studied in the context of Kitaev spin liquids, we investigate the possibility to realize superconductivity in the hyper-honeycomb lattice. Based on a t-J model we discuss the effect of the band structure and spin-orbit coupling on the most stable superconducting state. Using group theory we construct all symmetry allowed superconducting states and show that we naturally get Dirac line nodes protected by the non-symmorphic symmetries.
Confinement of Dirac electrons in graphene quantum dots
NASA Astrophysics Data System (ADS)
Jolie, Wouter; Craes, Fabian; Petrović, Marin; Atodiresei, Nicolae; Caciuc, Vasile; Blügel, Stefan; Kralj, Marko; Michely, Thomas; Busse, Carsten
2014-04-01
We observe spatial confinement of Dirac states on epitaxial graphene quantum dots with low-temperature scanning tunneling microscopy after using oxygen as an intercalant to suppress the surface state of Ir(111) and to effectively decouple graphene from its metal substrate. We analyze the confined electronic states with a relativistic particle-in-a-box model and find a linear dispersion relation. The oxygen-intercalated graphene is p doped [ED=0.64±0.07 eV] and has a Fermi velocity close to the one of free-standing graphene [vF=0.96±0.07×106 m/s].
Spin-polarized gapped Dirac spectrum of unsupported silicene
NASA Astrophysics Data System (ADS)
Podsiadły-Paszkowska, A.; Krawiec, M.
2016-06-01
We study effects of the spin-orbit interaction and the atomic reconstruction of silicene on its electronic spectrum. As an example we consider unsupported silicene pulled off from Pb(111) substrate. Using first principles density functional theory we show that the inversion symmetry broken arrangement of atoms and the spin-orbit interaction generate a spin-polarized electronic spectrum with an energy gap in the Dirac cone. These findings are particularly interesting in view of the quantum anomalous and quantum valley Hall effects and should be observable in weakly interacting silicene-substrate systems.
Ultrafast exciton-polariton scattering towards the Dirac points.
Kovalev, V M; Savenko, I G; Iorsh, I V
2016-03-16
Using the Feynman-Dyson diagram technique, we study nonlinear polariton-polariton scattering in a two-dimensional micropillar-based optical superlattice with hexagonal symmetry. We demonstrate that both the emerging polariton chirality and the loop Feynman diagrams up to infinite order should be strictly accounted for in the evaluation of the self-energy of the system. Further, we explicitly show that in such a design the time of polariton scattering towards the Dirac points can be drastically decreased which can be used, for instance, in engineering novel classes of polariton lasers with substantially reduced thresholds. PMID:26886717
Phase-integral method for the radial Dirac equation
Linnæus, Staffan
2014-09-15
A phase-integral (WKB) solution of the radial Dirac equation is calculated up to the third order of approximation, retaining perfect symmetry between the two components of the wave function and introducing no singularities except at the zeroth-order transition points. The potential is allowed to be of scalar, vector, or tensor type, or any combination of these. The connection problem is investigated in detail. Explicit formulas are given for single-turning-point phase shifts and single-well energy levels.
The bundles of algebraic and Dirac-Hestenes spinor fields
NASA Astrophysics Data System (ADS)
Mosna, Ricardo A.; Rodrigues, Waldyr A.
2004-07-01
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,∇,τg,↑) 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 (ClSpin1,3el(M)) and right (ClSpin1,3er(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 ClSpin1,3el(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∈sec ClSpin1,3el(M) (denoted DECll) on a Lorentzian spacetime is found. We also obtain a representation of the DECll in the Clifford bundle Cl(M,g). It is such equation that we call the DHE and it is satisfied by Clifford fields ψⅪ∈sec Cl(M,g). This means that to each DHSF Ψ∈sec ClSpin1,3el(M) and spin frame Ⅺ∈sec PSpin1,3e(M), there is a well-defined sum of even multivector fields ψⅪ∈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 DECll and the DHE, although related, are equations of different mathematical natures. We study also the local Lorentz invariance and the electromagnetic gauge invariance and show that only for the DHE such
A generally relativistic gauge classification of the Dirac fields
NASA Astrophysics Data System (ADS)
Fabbri, Luca
2016-04-01
We consider generally relativistic gauge transformations for the spinorial fields finding two mutually exclusive but together exhaustive classes in which fermions are placed adding supplementary information to the results obtained by Lounesto, and identifying quantities analogous to the momentum vector and the Pauli-Lubanski axial vector. We discuss how our results are similar to those obtained by Wigner by taking into account the system of Dirac field equations. We will investigate the consequences for the dynamics and in particular we shall address the problem of getting the nonrelativistic approximation in a consistent way. We are going to comment on extensions.
On the Pauli-Weisskopf anti-Dirac paper
NASA Astrophysics Data System (ADS)
Dittrich, Walter
2015-03-01
We review in this article the role which the work of Pauli and Weisskopf played in formulating a quantum field theory of spinless particles. To make our computations as transparent as possible, we offer a physicist's derivation of the Klein-Gordon-Fock equation. Since invariant functions play a significant part in our paper, we will discuss them in great detail. We emphasize Pauli's and Weisskopf's view that Dirac's hole theory is totally obsolete in formulating a consistent quantum field theory, be it for scalar or spinor particles. As an important example we present the calculation for producing charged scalar particles in an external electric field.
