Weyl consistency conditions and a local renormalisation group equation for general renormalisable field theories

International Nuclear Information System (INIS)

Osborn, H.

1991-01-01

A local renormalisation group equation which realises infinitesimal Weyl rescalings of the metric and which is an extension of the usual Callan-Symanzik equation is described. In order to ensure that any local composite operators, with dimensions so that on addition to the basic lagrangian they preserve renormalisability, are well defined for arbitrarily many insertions into correlation functions the couplings are assumed to depend on χ. Local operators are then defined by functional differentiation with respect to the couplings just as the energy-momentum tensor is given by functional differentiation with respect to the metric. The local renormalisation group equation contains terms depending on derivatives of the couplings as well as the curvature tensor formed from the metric, constrained by power counting. Various consistency relations arising from the commutativity of Weyl transformations are derived, extending previous one-loop results for the trace anomaly to all orders. In two dimensions the relations give an alternative derivation of the c-theorem and similar extensions are obtained in four dimensions. The equations are applied in detail to general renormalisable σ-models in two dimensions. The Curci-Paffuti relation is derived without any commitment to a particular regularisation scheme and further equations used to construct an action for the vanishing of the β-functions are also obtained. The discussion is also extended to σ-models with a boundary, as appropriate for open strings, and relations for the additional β-functions present in such models are obtained. (orig.)

The role of Weyl symmetry in hydrodynamics

Science.gov (United States)

Diles, Saulo

2018-04-01

This article is dedicated to the analysis of Weyl symmetry in the context of relativistic hydrodynamics. Here is discussed how this symmetry is properly implemented using the prescription of minimal coupling: ∂ → ∂ + ωA. It is shown that this prescription has no problem to deal with curvature since it gives the correct expressions for the commutator of covariant derivatives. In hydrodynamics, Weyl gauge connection emerges from the degrees of freedom of the fluid: it is a combination of the expansion and entropy gradient. The remaining degrees of freedom, shear, vorticity and the metric tensor, are see in this context as charged fields under the Weyl gauge connection. The gauge nature of the connection provides natural dynamics to it via equations of motion analogous to the Maxwell equations for electromagnetism. As a consequence, a charge for the Weyl connection is defined and the notion of local charge is analyzed generating the conservation law for the Weyl charge.

Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation

International Nuclear Information System (INIS)

Caraballo, Tomas; Kloeden, Peter E.; Schmalfuss, Bjoern

2004-01-01

We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of anon-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities

Dirac and Weyl semimetals with holographic interactions

NARCIS (Netherlands)

Jacobs, V.P.J.

2015-01-01

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

Towards exact solutions of the non-linear Heisenberg-Pauli-Weyl spinor equation

International Nuclear Information System (INIS)

Mielke, E.W.

1980-03-01

In ''color geometrodynamics'' fundamental spinor fields are assumed to obey a GL(2f,C) x GL(2c,C) gauge-invariant nonlinear spinor equation of the Heisenberg-Pauli-Weyl type. Quark confinement, assimilating a scheme of Salam and Strathdee, is (partially) mediated by the tensor ''gluons'' of strong gravity. This hypothesis is incorporated into the model by considering the nonlinear Dirac equation in a curved space-time of hadronic dimensions. Disregarding internal degrees of freedom, it is then feasible, for a particular background space-time, to obtain exact solutions of the spherical bound-state problem. Finally, these solutions are tentatively interpreted as droplet-type solitons and remarks on their interrelation with Wheeler's geon construction are made. (author)

STABLE STATIONARY STATES OF NON-LOCAL INTERACTION EQUATIONS

KAUST Repository

FELLNER, KLEMENS

2010-12-01

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

Possible physical manifestation of the Weyl non-Abelian gauge field

International Nuclear Information System (INIS)

Barbashov, B.M.; Pestov, A.B.

1998-01-01

On the basis of the Weyl equations of congruent transference, we consider a possible influence of the Weyl non-Abelian gauge field defining the transference on the precession of a gyroscope. Plane-wave solutions to the equations of the Abelian gauge field are derived

On behaviour of Weyl's gauge field

International Nuclear Information System (INIS)

Yuan Zhong Zhang.

1990-05-01

We consider a system, consisting of a metric tensor g μυ , a scalar field φ, a Weyl's gauge field A μ and a scalar matter field Φ, which is invariant under general coordinate transformation and Weyl's gauge transformation. Two kinds of identities and field equations are given and discussed. A special space-time with g μυ =φ -2 η μυ is considered in a gauge-independent manner. We point out that in a correct treatment where g μυ is not regarded as an independent variable, an auxiliary condition for Weyl's gauge field cannot be obtained. Therefore Weyl's gauge field can be treated as a usual field of positive norm. (author). 11 refs

On the stationary Einstein-Maxwell-Klein-Gordon equations

International Nuclear Information System (INIS)

Gegenberg, J.D.

1981-05-01

The stationary Einstein-Maxwell-Klein-Gordon (EMKG) equations for interacting gravitational, electromagnetic and meson fields are examined. The theory is cast into the formalism of principal fiber bundles with a connection, wherein its relationship to current trends in theoretical physics is made manifest. The EMKG equations are shown to admit a Higgs-like mechanism for giving mass to the gauge field. A theorem specifying sufficient conditions for the stationarity of the spacetime metric to imply stationarity of the other fields is proved. By imposing additional constraints and symmetries, the EMKG equations are considerably simplified. An attempt is made to apply a solution-generation technique, and this meets with only partial success. Finally, a stationary but non-static solution is found, and the geometric and physical properties are discussed

Poisson-Nernst-Planck equations with steric effects - non-convexity and multiple stationary solutions

Science.gov (United States)

Gavish, Nir

2018-04-01

We study the existence and stability of stationary solutions of Poisson-Nernst-Planck equations with steric effects (PNP-steric equations) with two counter-charged species. We show that within a range of parameters, steric effects give rise to multiple solutions of the corresponding stationary equation that are smooth. The PNP-steric equation, however, is found to be ill-posed at the parameter regime where multiple solutions arise. Following these findings, we introduce a novel PNP-Cahn-Hilliard model, show that it is well-posed and that it admits multiple stationary solutions that are smooth and stable. The various branches of stationary solutions and their stability are mapped utilizing bifurcation analysis and numerical continuation methods.

Weyl Group Multiple Dirichlet Series Type A Combinatorial Theory (AM-175)

CERN Document Server

Brubaker, Ben; Friedberg, Solomon

2011-01-01

Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series an

The Pathwise Numerical Approximation of Stationary Solutions of Semilinear Stochastic Evolution Equations

International Nuclear Information System (INIS)

Caraballo, T.; Kloeden, P.E.

2006-01-01

Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the reaction-diffusion type is shown to have a unique stochastic stationary solution which pathwise attracts all other solutions. A similar situation holds for each Galerkin approximation and each implicit Euler scheme applied to these Galerkin approximations. Moreover, the stationary solution of the Euler scheme converges pathwise to that of the Galerkin system as the stepsize tends to zero and the stationary solutions of the Galerkin systems converge pathwise to that of the evolution equation as the dimension increases. The analysis is carried out on random partial and ordinary differential equations obtained from their stochastic counterparts by subtraction of appropriate Ornstein-Uhlenbeck stationary solutions

Weyl gravity as a gauge theory

Science.gov (United States)

Trujillo, Juan Teancum

In 1920, Rudolf Bach proposed an action based on the square of the Weyl tensor or CabcdCabcd where the Weyl tensor is an invariant under a scaling of the metric. A variation of the metric leads to the field equation known as the Bach equation. In this dissertation, the same action is analyzed, but as a conformal gauge theory. It is shown that this action is a result of a particular gauging of this group. By treating it as a gauge theory, it is natural to vary all of the gauge fields independently, rather than performing the usual fourth-order metric variation only. We show that solutions of the resulting vacuum field equations are all solutions to the vacuum Einstein equation, up to a conformal factor---a result consistent with local scale freedom. We also show how solutions for the gauge fields imply there is no gravitational self energy.

Randomly forced CGL equation stationary measures and the inviscid limit

CERN Document Server

Kuksin, S

2003-01-01

We study a complex Ginzburg-Landau (CGL) equation perturbed by a random force which is white in time and smooth in the space variable~$x$. Assuming that $\\dim x\\le4$, we prove that this equation has a unique solution and discuss its asymptotic in time properties. Next we consider the case when the random force is proportional to the square root of the viscosity and study the behaviour of stationary solutions as the viscosity goes to zero. We show that, under this limit, a subsequence of solutions in question converges to a nontrivial stationary process formed by global strong solutions of the nonlinear Schr\\"odinger equation.

The Weyl approach to the representation theory of reflection equation algebra

International Nuclear Information System (INIS)

Saponov, P A

2004-01-01

The present paper deals with the representation theory of reflection equation algebra, connected to a Hecke type R-matrix. Up to some reasonable additional conditions, the R-matrix is arbitrary (not necessary originating from quantum groups). We suggest a universal method for constructing finite dimensional irreducible representations in the framework of the Weyl approach well known in the representation theory of classical Lie groups and algebras. With this method a series of irreducible modules is constructed. The modules are parametrized by Young diagrams. The spectrum of central elements s k Tr q L k is calculated in the single-row and single-column representations. A rule for the decomposition of the tensor product of modules into a direct sum of irreducible components is also suggested

Handbook of differential equations stationary partial differential equations

CERN Document Server

Chipot, Michel

2006-01-01

This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Ke

Sigma-convergence of stationary Navier-Stokes type equations

Directory of Open Access Journals (Sweden)

Gabriel Nguetseng

2009-06-01

Full Text Available In the framework of homogenization theory, the Sigma-convergence method is carried out on stationary Navier-Stokes type equations on a fixed domain. Our main tools are the two-scale convergence concept and the so-called homogenization algebras.

Semiclassical dynamics and magnetic Weyl calculus

International Nuclear Information System (INIS)

Lein, Maximilian Stefan

2011-01-01

Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is not covered by existing theory as proofs involving usual Weyl calculus break down. This is the regime of the so-called quantum Hall effect where quantization of transverse conductance is observed. To rigorously derive semiclassical equations of motion, one needs to systematically develop a magnetic Weyl calculus which contains a semiclassical parameter. Mathematically, the operators involved in the analysis are magnetic pseudodifferential operators, a topic which by itself is of interest for the mathematics and mathematical physics community alike. Hence, we will devote two additional chapters to further understanding of properties of those operators. (orig.)

Semiclassical dynamics and magnetic Weyl calculus

Energy Technology Data Exchange (ETDEWEB)

Lein, Maximilian Stefan

2011-01-19

Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is not covered by existing theory as proofs involving usual Weyl calculus break down. This is the regime of the so-called quantum Hall effect where quantization of transverse conductance is observed. To rigorously derive semiclassical equations of motion, one needs to systematically develop a magnetic Weyl calculus which contains a semiclassical parameter. Mathematically, the operators involved in the analysis are magnetic pseudodifferential operators, a topic which by itself is of interest for the mathematics and mathematical physics community alike. Hence, we will devote two additional chapters to further understanding of properties of those operators. (orig.)