Charge Puddles in Graphene near the Dirac Point
NASA Astrophysics Data System (ADS)
Samaddar, S.; Yudhistira, I.; Adam, S.; Courtois, H.; Winkelmann, C. B.
2016-03-01
The charge carrier density in graphene on a dielectric substrate such as SiO2 displays inhomogeneities, the so-called charge puddles. Because of the linear dispersion relation in monolayer graphene, the puddles are predicted to grow near charge neutrality, a markedly distinct property from conventional two-dimensional electron gases. By performing scanning tunneling microscopy and spectroscopy on a mesoscopic graphene device, we directly observe the puddles' growth, both in spatial extent and in amplitude, as the Fermi level approaches the Dirac point. Self-consistent screening theory provides a unified description of both the macroscopic transport properties and the microscopically observed charge disorder.
Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3
NASA Astrophysics Data System (ADS)
Fuhrer, Michael
2013-03-01
The three dimensional strong topological insulator (STI) is a new phase of electronic matter which is distinct from ordinary insulators in that it supports on its surface a conducting two-dimensional surface state whose existence is guaranteed by topology. I will discuss experiments on the STI material Bi2Se3, which has a bulk bandgap of 300 meV, much greater than room temperature, and a single topological surface state with a massless Dirac dispersion. Field effect transistors consisting of thin (3-20 nm) Bi2Se3 are fabricated from mechanically exfoliated from single crystals, and electrochemical and/or chemical gating methods are used to move the Fermi energy into the bulk bandgap, revealing the ambipolar gapless nature of transport in the Bi2Se3 surface states. The minimum conductivity of the topological surface state is understood within the self-consistent theory of Dirac electrons in the presence of charged impurities. The intrinsic finite-temperature resistivity of the topological surface state due to electron-acoustic phonon scattering is measured to be ~60 times larger than that of graphene largely due to the smaller Fermi and sound velocities in Bi2Se3, which will have implications for topological electronic devices operating at room temperature. As samples are made thinner, coherent coupling of the top and bottom topological surfaces is observed through the magnitude of the weak anti-localization correction to the conductivity, and, in the thinnest Bi2Se3 samples (~ 3 nm), in thermally-activated conductivity reflecting the opening of a bandgap.
Weak cosmic censorship, dyonic Kerr-Newman black holes and Dirac fields
NASA Astrophysics Data System (ADS)
Zsolt Tóth, Gábor
2016-06-01
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.
On the electronic viscosity of a Dirac fluid in deformed graphene
NASA Astrophysics Data System (ADS)
Sergeenkov, Sergei; Ausloos, Marcel
2016-03-01
We discuss the properties of the electronic viscosity of a Dirac fluid in deformed graphene by introducing a strain ? and a velocity gradient ?, as equivalent to a pseudo-magnetic ? and a pseudo-electric ? field respectively into the Dirac equation. It is thereby analytically established that the dynamic shear viscosity coefficient ? substantially decreases with the applied strain as ?, reaching as much as ? for ?.
Constraints on Space-Time Manifold in Euclidean Supergravity in Terms of Dirac Eigenvalues
NASA Astrophysics Data System (ADS)
Ciuhu, C.; Vancea, Ion V.
We generalize a previous work on Dirac eigenvalues as dynamical variables of Euclidean supergravity. The most general set of constraints on the curvatures of the tangent bundle and on the spinor bundle of the space-time manifold, under which space-time admits Dirac eigenvalues as observables, are derived.
On the symplectic two-form of gravity in terms of Dirac eigenvalues
NASA Astrophysics Data System (ADS)
Abdalla, M. C. B.; De Andrade, M. A.; Santos, M. A.; Vancea, I. V.
2002-11-01
The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equations defining the components of the symplectic form in this framework.
The Dirac Equation in the Bertotti-Robinson Space-Time
NASA Astrophysics Data System (ADS)
Sakalli, I.
2003-08-01
The Dirac equation is considered in the uniform electromagnetic field space of Bertotti-Robinson with charge coupling. The methods of separation of variables and decoupling are easily achieved. The separated axial equation is reduced to a rare Riccati type of differential equation. The behaviour of potentials, their asymptotic solutions and the conserved currents of the Dirac equation are found.
Comment on 'Zero-range potentials for Dirac particles: Scattering and related continuum problems'
Coutinho, F. A. B.; Nogami, Y.
2006-02-15
In a recent paper, Szmytkowski proposed zero-range potentials for Dirac particles in three space dimensions. On the other hand, there is a theorem, proved by Svendsen a long time ago, which implies that zero-range potentials cannot be defined for the Dirac equation in two and three space dimensions. We discuss a difficulty that underlies Szmytkowski's approach.