Classical Weyl transverse gravity

Energy Technology Data Exchange (ETDEWEB)

Oda, Ichiro [University of the Ryukyus, Department of Physics, Faculty of Science, Nishihara, Okinawa (Japan)

2017-05-15

We study various classical aspects of the Weyl transverse (WTDiff) gravity in a general space-time dimension. First of all, we clarify a classical equivalence among three kinds of gravitational theories, those are, the conformally invariant scalar tensor gravity, Einstein's general relativity and the WTDiff gravity via the gauge-fixing procedure. Secondly, we show that in the WTDiff gravity the cosmological constant is a mere integration constant as in unimodular gravity, but it does not receive any radiative corrections unlike the unimodular gravity. A key point in this proof is to construct a covariantly conserved energy-momentum tensor, which is achieved on the basis of this equivalence relation. Thirdly, we demonstrate that the Noether current for the Weyl transformation is identically vanishing, thereby implying that the Weyl symmetry existing in both the conformally invariant scalar tensor gravity and the WTDiff gravity is a ''fake'' symmetry. We find it possible to extend this proof to all matter fields, i.e. the Weyl-invariant scalar, vector and spinor fields. Fourthly, it is explicitly shown that in the WTDiff gravity the Schwarzschild black hole metric and a charged black hole one are classical solutions to the equations of motion only when they are expressed in the Cartesian coordinate system. Finally, we consider the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology and provide some exact solutions. (orig.)

Quantum walks and orbital states of a Weyl particle

International Nuclear Information System (INIS)

Katori, Makoto; Fujino, Soichi; Konno, Norio

2005-01-01

The time-evolution equation of a one-dimensional quantum walker is exactly mapped to the three-dimensional Weyl equation for a zero-mass particle with spin 1/2, in which each wave number k of the walker's wave function is mapped to a point q(k) in the three-dimensional momentum space and q(k) makes a planar orbit as k changes its value in [-π,π). The integration over k providing the real-space wave function for a quantum walker corresponds to considering an orbital state of a Weyl particle, which is defined as a superposition (curvilinear integration) of the energy-momentum eigenstates of a free Weyl equation along the orbit. Konno's novel distribution function of a quantum walker's pseudovelocities in the long-time limit is fully controlled by the shape of the orbit and how the orbit is embedded in the three-dimensional momentum space. The family of orbital states can be regarded as a geometrical representation of the unitary group U(2) and the present study will propose a new group-theoretical point of view for quantum-walk problems

Inertial algorithms for the stationary Navier-Stokes equations

NARCIS (Netherlands)

Hou, Yanren; Mattheij, R.M.M.

2003-01-01

Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed

Weyl states and Fermi arcs in parabolic bands

Science.gov (United States)

Doria, Mauro M.; Perali, Andrea

2017-07-01

Weyl fermions are shown to exist inside a parabolic band in a single electronic layer, where the kinetic energy of carriers is given by the non-relativistic Schroedinger equation. There are Fermi arcs as a direct consequence of the folding of a ring-shaped Fermi surface inside the first Brillouin zone. Our results stem from the decomposition of the kinetic energy into the sum of the square of the Weyl state, the coupling to the local magnetic field and the Rashba interaction. The Weyl fermions break the space and time reflection symmetries present in the kinetic energy, thus allowing for the onset of a weak three-dimensional magnetic field around the layer. This field brings topological stability to the current-carrying states through a Chern number. In the special limit for which the Weyl state becomes gapless, this magnetic interaction is shown to be purely attractive, thus suggesting the onset of a superconducting condensate of zero helicity states.

Weyl-Invariant Extension of the Metric-Affine Gravity

International Nuclear Information System (INIS)

Vazirian, R.; Tanhayi, M. R.; Motahar, Z. A.

2015-01-01

Metric-affine geometry provides a nontrivial extension of the general relativity where the metric and connection are treated as the two independent fundamental quantities in constructing the spacetime (with nonvanishing torsion and nonmetricity). In this paper, we study the generic form of action in this formalism and then construct the Weyl-invariant version of this theory. It is shown that, in Weitzenböck space, the obtained Weyl-invariant action can cover the conformally invariant teleparallel action. Finally, the related field equations are obtained in the general case.

Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method

Energy Technology Data Exchange (ETDEWEB)

Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.

2014-10-15

Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.

Weyl-Wigner correspondence in two space dimensions

DEFF Research Database (Denmark)

Dahl, Jens Peder; Varro, S.; Wolf, A.

2007-01-01

We consider Wigner functions in two space dimensions. In particular, we focus on Wigner functions corresponding to energy eigenstates of a non-relativistic particle moving in two dimensions in the absence of a potential. With the help of the Weyl-Wigner correspondence we first transform...... the eigenvalue equations for energy and angular momentum into phase space. As a result we arrive at partial differential equations in phase space which determine the corresponding Wigner function. We then solve the resulting equations using appropriate coordinates....

Torus as phase space: Weyl quantization, dequantization, and Wigner formalism

Energy Technology Data Exchange (ETDEWEB)

Ligabò, Marilena, E-mail: marilena.ligabo@uniba.it [Dipartimento di Matematica, Università di Bari, I-70125 Bari (Italy)

2016-08-15

The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of the Wigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols.

A rigorous derivation of the stationary compressible Reynolds equation via the Navier-Stokes equations

Czech Academy of Sciences Publication Activity Database

Ciuperca, I. S.; Feireisl, Eduard; Jai, M.; Petrov, A.

2018-01-01

Roč. 28, č. 4 (2018), s. 697-732 ISSN 0218-2025 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible fluids * stationary Navier-Stokes equations * thin films Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.860, year: 2016 https://www.worldscientific.com/doi/abs/10.1142/S0218202518500185

Approximate Forward Difference Equations for the Lower Order Non-Stationary Statistics of Geometrically Non-Linear Systems subject to Random Excitation

DEFF Research Database (Denmark)

Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.

Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....

Double gauge invariance and covariantly-constant vector fields in Weyl geometry

Science.gov (United States)

Kassandrov, Vladimir V.; Rizcallah, Joseph A.

2014-08-01

The wave equation and equations of covariantly-constant vector fields (CCVF) in spaces with Weyl nonmetricity turn out to possess, in addition to the canonical conformal-gauge, a gauge invariance of another type. On a Minkowski metric background, the CCVF system alone allows us to pin down the Weyl 4-metricity vector, identified herein with the electromagnetic potential. The fundamental solution is given by the ordinary Lienard-Wiechert field, in particular, by the Coulomb distribution for a charge at rest. Unlike the latter, however, the magnitude of charge is necessarily unity, "elementary", and charges of opposite signs correspond to retarded and advanced potentials respectively, thus establishing a direct connection between the particle/antiparticle asymmetry and the "arrow of time".

Faithful transformation of quasi-isotropic to Weyl-Papapetrou coordinates: a prerequisite to compare metrics

International Nuclear Information System (INIS)

Pappas, G; Apostolatos, T A

2008-01-01

We demonstrate how one should transform correctly quasi-isotropic coordinates to Weyl-Papapetrou coordinates in order to compare the metric around a rotating star, which has been constructed numerically in the former coordinates, with an axially symmetric stationary metric, which is given through an analytical form in the latter coordinates. (comments, replies and notes)

Faithful transformation of quasi-isotropic to Weyl-Papapetrou coordinates: a prerequisite to compare metrics

Energy Technology Data Exchange (ETDEWEB)

Pappas, G; Apostolatos, T A [Section of Astrophysics, Astronomy and Mechanics, Department of Physics, University of Athens, Panepistimiopolis Zografos GR15783, Athens (Greece)

2008-11-21

We demonstrate how one should transform correctly quasi-isotropic coordinates to Weyl-Papapetrou coordinates in order to compare the metric around a rotating star, which has been constructed numerically in the former coordinates, with an axially symmetric stationary metric, which is given through an analytical form in the latter coordinates. (comments, replies and notes)

On the Gross–Pitaevskii Equation with Pumping and Decay: Stationary States and Their Stability

KAUST Repository

Sierra Nunez, Jesus Alfredo; Kasimov, Aslan R.; Markowich, Peter A.; Weishä upl, Rada Maria

2015-01-01

We investigate the behavior of solutions of the complex Gross–Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose–Einstein condensates. The stationary radially symmetric solutions of the equation are studied, and their linear stability with respect to two-dimensional perturbations is analyzed. Using numerical continuation, we calculate not only the ground state of the system, but also a number of excited states. Accurate numerical integration is employed to study the general nonlinear evolution of the system from the unstable stationary solutions to the formation of stable vortex patterns.

On the Gross–Pitaevskii Equation with Pumping and Decay: Stationary States and Their Stability

KAUST Repository

Sierra Nunez, Jesus Alfredo

2015-02-11

We investigate the behavior of solutions of the complex Gross–Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose–Einstein condensates. The stationary radially symmetric solutions of the equation are studied, and their linear stability with respect to two-dimensional perturbations is analyzed. Using numerical continuation, we calculate not only the ground state of the system, but also a number of excited states. Accurate numerical integration is employed to study the general nonlinear evolution of the system from the unstable stationary solutions to the formation of stable vortex patterns.

Voltage-Driven Magnetization Switching and Spin Pumping in Weyl Semimetals

Science.gov (United States)

Kurebayashi, Daichi; Nomura, Kentaro

2016-10-01

We demonstrate electrical magnetization switching and spin pumping in magnetically doped Weyl semimetals. The Weyl semimetal is a three-dimensional gapless topological material, known to have nontrivial coupling between the charge and the magnetization due to the chiral anomaly. By solving the Landau-Lifshitz-Gilbert equation for a multilayer structure of a Weyl semimetal, an insulator and a metal while taking the charge-magnetization coupling into account, magnetization dynamics is analyzed. It is shown that the magnetization dynamics can be driven by the electric voltage. Consequently, switching of the magnetization with a pulsed electric voltage can be achieved, as well as precession motion with an applied oscillating electric voltage. The effect requires only a short voltage pulse and may therefore be energetically favorable for us in spintronics devices compared to conventional spin-transfer torque switching.

Quantum anomalous Bloch-Siegert shift in Weyl semimetal

Science.gov (United States)

Kumar, Upendra; Kumar, Vipin; Enamullah, Setlur, Girish S.

2018-05-01

A periodic exchange of energy between the light field and two level system is known as Rabi oscillations. The Bloch-Siegert shift (BSS) is a shift in Rabi oscillation resonance condition, when the driving field is sufficiently strong. There are new type of oscillations exhibit in Weyl semimetal at far from resonance, known as anomalous Rabi oscillation. In this work, we study the phenomenon of the Bloch-Siegert shift in Weyl semimetal at far from resonance called anomalous Bloch-Siegert shift (ABSS) by purely quantum mechanical treatment and describe it's anisotropic nature. A fully numerical solution of the Floquet-Bloch equations unequivocally establishes the presence of not only anomalous Rabi oscillations in these systems but also their massless character.

The Simon and Simon-Mars tensors for stationary Einstein-Maxwell fields

International Nuclear Information System (INIS)

Bini, Donato; Cherubini, Christian; Jantzen, Robert T; Miniutti, Giovanni

2004-01-01

Modulo conventional scale factors, the Simon and Simon-Mars tensors are defined for stationary vacuum spacetimes so that their equality follows from the Bianchi identities of the second kind. In the nonvacuum case one can absorb additional source terms into a redefinition of the Simon tensor so that this equality is maintained. Among the electrovacuum class of solutions of the Einstein-Maxwell equations, the expression for the Simon tensor in the Kerr-Newman-Taub-NUT spacetime in terms of the Ernst potential is formally the same as in the vacuum case (modulo a scale factor), and its vanishing guarantees the simultaneous alignment of the principal null directions of the Weyl tensor, the Papapetrou field associated with the timelike Killing vector field, the electromagnetic field of the spacetime and even the Killing-Yano tensor

On the reduction of the multidimensional stationary Schroedinger equation to a first-order equation and its relation to the pseudoanalytic function theory

Energy Technology Data Exchange (ETDEWEB)

Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)

2005-01-28

Given a particular solution of a one-dimensional stationary Schroedinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schroedinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schroedinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schroedinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schroedinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schroedinger equation. Moreover, for an ample

Apparent negative magnetoresistance without independent Weyl pockets in the Weyl semimetal TaP

Energy Technology Data Exchange (ETDEWEB)

Hassinger, Elena; Arnold, Frank; Naumann, Marcel; Wu, Shu-Chun; Sun, Yan; Donizeth dos Reis, Ricardo; Ajeesh, Mukkattu O.; Shekhar, Chandra; Kumar, Nitesh; Schmidt, Marcus; Baenitz, Michael; Borrmann, Horst; Nicklas, Michael; Felser, Claudia [Max Planck Institute for Chemical Physics of Solids, Dresden (Germany); Grushin, Adolfo; Bardarson, Jens [Max Planck Institute for Physics of Complex Systems, Dresden (Germany); Yan, Binghai [Max Planck Institute for Chemical Physics of Solids, Dresden (Germany); Max Planck Institute for Physics of Complex Systems, Dresden (Germany)

2016-07-01

In the recently discovered Weyl semimetals, an unconventional negative longitudinal magnetoresistance is expected due to a phenomenon called chiral anomaly. An open question is, how close the Fermi energy needs to be to the Weyl nodes, in order to detect this phenomenon. This question can only be addressed by knowing the electronic bandstructure, i.e. the position of the Fermi energy, and the intrinsic longitudinal magnetoresistance precisely. Here, we report the detailed Fermi surface topology of the Weyl semimetal TaP determined via angle-resolved quantum oscillation spectra combined with band-structure calculations. The Fermi surface consists of an electron and a hole banana without independent pockets around the Weyl points. Although the absence of independent Fermi surface pockets around the Weyl points means that no chiral anomaly is expected, we detect a negative longitudinal magnetoresistance. We discuss possible origins.

Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation

OpenAIRE

Wu, Lei

2014-01-01

We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in $L^{\\infty}$ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.

Classical local SU(3 gauge invariance in Weyl 2-spinor language and quark–gluon plasma equations of motion

Directory of Open Access Journals (Sweden)

J. Buitrago

Full Text Available In a new classical Weyl 2-spinor approach to non abelian gauge theories, starting with the U(1 gauge group in a previous work, we study now the SU(3 case corresponding to quarks (antiquarks interacting with color fields. The principal difference with the conventional approach is that particle-field interactions are not described by means of potentials but by the field strength magnitudes. Some analytical expressions showing similarities with electrodynamics are obtained. Classical equations that describe the behavior of quarks under gluon fields might be in principle applied to the quark–gluon plasma phase existing during the first instants of the Universe.

The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method

OpenAIRE

Maj, Omar

2004-01-01

The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also disc...

Matter with dilaton charge in Weyl-Cartan spacetime and evolution of the universe

International Nuclear Information System (INIS)

Babourova, Olga V; Frolov, Boris N

2003-01-01

The perfect dilaton-spin fluid (as a model of the dilaton matter, the particles of which are endowed with intrinsic spin and dilaton charge) is considered as the source of the gravitational field in a Weyl-Cartan spacetime. The variational formalism of the gravitational field in a Weyl-Cartan spacetime is developed in the exterior form language. A homogeneous and isotropic universe filled with the dilaton matter as the dark matter is considered and one of the field equations is represented as the Einstein-like equation which leads to the modified Friedmann-Lemaitre equation. From this equation the absence of the initial singularity in the cosmological solution follows. Also the existence of two points of inflection of the scale factor function is established, the first of which corresponds to the early stage of the universe and the second to the modern era when the expansion with deceleration is replaced by the expansion with acceleration. Possible equations of state for the self-interacting cold dark matter are found on the basis of the modern observational data. An inflation-like solution is obtained

Tunable axial gauge fields in engineered Weyl semimetals: semiclassical analysis and optical lattice implementations

Science.gov (United States)

Roy, Sthitadhi; Kolodrubetz, Michael; Goldman, Nathan; Grushin, Adolfo G.

2018-04-01

In this work, we describe a toolbox to realize and probe synthetic axial gauge fields in engineered Weyl semimetals. These synthetic electromagnetic fields, which are sensitive to the chirality associated with Weyl nodes, emerge due to spatially and temporally dependent shifts of the corresponding Weyl momenta. First, we introduce two realistic models, inspired by recent cold-atom developments, which are particularly suitable for the exploration of these synthetic axial gauge fields. Second, we describe how to realize and measure the effects of such axial fields through center-of-mass observables, based on semiclassical equations of motion and exact numerical simulations. In particular, we suggest realistic protocols to reveal an axial Hall response due to the axial electric field \

Order α'(two-loop) equivalence of the string equations of motion and the σ-model Weyl invariance conditions

International Nuclear Information System (INIS)

Metsaev, R.R.; Tseytlin, A.A.

1987-01-01

We prove the on-shell equivalence of the order α' terms in the string effective equations (for the graviton, dilaton and the antisymmetric tensor) to the vanishing of the corresponding (two-loop) terms in the Weyl anomaly coefficients for the general bosonic σ-model. We first determine the α' term in the string effective action starting with the known expression for the 3- and 4-point string amplitudes. Then we compute the two-loop β-function in the general σ-model with the antisymmetric tensor coupling. Special emphasis is made on the renormalization scheme dependence of the β-function. Our result disagrees with the previously known one and cannot be manifestly expressed in terms of the generalized curvature for the connection with torsion. We also prove (to the order α' 2 ) that the parallelizable spaces are solutions of the string equations of motion and establish the complete 3-loop expression for the 'central charge' coefficient. (orig.)

Stability of stationary states of non-local equations with singular interaction potentials

KAUST Repository

Fellner, Klemens

2011-04-01

We study the large-time behaviour of a non-local evolution equation for the density of particles or individuals subject to an external and an interaction potential. In particular, we consider interaction potentials which are singular in the sense that their first derivative is discontinuous at the origin.For locally attractive singular interaction potentials we prove under a linear stability condition local non-linear stability of stationary states consisting of a finite sum of Dirac masses. For singular repulsive interaction potentials we show the stability of stationary states of uniformly bounded solutions under a convexity condition.Finally, we present numerical simulations to illustrate our results. © 2010 Elsevier Ltd.

Solution of the stationary vacuum equations of relativity for conformally flat 3-spaces

International Nuclear Information System (INIS)

Perjes, Z.; Lukacs, B.; Sebestyen, A.; Valentini, A.; Sparling, G.A.J.

1983-08-01

The solution of Einstein's vacuum gravitational equations for stationary space-times with a conformally flat 3-space is presented. There is no other solution of this problem than the Ehlers-rotation generalizations of the three conformastat space-times including the Schwarzschild metric. (author)

R matrix: its relation to Titchmarsh-Weyl theory and its complex rotated analogue

International Nuclear Information System (INIS)

Elander, N.; Krylstedt, P.; Braendas, E.; Engdahl, E.

1986-01-01

The R matrix theory in its simplest form is discussed and analyzed in terms of the classical Titchmarsh-Weyl's theory for a singular second order differential equation. It is observed that the R matrix described as an abstract R operator is contained in the framework of Weyls classical extension to an infinite interval of finite Sturm-Liuoville theory. As a result they find that the exterior complex rotation method can be synthesized with the R matrix theory to obtain a method for deriving the S matrix poles out in the complex energy or momentum planes

THE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR

KAUST Repository

ARNOLD, ANTON

2012-11-01

We consider the linear WignerFokkerPlanck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique stationary solution in a weighted Sobolev space. A key ingredient of the proof is a new result on the existence of spectral gaps for FokkerPlanck type operators in certain weighted L 2-spaces. In addition we show that the steady state corresponds to a positive density matrix operator with unit trace and that the solutions of the time-dependent problem converge towards the steady state with an exponential rate. © 2012 World Scientific Publishing Company.

Nonlocal quantum effective actions in Weyl-Flat spacetimes

Science.gov (United States)

Bautista, Teresa; Benevides, André; Dabholkar, Atish

2018-06-01

Virtual massless particles in quantum loops lead to nonlocal effects which can have interesting consequences, for example, for primordial magnetogenesis in cosmology or for computing finite N corrections in holography. We describe how the quantum effective actions summarizing these effects can be computed efficiently for Weyl-flat metrics by integrating the Weyl anomaly or, equivalently, the local renormalization group equation. This method relies only on the local Schwinger-DeWitt expansion of the heat kernel and allows for a re-summation of the anomalous leading large logarithms of the scale factor, log a( x), in situations where the Weyl factor changes by several e-foldings. As an illustration, we obtain the quantum effective action for the Yang-Mills field coupled to massless matter, and the self-interacting massless scalar field. Our action reduces to the nonlocal action obtained using the Barvinsky-Vilkovisky covariant perturbation theory in the regime R 2 ≪ ∇2 R for a typical curvature scale R, but has a greater range of validity effectively re-summing the covariant perturbation theory to all orders in curvatures. In particular, it is applicable also in the opposite regime R 2 ≫ ∇2 R, which is often of interest in cosmology.

Nonlinear stationary solutions of the Wigner and Wigner-Poisson equations

OpenAIRE

Haas, F.; Shukla, P. K.

2008-01-01

Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved p...

The semiclassical coherent state propagator in the Weyl representation

International Nuclear Information System (INIS)

Braun, Carol; Li, Feifei; Garg, Anupam; Stone, Michael

2015-01-01

It is shown that the semiclassical coherent state propagator takes its simplest form when the quantum mechanical Hamiltonian is replaced by its Weyl symbol in defining the classical action, in that there is then no need for a Solari-Kochetov correction. It is also shown that such a correction exists if a symbol other than the Weyl symbol is chosen and that its form is different depending on the symbol chosen. The various forms of the propagator based on different symbols are shown to be equivalent provided the correspondingly correct Solari-Kochetov correction is included. All these results are shown for both particle and spin coherent state propagators. The global anomaly in the fluctuation determinant is further elucidated by a study of the connection between the discrete fluctuation determinant and the discrete Jacobi equation

Stationary solution of the compressible magnetohydrodynamic equation and its stability with respect to initial disturbance

Directory of Open Access Journals (Sweden)

WU Renchao

2016-06-01

Full Text Available In this paper, we consider three dimensional compressible viscous magnetohydro dynamic equations(MHD with external potentialforce. We first derive the corresponding non-constantstationary solutions. Then we show global well-posedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that rescribed initial data is close to the stationary solution.

Weyl solitons in three-dimensional optical lattices

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Shang, Ce; Zheng, Yuanlin; Malomed, Boris A.

2018-04-01

Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear systems. Ultracold atomic gases, featuring laser-assisted tunneling in three-dimensional optical lattices, can be used for the emulation of Weyl semimetals, including nonlinear effects induced by the collisional nonlinearity of atomic Bose-Einstein condensates. We demonstrate that this setting gives rise to topological states in the form of Weyl solitons at the surface of the underlying optical lattice. These nonlinear modes, being exceptionally robust, bifurcate from linear states for a given quasimomentum. The Weyl solitons may be used to design an efficient control scheme for topologically protected unidirectional propagation of excitations in light-matter-interaction physics. After the recently introduced Majorana and Dirac solitons, the Weyl solitons proposed in this work constitute the third (and the last) member in this family of topological solitons.

FMCEIR: a Monte Carlo program for solving the stationary neutron and gamma transport equation

International Nuclear Information System (INIS)

Taormina, A.

1978-05-01

FMCEIR is a three-dimensional Monte Carlo program for solving the stationary neutron and gamma transport equation. It is used to study the problem of neutron and gamma streaming in the GCFR and HHT reactor channels. (G.T.H.)

A note on generalized Weyl's theorem

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Zguitti, H.

2006-04-01

We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.