Spatial fluctuations of helical Dirac fermions on the surface of topological insulators
NASA Astrophysics Data System (ADS)
Beidenkopf, Haim; Roushan, Pedram; Seo, Jungpil; Gorman, Lindsay; Drozdov, Ilya; Hor, Yew San; Cava, R. J.; Yazdani, Ali
2011-12-01
Surfaces of topological insulators host a new class of states with Dirac dispersion and helical spin texture. Potential quantum computing and spintronic applications using these states require manipulation of their electronic properties at the Dirac energy of their band structure by inducing magnetism or superconductivity through doping and the proximity effect. Yet, the response of these states near the Dirac energy in their band structure to various perturbations has remained unexplored. Here we use spectroscopic mapping with the scanning tunnelling microscope to study their response to magnetic and non-magnetic bulk dopants in Bi2Te3 and Bi2Se3. Far from the Dirac energy, helicity provides remarkable resilience to backscattering even in the presence of ferromagnetism. However, approaching the Dirac point, where the surface states' wavelength diverges, bulk doping results in pronounced nanoscale spatial fluctuations of energy, momentum and helicity. Our results and their connection with similar studies of Dirac electrons in graphene demonstrate that although backscattering and localization are absent for Dirac topological surface states, reducing charge defects is required for both tuning the chemical potential to the Dirac energy and achieving high electrical mobility for these novel states.
Can neutrino-electron scattering tell us whether neutrinos are Dirac or Majorana particles
Kayser, B.
1988-04-01
There has recently been interest in the possibility that neutrino-electron scattering experiments could determine whether neutrinos are Dirac or Majorana particles by providing information on their electromagnetic structure. We try to explain why studies of neutrino electromagnetic structure actually cannot distinguish between Dirac and Majorana neutrinos. 9 refs.
Zeljkovic, Ilija; Okada, Yoshinori; Serbyn, Maksym; Sankar, R; Walkup, Daniel; Zhou, Wenwen; Liu, Junwei; Chang, Guoqing; Wang, Yung Jui; Hasan, M Zahid; Chou, Fangcheng; Lin, Hsin; Bansil, Arun; Fu, Liang; Madhavan, Vidya
2015-03-01
The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb1-xSnxSe for a wide range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons-a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent with our measurements. Finally, we discover the existence of surface states in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions and could be exploited in realizing superconductivity in these materials. PMID:25686261
Constraint Structure and Quantization of a Non-Abelian Gauge Theory by Means of Dirac Brackets
NASA Astrophysics Data System (ADS)
Bracken, Paul
An SO(3) non-Abelian gauge theory is introduced. The Hamiltonian density is determined and the constraint structure of the model is derived. The first-class constraints are obtained and gauge-fixing constraints are introduced into the model. Finally, using the constraints, the Dirac brackets can be determined and a canonical quantization is found using Dirac's procedure.
Photonic crystal surface-emitting lasers enabled by an accidental Dirac point
Chua, Song Liang; Lu, Ling; Soljacic, Marin
2014-12-02
A photonic-crystal surface-emitting laser (PCSEL) includes a gain medium electromagnetically coupled to a photonic crystal whose energy band structure exhibits a Dirac cone of linear dispersion at the center of the photonic crystal's Brillouin zone. This Dirac cone's vertex is called a Dirac point; because it is at the Brillouin zone center, it is called an accidental Dirac point. Tuning the photonic crystal's band structure (e.g., by changing the photonic crystal's dimensions or refractive index) to exhibit an accidental Dirac point increases the photonic crystal's mode spacing by orders of magnitudes and reduces or eliminates the photonic crystal's distributed in-plane feedback. Thus, the photonic crystal can act as a resonator that supports single-mode output from the PCSEL over a larger area than is possible with conventional PCSELs, which have quadratic band edge dispersion. Because output power generally scales with output area, this increase in output area results in higher possible output powers.
Aharonov–Bohm oscillations in Dirac semimetal Cd3As2 nanowires
Wang, Li-Xian; Li, Cai-Zhen; Yu, Da-Peng; Liao, Zhi-Min
2016-01-01
Three-dimensional Dirac semimetals, three-dimensional analogues of graphene, are unusual quantum materials with massless Dirac fermions, which can be further converted to Weyl fermions by breaking time reversal or inversion symmetry. Topological surface states with Fermi arcs are predicted on the surface and have been observed by angle-resolved photoemission spectroscopy experiments. Although the exotic transport properties of the bulk Dirac cones have been demonstrated, it is still a challenge to reveal the surface states via transport measurements due to the highly conductive bulk states. Here, we show Aharonov–Bohm oscillations in individual single-crystal Cd3As2 nanowires with low carrier concentration and large surface-to-volume ratio, providing transport evidence of the surface state in three-dimensional Dirac semimetals. Moreover, the quantum transport can be modulated by tuning the Fermi level using a gate voltage, enabling a deeper understanding of the rich physics residing in Dirac semimetals. PMID:26902716
Dirac cone shift of a passivated topological Bi2Se3 interface state
NASA Astrophysics Data System (ADS)
Jenkins, Gregory S.; Schmadel, Don C.; Sushkov, Andrei B.; Drew, H. Dennis; Bichler, Max; Koblmueller, Gregor; Brahlek, Matthew; Bansal, Namrata; Oh, Seongshik
2013-04-01
Gated terahertz cyclotron resonance measurements on epitaxial Bi2Se3 thin films capped with In2Se3 enable the first spectroscopic characterization of a single topological interface state from the vicinity of the Dirac point to above the conduction band edge. A precipitous drop in the scattering rate with Fermi energy is observed, which is interpreted as the surface state decoupling from bulk states and evidence of a shift of the Dirac point towards mid-gap. Near the Dirac point, potential fluctuations of 50 meV are deduced from an observed loss of differential optical spectral weight near the Dirac point. Potential fluctuations are reduced by a factor of two at higher surface Fermi levels in the vicinity of the conduction band edge inferred from the width of the scattering rate step. The passivated topological interface state attains a high mobility of 3500 cm2/V s near the Dirac point.