Path-sum solution of the Weyl quantum walk in 3 + 1 dimensions

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D'Ariano, G. M.; Mosco, N.; Perinotti, P.; Tosini, A.

2017-10-01

We consider the Weyl quantum walk in 3+1 dimensions, that is a discrete-time walk describing a particle with two internal degrees of freedom moving on a Cayley graph of the group , which in an appropriate regime evolves according to Weyl's equation. The Weyl quantum walk was recently derived as the unique unitary evolution on a Cayley graph of that is homogeneous and isotropic. The general solution of the quantum walk evolution is provided here in the position representation, by the analytical expression of the propagator, i.e. transition amplitude from a node of the graph to another node in a finite number of steps. The quantum nature of the walk manifests itself in the interference of the paths on the graph joining the given nodes. The solution is based on the binary encoding of the admissible paths on the graph and on the semigroup structure of the walk transition matrices. This article is part of the themed issue `Second quantum revolution: foundational questions'.

A finite state projection algorithm for the stationary solution of the chemical master equation

Science.gov (United States)

Gupta, Ankit; Mikelson, Jan; Khammash, Mustafa

2017-10-01

The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations that describes the evolution of probability density for each population vector in the state-space of the stochastic reaction dynamics. For many examples of interest, this state-space is infinite, making it difficult to obtain exact solutions of the CME. To deal with this problem, the Finite State Projection (FSP) algorithm was developed by Munsky and Khammash [J. Chem. Phys. 124(4), 044104 (2006)], to provide approximate solutions to the CME by truncating the state-space. The FSP works well for finite time-periods but it cannot be used for estimating the stationary solutions of CMEs, which are often of interest in systems biology. The aim of this paper is to develop a version of FSP which we refer to as the stationary FSP (sFSP) that allows one to obtain accurate approximations of the stationary solutions of a CME by solving a finite linear-algebraic system that yields the stationary distribution of a continuous-time Markov chain over the truncated state-space. We derive bounds for the approximation error incurred by sFSP and we establish that under certain stability conditions, these errors can be made arbitrarily small by appropriately expanding the truncated state-space. We provide several examples to illustrate our sFSP method and demonstrate its efficiency in estimating the stationary distributions. In particular, we show that using a quantized tensor-train implementation of our sFSP method, problems admitting more than 100 × 106 states can be efficiently solved.

A finite state projection algorithm for the stationary solution of the chemical master equation.

Science.gov (United States)

Gupta, Ankit; Mikelson, Jan; Khammash, Mustafa

2017-10-21

The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations that describes the evolution of probability density for each population vector in the state-space of the stochastic reaction dynamics. For many examples of interest, this state-space is infinite, making it difficult to obtain exact solutions of the CME. To deal with this problem, the Finite State Projection (FSP) algorithm was developed by Munsky and Khammash [J. Chem. Phys. 124(4), 044104 (2006)], to provide approximate solutions to the CME by truncating the state-space. The FSP works well for finite time-periods but it cannot be used for estimating the stationary solutions of CMEs, which are often of interest in systems biology. The aim of this paper is to develop a version of FSP which we refer to as the stationary FSP (sFSP) that allows one to obtain accurate approximations of the stationary solutions of a CME by solving a finite linear-algebraic system that yields the stationary distribution of a continuous-time Markov chain over the truncated state-space. We derive bounds for the approximation error incurred by sFSP and we establish that under certain stability conditions, these errors can be made arbitrarily small by appropriately expanding the truncated state-space. We provide several examples to illustrate our sFSP method and demonstrate its efficiency in estimating the stationary distributions. In particular, we show that using a quantized tensor-train implementation of our sFSP method, problems admitting more than 100 × 10 6 states can be efficiently solved.

Nonlinear stationary solutions of the Wigner and Wigner-Poisson equations

International Nuclear Information System (INIS)

Haas, F.; Shukla, P. K.

2008-01-01

Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved physically meaningful equilibrium Wigner functions are discussed.

Extremal Kähler metrics and Bach-Merkulov equations

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Koca, Caner

2013-08-01

In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach-Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein-Maxwell equations. Inspired by the work of C. LeBrun on Einstein-Maxwell equations on compact Kähler surfaces, we give a variational characterization of solutions to Bach-Merkulov equations as critical points of the Weyl functional. We also show that extremal Kähler metrics are solutions to these equations, although, contrary to the Einstein-Maxwell analogue, they are not necessarily minimizers of the Weyl functional. We illustrate this phenomenon by studying the Calabi action on Hirzebruch surfaces.

Weyl magnons in breathing pyrochlore antiferromagnets

Science.gov (United States)

Li, Fei-Ye; Li, Yao-Dong; Kim, Yong Baek; Balents, Leon; Yu, Yue; Chen, Gang

2016-01-01

Frustrated quantum magnets not only provide exotic ground states and unusual magnetic structures, but also support unconventional excitations in many cases. Using a physically relevant spin model for a breathing pyrochlore lattice, we discuss the presence of topological linear band crossings of magnons in antiferromagnets. These are the analogues of Weyl fermions in electronic systems, which we dub Weyl magnons. The bulk Weyl magnon implies the presence of chiral magnon surface states forming arcs at finite energy. We argue that such antiferromagnets present a unique example, in which Weyl points can be manipulated in situ in the laboratory by applied fields. We discuss their appearance specifically in the breathing pyrochlore lattice, and give some general discussion of conditions to find Weyl magnons, and how they may be probed experimentally. Our work may inspire a re-examination of the magnetic excitations in many magnetically ordered systems. PMID:27650053

Functional renormalization group approach to interacting three-dimensional Weyl semimetals

Science.gov (United States)

Sharma, Anand; Scammell, Arthur; Krieg, Jan; Kopietz, Peter

2018-03-01

We investigate the effect of long-range Coulomb interaction on the quasiparticle properties and the dielectric function of clean three-dimensional Weyl semimetals at zero temperature using a functional renormalization group (FRG) approach. The Coulomb interaction is represented via a bosonic Hubbard-Stratonovich field which couples to the fermionic density. We derive truncated FRG flow equations for the fermionic and bosonic self-energies and for the three-legged vertices with two fermionic and one bosonic external legs. We consider two different cutoff schemes—cutoff in fermionic or bosonic propagators—in order to calculate the renormalized quasiparticle velocity and the dielectric function for an arbitrary number of Weyl nodes and the interaction strength. If we approximate the dielectric function by its static limit, our results for the velocity and the dielectric function are in good agreement with that of A. A. Abrikosov and S. D. Beneslavskiĭ [Sov. Phys. JETP 32, 699 (1971)] exhibiting slowly varying logarithmic momentum dependence for small momenta. We extend their result for an arbitrary number of Weyl nodes and finite frequency by evaluating the renormalized velocity in the presence of dynamic screening and calculate the wave function renormalization.

Anomalous hydrodynamics of Weyl materials

Science.gov (United States)

Monteiro, Gustavo; Abanov, Alexander

Kinetic theory is a useful tool to study transport in Weyl materials when the band-touching points are hidden inside a Fermi surface. It accounts, for example, for the negative magnetoresistance caused by the chiral magnetic effect and quantum oscillations (SdH effect) in the magnetoresistance together within the same framework. As an alternative approach to kinetic theory we also consider the regime of strong interactions where hydrodynamics can be applicable. A variational principle of these hydrodynamic equations can be found in and provide a natural framework to study hydrodynamic surface modes which correspond to the strongly-interacting physics signature of Fermi arcs. G.M. acknowledges the financial support from FAPESP.

Republication of: New solutions to Einstein's equations of gravitation. B. Explicit determination of static, axially symmetric fields. By Rudolf Bach. With a supplement on the static two-body problem. By H. Weyl.

Science.gov (United States)

Bach, Rudolf; Weyl, Hermann

2012-03-01

This is the English translation of the third of a series of 3 papers by Hermann Weyl (the third one jointly with Rudolf Bach), first published in 1917-1922, in which the authors derived and discussed the now-famous Weyl two-body static axially symmetric vacuum solution of Einstein's equations. The English translations of the other two papers are published alongside this one. The papers have been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Gernot Neugebauer, David Petroff and Bahram Mashhoon, and by a brief biography of R. Bach, written by H. Goenner.

Weyl magnons in noncoplanar stacked kagome antiferromagnets

Science.gov (United States)

Owerre, S. A.

2018-03-01

Weyl nodes have been experimentally realized in photonic, electronic, and phononic crystals. However, magnonic Weyl nodes are yet to be seen experimentally. In this paper, we propose Weyl magnon nodes in noncoplanar stacked frustrated kagome antiferromagnets, naturally available in various real materials. Most crucially, the Weyl nodes in the current system occur at the lowest excitation and possess a topological thermal Hall effect, therefore they are experimentally accessible at low temperatures due to the population effect of bosonic quasiparticles. In stark contrast to other magnetic systems, the current Weyl nodes do not rely on time-reversal symmetry breaking by the magnetic order. Rather, they result from explicit macroscopically broken time reversal symmetry by the scalar spin chirality of noncoplanar spin textures and can be generalized to chiral spin liquid states. Moreover, the scalar spin chirality gives a real space Berry curvature which is not available in previously studied magnetic Weyl systems. We show the existence of magnon arc surface states connecting projected Weyl magnon nodes on the surface Brillouin zone. We also uncover the first realization of triply-degenerate nodal magnon point in the noncollinear regime with zero scalar spin chirality.

Shear-free perfect fluids with zero magnetic Weyl tensor

International Nuclear Information System (INIS)

Collins, C.B.

1984-01-01

Rotating, shear-free general-relativistic perfect fluids are investigated. It is first shown that, if the fluid pressure, p, and energy density, μ, are related by a barotropic equation of state p = p( μ) satifying μ+pnot =0, and if the magnetic part of the Weyl tensor (with respect to the fluid flow) vanishes, then the fluid's volume expansion is zero. The class of all such fluids is subsequently characterized. Further analysis of the solutions shows that, in general, the space-times may be regarded as being locally stationary and axisymmetric (they admit a two-dimensional Abelian isometry group with timelike orbits, which is in fact orthogonally transistive), although various specializations can occur, with the ''most special'' case being the well-known Goedel model, which is space-time homogeneous (it admits a five-dimensional isometry group acting multiply transitively on the space-time). all solutions are of Petrov type D. The fact that there are any solutions in the class at all means that a theorem appearing in the literature is invalid, and the existence of some special solutions in which the fluid's vorticity vector is orthogonal to the acceleration reveals the incompleteness of a previous study of a class of space-times, in which there are Killing vectors parallel to the fluid four-velocity and to the vorticity vector

A generalized Wigner function on the space of irreducible representations of the Weyl-Heisenberg group and its transformation properties

International Nuclear Information System (INIS)

Ibort, A; Man'ko, V I; Marmo, G; Simoni, A; Ventriglia, F

2009-01-01

A natural extension of the Wigner function to the space of irreducible unitary representations of the Weyl-Heisenberg group is discussed. The action of the automorphisms group of the Weyl-Heisenberg group onto Wigner functions and their generalizations and onto symplectic tomograms is elucidated. Some examples of physical systems are considered to illustrate some aspects of the characterization of the Wigner functions as solutions of differential equations

Gravitational and electromagnetic potentials of the stationary Einstein-Maxwell field equations

International Nuclear Information System (INIS)

Jones, T.C.

1979-01-01

Associated with the stationary Einstein-Maxwell field equations is an infinite hierarchy of potentials. The basic characteristics of these potentials are examined in general and then in greater detail for the particular case of the Reissner-Nordstrom metric. Thier essential utility in the process of solution generation is elucidated, and the necessary equations for solution generation are developed. Appropriate generating functions, which contain the complete infinite hierarchy of potentials, are developed and analyzed. Particular attention is paid to the inherent gauge freedom of these generating functions. Two methods of solution generation, which yield asymptotically flat solutions in vacuum, are generalized to include electromagnetism. One method, using potentials consistent with the Harrison transformation and the Reissner-Nordstrom metric, is discussed in detail, and its resultant difficulties are explored

Generation of new solutions of the stationary axisymmetric Einstein equations by a double complex function method

International Nuclear Information System (INIS)

Zhong, Z.

1985-01-01

A new approach to the solution of certain differential equations, the double complex function method, is developed, combining ordinary complex numbers and hyperbolic complex numbers. This method is applied to the theory of stationary axisymmetric Einstein equations in general relativity. A family of exact double solutions, double transformation groups, and n-soliton double solutions are obtained

Theory of Kerr and Faraday rotations and linear dichroism in Topological Weyl Semimetals.

Science.gov (United States)

Kargarian, Mehdi; Randeria, Mohit; Trivedi, Nandini

2015-08-03

We consider the electromagnetic response of a topological Weyl semimetal (TWS) with a pair of Weyl nodes in the bulk and corresponding Fermi arcs in the surface Brillouin zone. We compute the frequency-dependent complex conductivities σαβ(ω) and also take into account the modification of Maxwell equations by the topological θ-term to obtain the Kerr and Faraday rotations in a variety of geometries. For TWS films thinner than the wavelength, the Kerr and Faraday rotations, determined by the separation between Weyl nodes, are significantly larger than in topological insulators. In thicker films, the Kerr and Faraday angles can be enhanced by choice of film thickness and substrate refractive index. We show that, for radiation incident on a surface with Fermi arcs, there is no Kerr or Faraday rotation but the electric field develops a longitudinal component inside the TWS, and there is linear dichroism signal. Our results have implications for probing the TWS phase in various experimental systems.

Two-dimensional Haar wavelet Collocation Method for the solution of Stationary Neutron Transport Equation in a homogeneous isotropic medium

International Nuclear Information System (INIS)

Patra, A.; Saha Ray, S.

2014-01-01

Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet Collocation Method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: This paper emphasizes on finding the solution for a stationary transport equation using the technique of Haar wavelet Collocation Method (HWCM). Haar wavelet Collocation Method is efficient and powerful in solving wide class of linear and nonlinear differential equations. Recently Haar wavelet transform has gained the reputation of being a very effective tool for many practical applications. This paper intends to provide the great utility of Haar wavelets to nuclear science problem. In the present paper, two-dimensional Haar wavelets are applied for solution of the stationary Neutron Transport Equation in homogeneous isotropic medium. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency of the method, one test problem is discussed. It can be observed from the computational simulation that the numerical approximate solution is much closer to the exact solution

Stationary axially symmetric perturbations of a rotating black hole. [Space-time perturbation, Newman-Penrose formalism

Energy Technology Data Exchange (ETDEWEB)

Demianski, M [California Inst. of Tech., Pasadena (USA)

1976-07-01

A stationary axially symmetric perturbation of a rotating black hole due to a distribution of test matter is investigated. The Newman-Penrose spin coefficient formalism is used to derive a general set of equations describing the perturbed space-time. In a linear approximation it is shown that the mass and angular momentum of a rotating black hole is not affected by the perturbation. The metric perturbations near the horizon are given. It is concluded that given a perturbing test fluid distribution, one can always find a corresponding metric perturbation such that the mass and angular momentum of the black hole are not changed. It was also noticed that when a tends to M, those perturbed spin coefficients and components of the Weyl tensor which determine the intrinsic properties of the incoming null cone near the horizon grow indefinitely.

Bosonization of free Weyl fermions

Science.gov (United States)

Marino, E. C.

2017-03-01

We generalize the method of bosonization, in its complete form, to a spacetime with 3  +  1 dimensions, and apply it to free Weyl fermion fields, which thereby, can be expressed in terms of a boson field, namely the Kalb-Ramond anti-symmetric tensor gauge field. The result may have interesting consequences both in condensed matter and in particle physics. In the former, the bosonized form of the Weyl chiral currents provides a simple explanation for the angle-dependent magneto-conductance recently observed in materials known as Weyl semimetals. In the latter, conversely, since electrons can be thought of as a combination of left and right Weyl fermions, our result suggests the possibility of a unified description of the elementary particles, which undergo the fundamental interactions, with the mediators of such interactions, namely, the gauge fields. This would fulfill the pioneering attempt of Skyrme, to unify the particles with their interaction mediators (Skyrme 1962 Nucl. Phys. 31 556).

Solving the two-dimensional stationary transport equation with the aid of the nodal method

International Nuclear Information System (INIS)

Mesina, M.

1976-07-01

In this document the two-dimensional stationary transport equation for the geometry of a fuel assembly or for a system of square boxes has been formulated as an algebraic eigenvalue problem, and the solution was achieved with the computer code NODE 2 which was developed for this purpose. (orig.) [de

Stationary distributions of stochastic processes described by a linear neutral delay differential equation

International Nuclear Information System (INIS)

Frank, T D

2005-01-01

Stationary distributions of processes are derived that involve a time delay and are defined by a linear stochastic neutral delay differential equation. The distributions are Gaussian distributions. The variances of the Gaussian distributions are either monotonically increasing or decreasing functions of the time delays. The variances become infinite when fixed points of corresponding deterministic processes become unstable. (letter to the editor)

Localization and mass spectra of various matter fields on Weyl thin brane

Energy Technology Data Exchange (ETDEWEB)

Sui, Tao-Tao; Zhao, Li; Zhang, Yu-Peng [Lanzhou University, Institute of Theoretical Physics, Lanzhou (China); Xie, Qun-Ying [Lanzhou University, School of Information Science and Engineering, Lanzhou (China)

2017-06-15

It has been shown that the thin brane model in a five-dimensional Weyl gravity can deal with the wrong-signed Friedmann-like equation in the Randall-Sundrum-1 (RS1) model. In the Weyl brane model, there are also two branes with opposite brane tensions, but the four-dimensional graviton (the gravity zero mode) is localized near the negative tension brane, while our four-dimensional universe is localized on the positive tension brane. In this paper, we consider the mass spectra of various bulk matter fields (i.e., scalar, vector, and fermion fields) on the Weyl brane. It is shown that the zero modes of those matter fields can be localized on the positive tension brane under some conditions. The mass spectra of the bulk matter fields are equidistant for the higher excited states, and relatively sparse for the lower excited states. The size of the extra dimension determines the gap of the mass spectra. We also consider the correction to the Newtonian potential in this model and it is proportional to 1/r{sup 3}. (orig.)

Stationary solutions of linear stochastic delay differential equations: applications to biological systems.

Science.gov (United States)

Frank, T D; Beek, P J

2001-08-01

Recently, Küchler and Mensch [Stochastics Stochastics Rep. 40, 23 (1992)] derived exact stationary probability densities for linear stochastic delay differential equations. This paper presents an alternative derivation of these solutions by means of the Fokker-Planck approach introduced by Guillouzic [Phys. Rev. E 59, 3970 (1999); 61, 4906 (2000)]. Applications of this approach, which is argued to have greater generality, are discussed in the context of stochastic models for population growth and tracking movements.

Chiral Anomaly from Strain-Induced Gauge Fields in Dirac and Weyl Semimetals

Science.gov (United States)

Pikulin, D. I.; Chen, Anffany; Franz, M.

2016-10-01

Dirac and Weyl semimetals form an ideal platform for testing ideas developed in high-energy physics to describe massless relativistic particles. One such quintessentially field-theoretic idea of the chiral anomaly already resulted in the prediction and subsequent observation of the pronounced negative magnetoresistance in these novel materials for parallel electric and magnetic fields. Here, we predict that the chiral anomaly occurs—and has experimentally observable consequences—when real electromagnetic fields E and B are replaced by strain-induced pseudo-electromagnetic fields e and b . For example, a uniform pseudomagnetic field b is generated when a Weyl semimetal nanowire is put under torsion. In accordance with the chiral anomaly equation, we predict a negative contribution to the wire resistance proportional to the square of the torsion strength. Remarkably, left- and right-moving chiral modes are then spatially segregated to the bulk and surface of the wire forming a "topological coaxial cable." This produces hydrodynamic flow with potentially very long relaxation time. Another effect we predict is the ultrasonic attenuation and electromagnetic emission due to a time-periodic mechanical deformation causing pseudoelectric field e . These novel manifestations of the chiral anomaly are most striking in the semimetals with a single pair of Weyl nodes but also occur in Dirac semimetals such as Cd3 As2 and Na3Bi and Weyl semimetals with unbroken time-reversal symmetry.

New lumps of Veselov-Novikov integrable nonlinear equation and new exact rational potentials of two-dimensional stationary Schroedinger equation via ∂-macron-dressing method

International Nuclear Information System (INIS)

Dubrovsky, V.G.; Formusatik, I.B.

2003-01-01

The scheme for calculating via Zakharov-Manakov ∂-macron-dressing method of new rational solutions with constant asymptotic values at infinity of the famous two-dimensional Veselov-Novikov (VN) integrable nonlinear evolution equation and new exact rational potentials of two-dimensional stationary Schroedinger (2DSchr) equation with multiple pole wave functions is developed. As examples new lumps of VN nonlinear equation and new exact rational potentials of 2DSchr equation with multiple pole of order two wave functions are calculated. Among the constructed rational solutions are as nonsingular and also singular

Weyl curvature tensor in static spherical sources

International Nuclear Information System (INIS)

Ponce de Leon, J.

1988-01-01

The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed

Calculations of stationary solutions for the non linear viscous resistive MHD equations in slab geometry

International Nuclear Information System (INIS)

Edery, D.

1983-11-01

The reduced system of the non linear resistive MHD equations is used in the 2-D one helicity approximation in the numerical computations of stationary tearing modes. The critical magnetic Raynolds number S (S=tausub(r)/tausub(H) where tausub(R) and tausub(H) are respectively the characteristic resistive and hydro magnetic times) and the corresponding linear solution are computed as a starting approximation for the full non linear equations. These equations are then treated numerically by an iterative procedure which is shown to be rapidly convergent. A numerical application is given in the last part of this paper

Generalization of Einstein's gravitational field equations

Science.gov (United States)

Moulin, Frédéric

2017-12-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

Hermann Weyl and Representation Theory

Indian Academy of Sciences (India)

His work on the theory ofLie groups was motivated by his life-long interest in quantummechanics and relativity. When Weyl entered Lie theory,it mostly focussed on the infinitesimal, and he strove to bringin a global perspective. Time and again, Weyl's ideas arisingin one context have been adapted and applied to wholly ...

Truncated Painleve expansion: Tanh-traveling wave solutions and reduction of sine-Poisson equation to a quadrature for stationary and nonstationary three-dimensional collisionless cold plasma

International Nuclear Information System (INIS)

Ibrahim, R. S.; El-Kalaawy, O. H.

2006-01-01

The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painleve expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model

Weyl's Lagrangian in teleparallel form

International Nuclear Information System (INIS)

Burnett, James; Vassiliev, Dmitri

2009-01-01

The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable - the coframe (an orthonormal tetrad of covector fields). We show that when written in terms of this dynamical variable, the Weyl Lagrangian becomes remarkably simple: it is the wedge product of axial torsion of the teleparallel connection with a teleparallel lightlike element of the coframe. We also examine the issues of U(1)-invariance and conformal invariance. Examination of the latter motivates us to introduce a positive scalar field (equivalent to a density) as an additional dynamical variable; this makes conformal invariance self-evident.

The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

Science.gov (United States)

Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.