Aharonov-Bohm oscillations in Dirac semimetal Cd3As2 nanowires
NASA Astrophysics Data System (ADS)
Wang, Li-Xian; Li, Cai-Zhen; Yu, Da-Peng; Liao, Zhi-Min
2016-02-01
Three-dimensional Dirac semimetals, three-dimensional analogues of graphene, are unusual quantum materials with massless Dirac fermions, which can be further converted to Weyl fermions by breaking time reversal or inversion symmetry. Topological surface states with Fermi arcs are predicted on the surface and have been observed by angle-resolved photoemission spectroscopy experiments. Although the exotic transport properties of the bulk Dirac cones have been demonstrated, it is still a challenge to reveal the surface states via transport measurements due to the highly conductive bulk states. Here, we show Aharonov-Bohm oscillations in individual single-crystal Cd3As2 nanowires with low carrier concentration and large surface-to-volume ratio, providing transport evidence of the surface state in three-dimensional Dirac semimetals. Moreover, the quantum transport can be modulated by tuning the Fermi level using a gate voltage, enabling a deeper understanding of the rich physics residing in Dirac semimetals.
Magnetic Torque Anomaly in the Quantum Limit of Weyl and Dirac Semimetals
NASA Astrophysics Data System (ADS)
Nair, Nityan L.; Moll, Philip J. W.; Potter, Andrew C.; Ramshaw, Brad; Modic, Kimberly; Riggs, Scott; Zeng, Bin; Ghimire, Nirmal; Bauer, Eric; Kealhofer, Robert; Li, Zhenglu; Louie, Steven; Ronning, Filip; Analytis, James G.
Three dimensional Dirac and Weyl semimetals, characterized by bulk quasiparticles that behave as massless, linearly dispersing Dirac or Weyl fermions, have excited physicists with their unique topological properties and potential for applications. The experimental signatures of Weyl or Dirac fermions, however, are often subtle and indirect, especially in systems where they coexist with trivial electrons. Here, we report a novel method by which these topological systems can be unambiguously experimentally identified. Magnetic torque measurements were performed on the Weyl semimetal NbAs in high magnetic field, showing a large anomaly upon entering the quantum limit. The torque exhibits a striking sign reversal, corresponding to a change in the magnetic anisotropy that is a direct result of the topological properties of the charge carriers. This result can be generalized to other Dirac and Weyl semimetal systems and establishes quantum limit torque measurements as a simple and direct experimental method of distinguishing topologically non-trivial Weyl and Dirac systems from trivial semiconductors.
NASA Astrophysics Data System (ADS)
Bian, Guang; Chung, Ting-Fung; Chen, Chaoyu; Liu, Chang; Chang, Tay-Rong; Wu, Tailung; Belopolski, Ilya; Zheng, Hao; Xu, Su-Yang; Sanchez, Daniel S.; Alidoust, Nasser; Pierce, Jonathan; Quilliams, Bryson; Barletta, Philip P.; Lorcy, Stephane; Avila, José; Chang, Guoqing; Lin, Hsin; Jeng, Horng-Tay; Asensio, Maria-Carmen; Chen, Yong P.; Zahid Hasan, M.
2016-06-01
Graphene and topological insulators (TI) possess two-dimensional (2D) Dirac fermions with distinct physical properties. Integrating these two Dirac materials in a single device creates interesting opportunities for exploring new physics of interacting massless Dirac fermions. Here we report on a practical route to experimental fabrication of graphene–Sb2Te3 heterostructure. The graphene–TI heterostructures are prepared by using a dry transfer of chemical-vapor-deposition grown graphene film. ARPES measurements confirm the coexistence of topological surface states of Sb2Te3 and Dirac π bands of graphene, and identify the twist angle in the graphene–TI heterostructure. The results suggest a potential tunable electronic platform in which two different Dirac low-energy states dominate the transport behavior.
Hirata, Michihiro; Ishikawa, Kyohei; Miyagawa, Kazuya; Tamura, Masafumi; Berthier, Claude; Basko, Denis; Kobayashi, Akito; Matsuno, Genki; Kanoda, Kazushi
2016-01-01
The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials. PMID:27578363
Terahertz-induced acceleration of massive Dirac electrons in semimetal bismuth.