2018-04-01

We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

Topological responses from chiral anomaly in multi-Weyl semimetals

Science.gov (United States)

Huang, Ze-Min; Zhou, Jianhui; Shen, Shun-Qing

2017-08-01

Multi-Weyl semimetals are a kind of topological phase of matter with discrete Weyl nodes characterized by multiple monopole charges, in which the chiral anomaly, the anomalous nonconservation of an axial current, occurs in the presence of electric and magnetic fields. Electronic transport properties related to the chiral anomaly in the presence of both electromagnetic fields and axial electromagnetic fields in multi-Weyl semimetals are systematically studied. It has been found that the anomalous Hall conductivity has a modification linear in the axial vector potential from inhomogeneous strains. The axial electric field leads to an axial Hall current that is proportional to the distance of Weyl nodes in momentum space. This axial current may generate chirality accumulation of Weyl fermions through delicately engineering the axial electromagnetic fields even in the absence of external electromagnetic fields. Therefore this work provides a nonmagnetic mechanism of generation of chirality accumulation in Weyl semimetals and might shed new light on the application of Weyl semimetals in the emerging field of valleytronics.

Einstein gravity emerging from quantum weyl gravity

International Nuclear Information System (INIS)

Zee, A.

1983-01-01

We advocate a conformal invariant world described by the sum of the Weyl, Dirac, and Yang-Mills action. Quantum fluctuations bring back Einstein gravity so that the long-distance phenomenology is as observed. Formulas for the induced Newton's constant and Eddington's constant are derived in quantized Weyl gravity. We show that the analogue of the trace anomaly for the Weyl action is structurally similar to that for the Yang-Mills action

Parity-violating hybridization in heavy Weyl semimetals

Science.gov (United States)

Chang, Po-Yao; Coleman, Piers

2018-04-01

We introduce a simple model to describe the formation of heavy Weyl semimetals in noncentrosymmetric heavy fermion compounds under the influence of a parity-mixing, onsite hybridization. A key aspect of interaction-driven heavy Weyl semimetals is the development of surface Kondo breakdown, which is expected to give rise to a temperature-dependent reconfiguration of the Fermi arcs and the Weyl cyclotron orbits which connect them via the chiral bulk states. Our theory predicts a strong temperature-dependent transformation in the quantum oscillations at low temperatures. In addition to the effects of surface Kondo breakdown, the renormalization effects in heavy Weyl semimetals will appear in a variety of thermodynamic and transport measurements.

Note on Weyl versus conformal invariance in field theory

Energy Technology Data Exchange (ETDEWEB)

Wu, Feng [Nanchang University, Department of Physics, Nanchang (China)

2017-12-15

It was argued recently that conformal invariance in flat spacetime implies Weyl invariance in a general curved background for unitary theories and possible anomalies in the Weyl variation of scalar operators are identified. We argue that generically unitarity alone is not sufficient for a conformal field theory to be Weyl invariant. Furthermore, we show explicitly that when a unitary conformal field theory couples to gravity in a Weyl-invariant way, each primary scalar operator that is either relevant or marginal in the unitary conformal field theory corresponds to a Weyl-covariant operator in the curved background. (orig.)

Chiral Anomaly from Strain-Induced Gauge Fields in Dirac and Weyl Semimetals

Directory of Open Access Journals (Sweden)

D. I. Pikulin

2016-10-01

Full Text Available Dirac and Weyl semimetals form an ideal platform for testing ideas developed in high-energy physics to describe massless relativistic particles. One such quintessentially field-theoretic idea of the chiral anomaly already resulted in the prediction and subsequent observation of the pronounced negative magnetoresistance in these novel materials for parallel electric and magnetic fields. Here, we predict that the chiral anomaly occurs—and has experimentally observable consequences—when real electromagnetic fields E and B are replaced by strain-induced pseudo-electromagnetic fields e and b. For example, a uniform pseudomagnetic field b is generated when a Weyl semimetal nanowire is put under torsion. In accordance with the chiral anomaly equation, we predict a negative contribution to the wire resistance proportional to the square of the torsion strength. Remarkably, left- and right-moving chiral modes are then spatially segregated to the bulk and surface of the wire forming a “topological coaxial cable.” This produces hydrodynamic flow with potentially very long relaxation time. Another effect we predict is the ultrasonic attenuation and electromagnetic emission due to a time-periodic mechanical deformation causing pseudoelectric field e. These novel manifestations of the chiral anomaly are most striking in the semimetals with a single pair of Weyl nodes but also occur in Dirac semimetals such as Cd_{3}As_{2} and Na_{3}Bi and Weyl semimetals with unbroken time-reversal symmetry.

Tunable Magnon Weyl Points in Ferromagnetic Pyrochlores.

Science.gov (United States)

Mook, Alexander; Henk, Jürgen; Mertig, Ingrid

2016-10-07

The dispersion relations of magnons in ferromagnetic pyrochlores with Dzyaloshinskii-Moriya interaction are shown to possess Weyl points, i. e., pairs of topologically nontrivial crossings of two magnon branches with opposite topological charge. As a consequence of their topological nature, their projections onto a surface are connected by magnon arcs, thereby resembling closely Fermi arcs of electronic Weyl semimetals. On top of this, the positions of the Weyl points in reciprocal space can be tuned widely by an external magnetic field: rotated within the surface plane, the Weyl points and magnon arcs are rotated as well; tilting the magnetic field out of plane shifts the Weyl points toward the center Γ[over ¯] of the surface Brillouin zone. The theory is valid for the class of ferromagnetic pyrochlores, i. e., three-dimensional extensions of topological magnon insulators on kagome lattices. In this Letter, we focus on the (111) surface, identify candidates of established ferromagnetic pyrochlores which apply to the considered spin model, and suggest experiments for the detection of the topological features.

Holographic p-wave superconductor models with Weyl corrections

Directory of Open Access Journals (Sweden)

Lu Zhang

2015-04-01

Full Text Available We study the effect of the Weyl corrections on the holographic p-wave dual models in the backgrounds of AdS soliton and AdS black hole via a Maxwell complex vector field model by using the numerical and analytical methods. We find that, in the soliton background, the Weyl corrections do not influence the properties of the holographic p-wave insulator/superconductor phase transition, which is different from that of the Yang–Mills theory. However, in the black hole background, we observe that similarly to the Weyl correction effects in the Yang–Mills theory, the higher Weyl corrections make it easier for the p-wave metal/superconductor phase transition to be triggered, which shows that these two p-wave models with Weyl corrections share some similar features for the condensation of the vector operator.

Particle creation phenomenology, Dirac sea and the induced Weyl and Einstein-dilaton gravity

Energy Technology Data Exchange (ETDEWEB)

Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N., E-mail: berezin@inr.ac.ru, E-mail: dokuchaev@inr.ac.ru, E-mail: eroshenko@inr.ac.ru [Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary Prospect 7a, 117312 Moscow (Russian Federation)

2017-01-01

We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the 'usual' hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by 'the particle creation law', proportional to the square of the Weyl tensor (following the famous result by Ya.B. Zel'dovich and A.A. Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein-Hilbert gravity action integral with dilaton field. Thus, we obtained something like the induced gravity suggested first by A.D. Sakharov. It is shown that the resulting system is self-consistent. We considered also the vacuum equations. It is shown that, beside the 'empty vacuum', there may exist the 'dynamical vacuum', which is nothing more but the Dirac sea. The latter is described by the unexpectedly elegant equation which includes both the Bach and Einstein tensors and the cosmological terms.

Weyl tensors for asymmetric complex curvatures

International Nuclear Information System (INIS)

Oliveira, C.G.

Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt

Linear Magnetochiral effect in Weyl Semimetals

Science.gov (United States)

Cortijo, Alberto

We describe the presence of a linear magnetochiral effect in time reversal breaking Weyl semimetals. The magnetochiral effect consists in a simultaneous linear dependence of the magnetotransport coefficients with the magnetic field and a momentum vector. This simultaneous dependence is allowed by the Onsager reciprocity relations, being the separation vector between the Weyl nodes the vector that plays such role. This linear magnetochiral effect constitutes a new transport effect associated to the topological structures linked to time reversal breaking Weyl semimetals. European Union structural funds and the Comunidad de Madrid MAD2D-CM Program (S2013/MIT-3007) and MINECO (Spain) Grant No. FIS2015-73454-JIN.

Recovery of the Dirac system from the rectangular Weyl matrix function

International Nuclear Information System (INIS)

Fritzsche, B; Kirstein, B; Roitberg, I Ya; Sakhnovich, A L

2012-01-01

Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non-expansive in the upper semi-plane. Inverse problems are studied for such Weyl functions, and some results are new even for the square Weyl functions. High-energy asymptotics of Weyl functions and Borg–Marchenko-type uniqueness results are derived too. (paper)

Evidence for topological type-II Weyl semimetal WTe2

KAUST Repository

Li, Peng; Wen, Yan; He, Xin; Zhang, Qiang; Xia, Chuan; Yu, Zhi-Ming; Yang, Shengyuan A.; Zhu, Zhiyong; Alshareef, Husam N.; Zhang, Xixiang

2017-01-01

-called Fermi arcs. Although WTe2 was the first material suggested as a type-II Weyl semimetal, the direct observation of its tilting Weyl cone and Fermi arc has not yet been successful. Here, we show strong evidence that WTe2 is a type-II Weyl semimetal

Evidence for topological type-II Weyl semimetal WTe2

KAUST Repository

Li, Peng

2017-12-11

Recently, a type-II Weyl fermion was theoretically predicted to appear at the contact of electron and hole Fermi surface pockets. A distinguishing feature of the surfaces of type-II Weyl semimetals is the existence of topological surface states, so-called Fermi arcs. Although WTe2 was the first material suggested as a type-II Weyl semimetal, the direct observation of its tilting Weyl cone and Fermi arc has not yet been successful. Here, we show strong evidence that WTe2 is a type-II Weyl semimetal by observing two unique transport properties simultaneously in one WTe2 nanoribbon. The negative magnetoresistance induced by a chiral anomaly is quite anisotropic in WTe2 nanoribbons, which is present in b-axis ribbon, but is absent in a-axis ribbon. An extra-quantum oscillation, arising from a Weyl orbit formed by the Fermi arc and bulk Landau levels, displays a two dimensional feature and decays as the thickness increases in WTe2 nanoribbon.

Recipe for generating Weyl semimetals with extended topologically protected features

Science.gov (United States)

Wang, R.; Zhao, J. Z.; Jin, Y. J.; Xu, W. P.; Gan, L.-Y.; Wu, X. Z.; Xu, H.; Tong, S. Y.

2017-09-01

We present a recipe that leads to Weyl semimetals with extended topologically protected features. We show that compounds in a family that possess time-reversal symmetry and share a noncentrosymmetric cubic structure with the space group F -43 m (no. 216) host robust Weyl fermions with extended and easily measurable protected features. The candidates in this family are compounds with different chemical formulas, A B2 , ABC, AB C2 , and ABCD, and their Fermi levels are predominantly populated by nontrivial Weyl fermions. Symmetry of the system requires that the Weyl nodes with opposite chirality are well separated in momentum space. Adjacent Weyl points have the same chirality; thus these Weyl nodes would not annihilate each other with respect to lattice perturbations. As Fermi arcs and surface states connect Weyl nodes with opposite chirality, the large separation of the latter in momentum space guarantees the appearance of very long arcs and surface states. This work demonstrates that the use of system symmetry by first-principles calculations is a powerful approach for discovering new Weyl semimetals with attractive features whose protected fermions may be candidates of many applications.