Minami, Yasuo; Araki, Kotaro; Dao, Thang Duy; Nagao, Tadaaki; Kitajima, Masahiro; Takeda, Jun; Katayama, Ikufumi
2015-01-01
Dirac-like electrons in solid state have been of great interest since they exhibit many peculiar physical behaviors analogous to relativistic mechanics. Among them, carriers in graphene and surface states of topological insulators are known to behave as massless Dirac fermions with a conical band structure in the two-dimensional momentum space, whereas electrons in semimetal bismuth (Bi) are expected to behave as massive Dirac-like fermions in the three-dimensional momentum space, whose dynamics is of particular interest in comparison with that of the massless Dirac fermions. Here, we demonstrate that an intense terahertz electric field transient accelerates the massive Dirac-like fermions in Bi from classical Newtonian to the relativistic regime; the electrons are accelerated approaching the effective "speed of light" with the "relativistic" beta β = 0.89 along the asymptotic linear band structure. As a result, the effective electron mass is enhanced by a factor of 2.4. PMID:26522668
Aharonov-Bohm oscillations in Dirac semimetal Cd3As2 nanowires.
Wang, Li-Xian; Li, Cai-Zhen; Yu, Da-Peng; Liao, Zhi-Min
2016-01-01
Three-dimensional Dirac semimetals, three-dimensional analogues of graphene, are unusual quantum materials with massless Dirac fermions, which can be further converted to Weyl fermions by breaking time reversal or inversion symmetry. Topological surface states with Fermi arcs are predicted on the surface and have been observed by angle-resolved photoemission spectroscopy experiments. Although the exotic transport properties of the bulk Dirac cones have been demonstrated, it is still a challenge to reveal the surface states via transport measurements due to the highly conductive bulk states. Here, we show Aharonov-Bohm oscillations in individual single-crystal Cd3As2 nanowires with low carrier concentration and large surface-to-volume ratio, providing transport evidence of the surface state in three-dimensional Dirac semimetals. Moreover, the quantum transport can be modulated by tuning the Fermi level using a gate voltage, enabling a deeper understanding of the rich physics residing in Dirac semimetals. PMID:26902716
Higher-degree Dirac currents of twistor and Killing spinors in supergravity theories
NASA Astrophysics Data System (ADS)
Açık, Özgür; Ertem, Ümit
2015-09-01
We show that higher degree Dirac currents of twistor and Killing spinors correspond to the hidden symmetries of the background spacetime which are generalizations of conformal Killing and Killing vector fields respectively. They are the generalizations of one-form Dirac currents to higher degrees which are used in constructing the bosonic supercharges in supergravity theories. In the case of Killing spinors, we find that the equations satisfied by the higher degree Dirac currents are related to Maxwell-like and Duffin-Kemmer-Petiau equations. Correspondence between the Dirac currents and harmonic forms for parallel and pure spinor cases is determined. We also analyze the supergravity twistor and Killing spinor cases in ten and eleven-dimensional supergravity theories and find that although different inner product classes induce different involutions on spinors, the higher degree Dirac currents still correspond to the hidden symmetries of the spacetime.
Field-induced polarization of Dirac valleys in bismuth
NASA Astrophysics Data System (ADS)
Behnia, Kamran; Zhu, Zengwei; Callaudin, Aurelie; Fauque, Benoit; Kang, Woun
2012-02-01
The principal challenge in the field of ``valleytronics'' is to lift the valley degeneracy of electrons in a controlled way. In graphene, a number of methods to generate a valley-polarized flow of electrons have been proposed, which are yet to be experimentally realized. In bulk semi-metallic bismuth, the Fermi surface includes three cigar-shaped electron valleys lying almost perpendicular to the high-symmetry axis known as the trigonal axis. The in-plane mass anisotropy of each valley exceeds 200 as a consequence of Dirac dispersion, which drastically reduces the effective mass along two out of the three orientations. We present a study of angle-dependent magnetoresistance in bismuth which shows that a flow of Dirac electrons along the trigonal axis is extremely sensitive to the orientation of in-plane magnetic field. The effect is visible even at room temperature. Thus, a rotatable magnetic field can be used as a valley valve to tune the contribution of each valley to the total conductivity. At high temperature and low magnetic field, the three valleys are interchangeable and the three-fold symmetry of the underlying lattice is respected. As the temperature is decreased or the magnetic field increased, this symmetry is spontaneously lost. This loss may be an experimental manifestation of the recently proposed valley-nematic Fermi liquid state.
Size quantization of Dirac fermions in graphene constrictions
Terrés, B.; Chizhova, L. A.; Libisch, F.; Peiro, J.; Jörger, D.; Engels, S.; Girschik, A.; Watanabe, K.; Taniguchi, T.; Rotkin, S. V.; Burgdörfer, J.; Stampfer, C.
2016-01-01
Quantum point contacts are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wavelength in high-quality bulk graphene can be tuned up to hundreds of nanometres, the observation of quantum confinement of Dirac electrons in nanostructured graphene has proven surprisingly challenging. Here we show ballistic transport and quantized conductance of size-confined Dirac fermions in lithographically defined graphene constrictions. At high carrier densities, the observed conductance agrees excellently with the Landauer theory of ballistic transport without any adjustable parameter. Experimental data and simulations for the evolution of the conductance with magnetic field unambiguously confirm the identification of size quantization in the constriction. Close to the charge neutrality point, bias voltage spectroscopy reveals a renormalized Fermi velocity of ∼1.5 × 106 m s−1 in our constrictions. Moreover, at low carrier density transport measurements allow probing the density of localized states at edges, thus offering a unique handle on edge physics in graphene devices. PMID:27198961
Dirac plasmons in bipartite lattices of metallic nanoparticles
NASA Astrophysics Data System (ADS)
Jebb Sturges, Thomas; Woollacott, Claire; Weick, Guillaume; Mariani, Eros
2015-03-01
We study theoretically ‘graphene-like’ plasmonic metamaterials constituted by two-dimensional arrays of metallic nanoparticles, including perfect honeycomb structures with and without inversion symmetry, as well as generic bipartite lattices. The dipolar interactions between localized surface plasmons (LSPs) in different nanoparticles gives rise to collective plasmons (CPs) that extend over the whole lattice. We study the band structure of CPs and unveil its tunability with the orientation of the dipole moments associated with the LSPs. Depending on the dipole orientation, we identify a phase diagram of gapless or gapped phases in the CP dispersion. We show that the gapless phases in the phase diagram are characterized by CPs behaving as massless chiral Dirac particles, in analogy with electrons in graphene. When the inversion symmetry of the honeycomb structure is broken, CPs are described as gapped chiral Dirac modes with an energy-dependent Berry phase. We further relax the geometric symmetry of the honeycomb structure by analysing generic bipartite hexagonal lattices. In this case we study the evolution of the phase diagram and unveil the emergence of a sequence of topological phase transitions when one hexagonal sublattice is progressively shifted with respect to the other.
Are the surface Fermi arcs in Dirac semimetals topologically protected?
NASA Astrophysics Data System (ADS)
Lu, Yuan Ming; Kargarian, Mehdi; Randeria, Mohit
Motivated by recent experiments probing double Fermi arcs on the surface of Dirac semimetals (DSMs) Na3Bi and Cd3As2, we raise the question posed in the title. We find that, in marked contrast to Weyl semimetals, the Fermi arcs of DSMs are not topologically protected in general, except at certain time-reversal invariant momenta. For a simple 4-band model with a pair of Dirac nodes at k = (0, 0, +/-Q) gapless surface states are protected only at kz = 0. We identify symmetry allowed bulk perturbations that destroy Fermi arcs, but show that they are necessarily ``small'', i.e., higher order than terms kept in usual k . p theory. We validate our conclusions about the absence of a topological invariant protecting the surface states in DSMs using a K-theory analysis for the space groups of Na3Bi and Cd3As2 The authors acknowledge the support of the CEM, an NSF MRSEC, under Grant DMR-1420451.
The Talbot Effect for two-dimensional massless Dirac fermions
Walls, Jamie D.; Hadad, Daniel
2016-01-01
A monochromatic beam of wavelength λ transmitted through a periodic one-dimensional diffraction grating with lattice constant d will be spatially refocused at distances from the grating that are integer multiples of . This self-refocusing phenomena, commonly referred to as the Talbot effect, has been experimentally demonstrated in a variety of systems ranging from optical to matter waves. Theoretical predictions suggest that the Talbot effect should exist in the case of relativistic Dirac fermions with nonzero mass. However, the Talbot effect for massless Dirac fermions (mDfs), such as those found in monolayer graphene or in topological insulator surfaces, has not been previously investigated. In this work, the theory of the Talbot effect for two-dimensional mDfs is presented. It is shown that the Talbot effect for mDfs exists and that the probability density of the transmitted mDfs waves through a periodic one-dimensional array of localized scatterers is also refocused at integer multiples of zT. However, due to the spinor nature of the mDfs, there are additional phase-shifts and amplitude modulations in the probability density that are most pronounced for waves at non-normal incidence to the scattering array. PMID:27221604
Asymmetric capture of Dirac dark matter by the Sun
Blennow, Mattias; Clementz, Stefan
2015-08-18
Current problems with the solar model may be alleviated if a significant amount of dark matter from the galactic halo is captured in the Sun. We discuss the capture process in the case where the dark matter is a Dirac fermion and the background halo consists of equal amounts of dark matter and anti-dark matter. By considering the case where dark matter and anti-dark matter have different cross sections on solar nuclei as well as the case where the capture process is considered to be a Poisson process, we find that a significant asymmetry between the captured dark particles and anti-particles is possible even for an annihilation cross section in the range expected for thermal relic dark matter. Since the captured number of particles are competitive with asymmetric dark matter models in a large range of parameter space, one may expect solar physics to be altered by the capture of Dirac dark matter. It is thus possible that solutions to the solar composition problem may be searched for in these type of models.