A Model for Solving the Maxwell Quasi Stationary Equations in a 3-Phase Electric Reduction Furnace

Directory of Open Access Journals (Sweden)

S. Ekrann

1982-10-01

Full Text Available A computer code has been developed for the approximate computation of electric and magnetic fields within an electric reduction furnace. The paper describes the numerical methods used to solve Maxwell's quasi-stationary equations, which are the governing equations for this problem. The equations are discretized by a staggered grid finite difference technique. The resulting algebraic equations are solved by iterating between computations of electric and magnetic quantities. This 'outer' iteration converges only when the skin depth is larger or of about the same magnitude as the linear dimensions of the computational domain. In solving for electric quantities with magnetic quantities being regarded as known, and vice versa, the central computational task is the solution of a Poisson equation for a scalar potential. These equations are solved by line successive overrelaxation combined with a rebalancing technique.

Hydrodynamic electron flow in a Weyl semimetal slab: Role of Chern-Simons terms

Science.gov (United States)

Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.; Sukhachov, P. O.

2018-05-01

The hydrodynamic flow of the chiral electron fluid in a Weyl semimetal slab of finite thickness is studied by using the consistent hydrodynamic theory. The latter includes viscous, anomalous, and vortical effects, as well as accounts for dynamical electromagnetism. The energy and momentum separations between the Weyl nodes are taken into account via the topological Chern-Simons contributions in the electric current and charge densities in Maxwell's equations. When an external electric field is applied parallel to the slab, it is found that the electron fluid velocity has a nonuniform profile determined by the viscosity and the no-slip boundary conditions. Most remarkably, the fluid velocity field develops a nonzero component across the slab that gradually dissipates when approaching the surfaces. This abnormal component of the flow arises due to the anomalous Hall voltage induced by the topological Chern-Simons current. Another signature feature of the hydrodynamics in Weyl semimetals is a strong modification of the anomalous Hall current along the slab in the direction perpendicular to the applied electric field. Additionally, it is found that the topological current induces an electric potential difference between the surfaces of the slab that is strongly affected by the hydrodynamic flow.

Generalization of Einstein's gravitational field equations

International Nuclear Information System (INIS)

Moulin, Frederic

2017-01-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)

Generalization of Einstein's gravitational field equations

Energy Technology Data Exchange (ETDEWEB)

Moulin, Frederic [Ecole Normale Superieure Paris-Saclay, Departement de Physique, Cachan (France)

2017-12-15

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)

Symmetry and exact solutions of nonlinear spinor equations

International Nuclear Information System (INIS)

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

1989-01-01

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

Numerical solution of the Schrodinger equation for stationary bound states using nodel theorem

International Nuclear Information System (INIS)

Chen Zhijiang; Kong Fanmei; Din Yibin

1987-01-01

An iterative procedure for getting the numerical solution of Schrodinger equation on stationary bound states is introduced. The theoretical foundtion, the practical steps and the method are presented. An example is added at the end. Comparing with other methods, the present one requires less storage, less running time but posesses higher accuracy. It can be run on the personal computer or microcomputer with 256 K memory and 16 bit word length such as IBM/PC, MC68000/83/20, PDP11/23 etc

Asymptotic Theory for the QMLE in GARCH-X Models with Stationary and Non-Stationary Covariates

DEFF Research Database (Denmark)

Han, Heejoon; Kristensen, Dennis

as captured by its long-memory parameter dx; in particular, we allow for both stationary and non-stationary covariates. We show that the QMLE'’s of the regression coefficients entering the volatility equation are consistent and normally distributed in large samples independently of the degree of persistence....... This implies that standard inferential tools, such as t-statistics, do not have to be adjusted to the level of persistence. On the other hand, the intercept in the volatility equation is not identifi…ed when the covariate is non-stationary which is akin to the results of Jensen and Rahbek (2004, Econometric...

Generalized Weyl modules for twisted current algebras

Science.gov (United States)

Makedonskyi, I. A.; Feigin, E. B.

2017-08-01

We introduce the notion of generalized Weyl modules for twisted current algebras. We study their representation-theoretic and combinatorial properties and also their connection with nonsymmetric Macdonald polynomials. As an application, we compute the dimension of the classical Weyl modules in the remaining unknown case.

The Weyl law for contractive maps

Science.gov (United States)

Spina, Maria E.; Rivas, Alejandro M. F.; Carlo, Gabriel

2013-11-01

We find an empirical Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the fractal Weyl law emergence in scattering systems (i.e., having a projective opening) is based on the classical phase space distributions evolved up to the quantum to classical correspondence (Ehrenfest) time. In the contractive case this reasoning fails to describe it. Instead, we conjecture that the support for this behavior is essentially given by the strong non-orthogonality of the eigenvectors of the contractive superoperator. We test the validity of the Weyl law and this conjecture on two paradigmatic systems, the dissipative baker and kicked top maps.

The Weyl law for contractive maps

International Nuclear Information System (INIS)

Spina, Maria E; Rivas, Alejandro M F; Carlo, Gabriel

2013-01-01

We find an empirical Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the fractal Weyl law emergence in scattering systems (i.e., having a projective opening) is based on the classical phase space distributions evolved up to the quantum to classical correspondence (Ehrenfest) time. In the contractive case this reasoning fails to describe it. Instead, we conjecture that the support for this behavior is essentially given by the strong non-orthogonality of the eigenvectors of the contractive superoperator. We test the validity of the Weyl law and this conjecture on two paradigmatic systems, the dissipative baker and kicked top maps. (paper)

Giant anomalous Hall angle in a half-metallic magnetic Weyl semimetal

OpenAIRE

Liu, Enke; Sun, Yan; Müchler, Lukas; Sun, Aili; Jiao, Lin; Kroder, Johannes; Süß, Vicky; Borrmann, Horst; Wang, Wenhong; Schnelle, Walter; Wirth, Steffen; Goennenwein, Sebastian T. B.; Felser, Claudia

2017-01-01

Magnetic Weyl semimetals (WSMs) with time reversal symmetry breaking exhibit Weyl nodes that act as monopoles of Berry curvature and are thus expected to generate a large intrinsic anomalous Hall effect (AHE). However, in most magnetic WSMs, the Weyl nodes are located far from the Fermi energy, making it difficult to observe the Weyl-node dominated intrinsic AHE in experiments. Here we report a novel half-metallic magnetic WSM in the Kagome-lattice Shandite compound Co3Sn2S2. The Weyl nodes, ...

Geon-type solutions of the non-linear Heisenberg-Klein-Gordon equation

International Nuclear Information System (INIS)

Mielke, E.W.; Scherzer, R.

1980-10-01

As a model for a ''unitary'' field theory of extended particles we consider the non-linear Klein-Gordon equation - associated with a ''squared'' Heisenberg-Pauli-Weyl non-linear spinor equation - coupled to strong gravity. Using a stationary spherical ansatz for the complex scalar field as well as for the background metric generated via Einstein's field equation, we are able to study the effects of the scalar self-interaction as well as of the classical tensor forces. By numerical integration we obtain a continuous spectrum of localized, gravitational solitons resembling the geons previously constructed for the Einstein-Maxwell system by Wheeler. A self-generated curvature potential originating from the curved background partially confines the Schroedinger type wave functions within the ''scalar geon''. For zero angular momentum states and normalized scalar charge the spectrum for the total gravitational energy of these solitons exhibits a branching with respect to the number of nodes appearing in the radial part of the scalar field. Preliminary studies for higher values of the corresponding ''principal quantum number'' reveal that a kind of fine splitting of the energy levels occurs, which may indicate a rich, particle-like structure of these ''quantized geons''. (author)

Pseudo-classical theory of Majorana-Weyl particle

International Nuclear Information System (INIS)

Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.

1996-01-01

A pseudo-classical theory of Weyl particle in the space-time dimensions D = 2 n is constructed. The canonical quantization of that pseudo-classical theory is carried out and it results in the theory of the D = 2 n dimensional Weyl particle in the Foldy-Wouthuysen representation. 28 refs

Spacetimes of Weyl and Ricci type N in higher dimensions

International Nuclear Information System (INIS)

Kuchynka, M; Pravdová, A

2016-01-01

We study the geometrical properties of null congruences generated by an aligned null direction of the Weyl tensor (WAND) in spacetimes of Weyl and Ricci type N (possibly with a non-vanishing cosmological constant) in an arbitrary dimension. We prove that a type N Ricci tensor and a type III or N Weyl tensor have to be aligned. In such spacetimes, the multiple WAND has to be geodetic. For spacetimes with type N aligned Weyl and Ricci tensors, the canonical form of the optical matrix in the twisting and non-twisting cases is derived and the dependence of the Weyl and the Ricci tensors and Ricci rotation coefficients on the affine parameter of the geodetic null congruence generated by the WAND is obtained. (paper)

Weyl holographic superconductor in the Lifshitz black hole background

International Nuclear Information System (INIS)

Mansoori, S. A. Hosseini; Mirza, B.; Mokhtari, A.; Dezaki, F. Lalehgani; Sherkatghanad, Z.

2016-01-01

We investigate analytically the properties of the Weyl holographic superconductor in the Lifshitz black hole background. We find that the critical temperature of the Weyl superconductor decreases with increasing Lifshitz dynamical exponent, z, indicating that condensation becomes difficult. In addition, it is found that the critical temperature and condensation operator could be affected by applying the Weyl coupling, γ. Moreover, we compute the critical magnetic field and investigate its dependence on the parameters γ and z. Finally, we show numerically that the Weyl coupling parameter γ and the Lifshitz dynamical exponent z together control the size and strength of the conductivity peak and the ratio of gap frequency over critical temperature ω_g/T_c.

Weyl holographic superconductor in the Lifshitz black hole background

Energy Technology Data Exchange (ETDEWEB)

Mansoori, S. A. Hosseini [Department of Physics, Boston University,590 Commonwealth Ave., Boston, MA 02215 (United States); Department of Physics, Isfahan University of Technology,Isfahan 84156-83111 (Iran, Islamic Republic of); Mirza, B. [Department of Physics, Isfahan University of Technology,Isfahan 84156-83111 (Iran, Islamic Republic of); Mokhtari, A. [Department of Physics, Tarbiat Modares University,Tehran 14155-4838 (Iran, Islamic Republic of); Dezaki, F. Lalehgani; Sherkatghanad, Z. [Department of Physics, Isfahan University of Technology,Isfahan 84156-83111 (Iran, Islamic Republic of)

2016-07-21

We investigate analytically the properties of the Weyl holographic superconductor in the Lifshitz black hole background. We find that the critical temperature of the Weyl superconductor decreases with increasing Lifshitz dynamical exponent, z, indicating that condensation becomes difficult. In addition, it is found that the critical temperature and condensation operator could be affected by applying the Weyl coupling, γ. Moreover, we compute the critical magnetic field and investigate its dependence on the parameters γ and z. Finally, we show numerically that the Weyl coupling parameter γ and the Lifshitz dynamical exponent z together control the size and strength of the conductivity peak and the ratio of gap frequency over critical temperature ω{sub g}/T{sub c}.

Weyl holographic superconductor in the Lifshitz black hole background

Science.gov (United States)

Mansoori, S. A. Hosseini; Mirza, B.; Mokhtari, A.; Dezaki, F. Lalehgani; Sherkatghanad, Z.

2016-07-01

We investigate analytically the properties of the Weyl holographic superconductor in the Lifshitz black hole background. We find that the critical temperature of the Weyl superconductor decreases with increasing Lifshitz dynamical exponent, z, indicating that condensation becomes difficult. In addition, it is found that the critical temperature and condensation operator could be affected by applying the Weyl coupling, γ. Moreover, we compute the critical magnetic field and investigate its dependence on the parameters γ and z. Finally, we show numerically that the Weyl coupling parameter γ and the Lifshitz dynamical exponent z together control the size and strength of the conductivity peak and the ratio of gap frequency over critical temperature ω g /T c .