Dirac equation for particles with arbitrary half-integral spin
NASA Astrophysics Data System (ADS)
Guseinov, I. I.
2011-11-01
The sets of ? -component irreducible and Clifford algebraic Hermitian and unitary matrices through the two-component Pauli matrices are suggested, where s = 1/2, 3/2, 5/2, … . Using these matrix sets, the eigenvalues of which are ? , the ? -component generalized Dirac equation for a description of arbitrary half-integral spin particles is constructed. In accordance with the correspondence principle, the generalized Dirac equation suggested arises from the condition of relativistic invariance. This equation is reduced to the sets of two-component matrix equations the number of which is equal to ? . The new relativistic invariant equation of motion leads to an equation of continuity with a positive-definite probability density and also to the Klein-Gordon equation. This relativistic equation is causal in the presence of an external electromagnetic field interaction. It is shown that, in the case of nonrelativistic limit, the relativistic equation presented is reduced to the Pauli equation describing the motion of half-integral spin particle in the electromagnetic field.
Dirac fields, torsion and Barbero-Immirzi parameter in cosmology
Berredo-Peixoto, G. de; Shapiro, I.L.; Souza, C.A. de; Freidel, L. E-mail: lfreidel@perimeterinstitute.ca E-mail: abrahaocleber@gmail.com
2012-06-01
We consider cosmological solution for Einstein gravity with massive fermions with a four-fermion coupling, which emerges from the Holst action and is related to the Barbero-Immirzi (BI) parameter. This gravitational action is an important object of investigation in a non-perturbative formalism of quantum gravity. We study the equation of motion for the Dirac field within the standard Friedman-Robertson-Walker (FRW) metric. Finally, we show the theory with BI parameter and minimally coupling Dirac field, in the zero mass limit, is equivalent to an additional term which looks like a perfect fluid with the equation of state p = wρ, with w = 1 which is independent of the BI parameter. The existence of mass imposes a variable w, which creates either an inflationary phase with w = −1, or assumes an ultra hard equation of states w = 1 for very early universe. Both phases relax to a pressure less fluid w = 0 for late universe (corresponding to the limit m → ∞)
Multiple Scattering of Dirac Fermions in Two Dimensions
NASA Astrophysics Data System (ADS)
Asmar, Mahmoud M.; Ulloa, Sergio E.
2014-03-01
The low energy dispersion of electrons in graphene-as well as surface states of three dimensional topological insulators- are characterized by a linear dispersion, leading to interesting dynamical properties. The presence of potential scattering centers, such as impurities in real samples or artificially created gated regions, also reflect the ``massless'' nature of electrons in these materials. The study of Dirac fermion scattering from single potential obstacles is made possible through partial wave methods. In the case of closely-spaced potential obstacles (high defect concentration), one should consider multiple scattering effects. Using separation of variables, Graf's addition rules, and far field matching, one can generalize the partial wave method to the case of many scatterers, and obtain physical observables for such problem. We present our study of the scattering problem of Dirac fermions from multiple potential obstacles, with focus on the two-center problem. We discuss the dependence of the differential cross section on the separation, and different potential shifts caused by these obstacles, and compare these results with the differential cross section for a single scattering center. We also study the minimal conditions that allow the observation of Klein tunneling. Supported by MWN/CIAM-NSF and AvH.
Observation of Dirac electrons in germanene on diboride thin films
NASA Astrophysics Data System (ADS)
Fleurence, Antoine; Friedlein, Rainer; Yamane, Hiroyuki; Kim, Howon; Awatani, Yuuto; Yoshimoto, Shinya; Mukai, Kozo; Koitaya, Takanori; Hasegawa, Yukio; Yoshinobu, Jun; Kosugi, Nobuhiro; Yamada-Takamura, Yukiko
Germanene is a single atom thick honeycomb lattice of Ge atoms. Just like silicene, free-standing germanene is predicted to feature π bands forming graphene-like Dirac cones. Epitaxial germanene was already claimed to form on number of substrates, but no evidence for the existence of a π electronic system has been reported yet. In the present work, we demonstrate experimentally that Ge atoms segregated on the (0001) surface of zirconium diboride (ZrB2) thin films grown on Ge(111) form a germanene layer. ZrB2(0001) with germanene is (3 √3X3 √3)-reconstructed at low-temperature and (√3X √3)-reconstructed at room temperature. The (3 √3X3 √3) reconstruction originates from the matching of this unit cell with the (4X4) unit cell of a Ge honeycomb lattice. Evidence for its germanene nature stems from the observation of the Dirac cone-like dispersion at the K point of its Brillouin zone.
Distinguishing Dirac/Majorana sterile neutrinos at the LHC
NASA Astrophysics Data System (ADS)
Dib, Claudio O.; Kim, C. S.; Wang, Kechen; Zhang, Jue
2016-07-01
We study the purely leptonic decays of W±→e±e±μ∓ν and μ±μ±e∓ν produced at the LHC, induced by sterile neutrinos with mass mN below MW in the intermediate state. Since the final state neutrino escapes detection, one cannot tell whether this process violates lepton number, which would indicate a Majorana character for the intermediate sterile neutrino. Our study shows that when the sterile neutrino mixings with electrons and muons are different enough, one can still discriminate between the Dirac and Majorana character of this intermediate neutrino by simply counting and comparing the above decay rates. After performing collider simulations and statistical analysis, we find that at the 14 TeV LHC with an integrated luminosity of 3000 fb-1, for two benchmark scenarios mN=20 and 50 GeV, at least a 3 σ level of exclusion on the Dirac case can be achieved for disparities as mild as, e.g., |UN e|2<0.7 |UN μ|2 or |UN μ|2<0.7 |UN e|2 , provided that |UN e|2 and |UN μ|2 are both above ˜2 ×10-6.
Aneesur Rahman Prize for Computational Physics Lecture: Addressing Dirac's Challenge
NASA Astrophysics Data System (ADS)
Chelikowsky, James
2013-03-01
After the invention of quantum mechanics, P. A. M. Dirac made the following observation: ``The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems...'' The creation of ``approximate practical methods'' in response to Dirac's challenge has included the one electron picture, density functional theory and the pseudopotential concept. The combination of such methods in conjunction with contemporary computational platforms and new algorithms offer the possibility of predicting properties of materials solely from knowledge of the atomic species present. I will give an overview of progress in this field with an emphasis on materials at the nanoscale. Support from the Department of Energy and the National Science Foundation is acknowledged.
Dirac fields, torsion and Barbero-Immirzi parameter in cosmology
NASA Astrophysics Data System (ADS)
de Berredo-Peixoto, G.; Freidel, L.; Shapiro, I. L.; de Souza, C. A.
2012-06-01
We consider cosmological solution for Einstein gravity with massive fermions with a four-fermion coupling, which emerges from the Holst action and is related to the Barbero-Immirzi (BI) parameter. This gravitational action is an important object of investigation in a non-perturbative formalism of quantum gravity. We study the equation of motion for the Dirac field within the standard Friedman-Robertson-Walker (FRW) metric. Finally, we show the theory with BI parameter and minimally coupling Dirac field, in the zero mass limit, is equivalent to an additional term which looks like a perfect fluid with the equation of state p = wρ, with w = 1 which is independent of the BI parameter. The existence of mass imposes a variable w, which creates either an inflationary phase with w = -1, or assumes an ultra hard equation of states w = 1 for very early universe. Both phases relax to a pressure less fluid w = 0 for late universe (corresponding to the limit m → ∞).
Dirac Cellular Automaton from Split-step Quantum Walk
NASA Astrophysics Data System (ADS)
Mallick, Arindam; Chandrashekar, C. M.
2016-05-01
Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory.
Detection of chiral anomaly and valley transport in Dirac semimetals
NASA Astrophysics Data System (ADS)
Zhang, Cheng; Zhang, Enze; Liu, Yanwen; Chen, Zhigang; Liang, Sihang; Cao, Junzhi; Yuan, Xiang; Tang, Lei; Li, Qian; Gu, Teng; Wu, Yizheng; Zou, Jin; Xiu, Faxian
Chiral anomaly is a non-conservation of chiral charge pumped by the topological nontrivial gauge field, which has been predicted to exist in the emergent quasiparticle excitations in Dirac and Weyl semimetals. However, so far, such pumping process hasn't been clearly demonstrated and lacks a convincing experimental identification. Here, we report the detection of the charge pumping effect and the related valley transport in Cd3As2 driven by external electric and magnetic fields (EB). We find that the chiral imbalance leads to a non-zero gyrotropic coefficient, which can be confirmed by the EB-generated Kerr effect. By applying B along the current direction, we observe a negative magnetoresistance despite the giant positive one at other directions, a clear indication of the chiral anomaly. Remarkably, a robust nonlocal response in valley diffusion originated from the chiral anomaly is persistent up to room temperature when B is parallel to E. The ability to manipulate the valley polarization in Dirac semimetal opens up a brand-new route to understand its fundamental properties through external fields and utilize the chiral fermions in valleytronic applications.
Free-Dirac-particle evolution as a quantum random walk
NASA Astrophysics Data System (ADS)
Bracken, A. J.; Ellinas, D.; Smyrnakis, I.
2007-02-01
It is known that any positive-energy state of a free Dirac particle that is initially highly localized evolves in time by spreading at speeds close to the speed of light. As recently indicated by Strauch, this general phenomenon, and the resulting “two-horned” distributions of position probability along any axis through the point of initial localization, can be interpreted in terms of a quantum random walk, in which the roles of “coin” and “walker” are naturally associated with the spin and translational degrees of freedom in a discretized version of Dirac’s equation. We investigate the relationship between these two evolutions analytically and show how the evolved probability density on the x axis for the Dirac particle at any time t can be obtained from the asymptotic form of the probability distribution for the position of a “quantum walker.” The case of a highly localized initial state is discussed as an example.