Gauge invariance and Weyl-polymer quantization

CERN Document Server

Strocchi, Franco

2016-01-01

The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable.  The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators). However, in physically interesting cases -- typically in the presence of a gauge symmetry -- non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the observable algebra. In general, a gauge invariant ground state defines a non-regular representation of the gauge dependent Weyl operators, providing a mathematically consistent treatment of familiar quantum systems -- such as the electron in a periodic potential (Bloch electron), the Quantum Hall electron, or the quantum particle on a circle -- where the gauge transformations are, respectively, the lattice translations, the magne...

Metric reconstruction from Weyl scalars

Energy Technology Data Exchange (ETDEWEB)

Whiting, Bernard F; Price, Larry R [Department of Physics, PO Box 118440, University of Florida, Gainesville, FL 32611 (United States)

2005-08-07

The Kerr geometry has remained an elusive world in which to explore physics and delve into the more esoteric implications of general relativity. Following the discovery, by Kerr in 1963, of the metric for a rotating black hole, the most major advance has been an understanding of its Weyl curvature perturbations based on Teukolsky's discovery of separable wave equations some ten years later. In the current research climate, where experiments across the globe are preparing for the first detection of gravitational waves, a more complete understanding than concerns just the Weyl curvature is now called for. To understand precisely how comparatively small masses move in response to the gravitational waves they emit, a formalism has been developed based on a description of the whole spacetime metric perturbation in the neighbourhood of the emission region. Presently, such a description is not available for the Kerr geometry. While there does exist a prescription for obtaining metric perturbations once curvature perturbations are known, it has become apparent that there are gaps in that formalism which are still waiting to be filled. The most serious gaps include gauge inflexibility, the inability to include sources-which are essential when the emitting masses are considered-and the failure to describe the l = 0 and 1 perturbation properties. Among these latter properties of the perturbed spacetime, arising from a point mass in orbit, are the perturbed mass and axial component of angular momentum, as well as the very elusive Carter constant for non-axial angular momentum. A status report is given on recent work which begins to repair these deficiencies in our current incomplete description of Kerr metric perturbations.

Metric reconstruction from Weyl scalars

International Nuclear Information System (INIS)

Whiting, Bernard F; Price, Larry R

2005-01-01

The Kerr geometry has remained an elusive world in which to explore physics and delve into the more esoteric implications of general relativity. Following the discovery, by Kerr in 1963, of the metric for a rotating black hole, the most major advance has been an understanding of its Weyl curvature perturbations based on Teukolsky's discovery of separable wave equations some ten years later. In the current research climate, where experiments across the globe are preparing for the first detection of gravitational waves, a more complete understanding than concerns just the Weyl curvature is now called for. To understand precisely how comparatively small masses move in response to the gravitational waves they emit, a formalism has been developed based on a description of the whole spacetime metric perturbation in the neighbourhood of the emission region. Presently, such a description is not available for the Kerr geometry. While there does exist a prescription for obtaining metric perturbations once curvature perturbations are known, it has become apparent that there are gaps in that formalism which are still waiting to be filled. The most serious gaps include gauge inflexibility, the inability to include sources-which are essential when the emitting masses are considered-and the failure to describe the l = 0 and 1 perturbation properties. Among these latter properties of the perturbed spacetime, arising from a point mass in orbit, are the perturbed mass and axial component of angular momentum, as well as the very elusive Carter constant for non-axial angular momentum. A status report is given on recent work which begins to repair these deficiencies in our current incomplete description of Kerr metric perturbations

Stationary scattering theory

International Nuclear Information System (INIS)

Combes, J.M.

1980-10-01

A complementary approach to the time dependent scattering theory for one-body Schroedinger operators is presented. The stationary theory is concerned with objects of quantum theory like scattering waves and amplitudes. In the more recent abstract stationary theory some generalized form of the Lippman-Schwinger equation plays the basic role. Solving this equation leads to a linear map between generalized eigenfunctions of the perturbed and unperturbed operators. This map is the section at fixed energy of the wave-operator from the time dependent theory. Although the radiation condition does not appears explicitely in this formulation it can be shown to hold a posteriori in a variety of situations thus restoring the link with physical theories

Stationary black holes with stringy hair

Science.gov (United States)

Boos, Jens; Frolov, Valeri P.

2018-01-01

We discuss properties of black holes which are pierced by special configurations of cosmic strings. For static black holes, we consider radial strings in the limit when the number of strings grows to infinity while the tension of each single string tends to zero. In a properly taken limit, the stress-energy tensor of the string distribution is finite. We call such matter stringy matter. We present a solution of the Einstein equations for an electrically charged static black hole with the stringy matter, with and without a cosmological constant. This solution is a warped product of two metrics. One of them is a deformed 2-sphere, whose Gaussian curvature is determined by the energy density of the stringy matter. We discuss the embedding of a corresponding distorted sphere into a three-dimensional Euclidean space and formulate consistency conditions. We also found a relation between the square of the Weyl tensor invariant of the four-dimensional spacetime of the stringy black holes and the energy density of the stringy matter. In the second part of the paper, we discuss test stationary strings in the Kerr geometry and in its Kerr-NUT-(anti-)de Sitter generalizations. Explicit solutions for strings that are regular at the event horizon are obtained. Using these solutions, the stress-energy tensor of the stringy matter in these geometries is calculated. Extraction of the angular momentum from rotating black holes by such strings is also discussed.

Ulam method and fractal Weyl law for Perron-Frobenius operators

Science.gov (United States)

Ermann, L.; Shepelyansky, D. L.

2010-06-01

We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d0/2 where d0 is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.

Stationary black holes: large D analysis

International Nuclear Information System (INIS)

Suzuki, Ryotaku; Tanabe, Kentaro

2015-01-01

We consider the effective theory of large D stationary black holes. By solving the Einstein equations with a cosmological constant using the 1/D expansion in near zone of the black hole we obtain the effective equation for the stationary black hole. The effective equation describes the Myers-Perry black hole, bumpy black holes and, possibly, the black ring solution as its solutions. In this effective theory the black hole is represented as an embedded membrane in the background, e.g., Minkowski or Anti-de Sitter spacetime and its mean curvature is given by the surface gravity redshifted by the background gravitational field and the local Lorentz boost. The local Lorentz boost property of the effective equation is observed also in the metric itself. In fact we show that the leading order metric of the Einstein equation in the 1/D expansion is generically regarded as a Lorentz boosted Schwarzschild black hole. We apply this Lorentz boost property of the stationary black hole solution to solve perturbation equations. As a result we obtain an analytic formula for quasinormal modes of the singly rotating Myers-Perry black hole in the 1/D expansion.

Weyl nodes in Andreev spectra of multiterminal Josephson junctions: Chern numbers, conductances, and supercurrents

Science.gov (United States)

Xie, Hong-Yi; Vavilov, Maxim G.; Levchenko, Alex

2018-02-01

We consider mesoscopic four-terminal Josephson junctions and study emergent topological properties of the Andreev subgap bands. We use symmetry-constrained analysis for Wigner-Dyson classes of scattering matrices to derive band dispersions. When the scattering matrix of the normal region connecting superconducting leads is energy independent, the determinant formula for Andreev spectrum can be reduced to a palindromic equation that admits a complete analytical solution. Band topology manifests with an appearance of the Weyl nodes which serve as monopoles of finite Berry curvature. The corresponding fluxes are quantified by Chern numbers that translate into a quantized nonlocal conductance that we compute explicitly for the time-reversal-symmetric scattering matrix. The topological regime can also be identified by supercurrents as Josephson current-phase relationships exhibit pronounced nonanalytic behavior and discontinuities near Weyl points that can be controllably accessed in experiments.

Transversal magnetotransport in Weyl semimetals: Exact numerical approach

Science.gov (United States)

Behrends, Jan; Kunst, Flore K.; Sbierski, Björn

2018-02-01

Magnetotransport experiments on Weyl semimetals are essential for investigating the intriguing topological and low-energy properties of Weyl nodes. If the transport direction is perpendicular to the applied magnetic field, experiments have shown a large positive magnetoresistance. In this work we present a theoretical scattering matrix approach to transversal magnetotransport in a Weyl node. Our numerical method confirms and goes beyond the existing perturbative analytical approach by treating disorder exactly. It is formulated in real space and is applicable to mesoscopic samples as well as in the bulk limit. In particular, we study the case of clean and strongly disordered samples.

Electronic properties of disordered Weyl semimetals at charge neutrality

Science.gov (United States)

Holder, Tobias; Huang, Chia-Wei; Ostrovsky, Pavel M.

2017-11-01

Weyl semimetals have been intensely studied as a three-dimensional realization of a Dirac-like excitation spectrum where the conduction bands and valence bands touch at isolated Weyl points in momentum space. Like in graphene, this property entails various peculiar electronic properties. However, recent theoretical studies have suggested that resonant scattering from rare regions can give rise to a nonzero density of states even at charge neutrality. Here, we give a detailed account of this effect and demonstrate how the semimetallic nature is suppressed at the lowest scales. To this end, we develop a self-consistent T -matrix approach to investigate the density of states beyond the limit of weak disorder. Our results show a nonvanishing density of states at the Weyl point, which exhibits a nonanalytic dependence on the impurity density. This unusually strong effect of rare regions leads to a revised estimate for the conductivity close to the Weyl point and emphasizes possible deviations from semimetallic behavior in dirty Weyl semimetals at charge neutrality even with very low impurity concentration.

Stationary axially symmetric exterior solutions in the five-dimensional representation of the Brans-Dicke-Jordan theory of gravitation

International Nuclear Information System (INIS)

Bruckman, W.

1986-01-01

The inverse scattering method of Belinsky and Zakharov is used to investigate axially symmetric stationary vacuum soliton solutions in the five-dimensional representation of the Brans-Dicke-Jordan theory of gravitation, where the scalar field of the theory is an element of a five-dimensional metric. The resulting equations for the spacetime metric are similar to those of solitons in general relativity, while the scalar field generated is the product of a simple function of the coordinates and an already known scalar field solution. A family of solutions is considered that reduce, in the absence of rotation, to the five-dimensional form of a well-known Weyl-Levi Civita axially symmetric static vacuum solution. With a suitable choice of parameters, this static limit becomes equivalent to the spherically symmetric solution of the Brans-Dicke theory. An exact metric, in which the Kerr-scalar McIntosh solution is a special case, is given explicitly

Some strange numerical solutions of the non-stationary Navier-Stokes equations in pipes

Energy Technology Data Exchange (ETDEWEB)

Rummler, B.

2001-07-01

A general class of boundary-pressure-driven flows of incompressible Newtonian fluids in three-dimensional pipes with known steady laminar realizations is investigated. Considering the laminar velocity as a 3D-vector-function of the cross-section-circle arguments, we fix the scale for the velocity by the L{sub 2}-norm of the laminar velocity. The usual new variables are introduced to get dimension-free Navier-Stokes equations. The characteristic physical and geometrical quantities are subsumed in the energetic Reynolds number Re and a parameter {psi}, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form u=u{sub L}+u, where u{sub L} is the scaled laminar velocity and periodical conditions in center-line-direction are prescribed for u. An autonomous system (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction is got by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u. The finite-dimensional approximations u{sub N({lambda}}{sub )} of u are defined in the usual way. (orig.)

Stationary closed strings in five-dimensional flat spacetime

Science.gov (United States)

Igata, Takahisa; Ishihara, Hideki; Nishiwaki, Keisuke

2012-11-01

We investigate stationary rotating closed Nambu-Goto strings in five-dimensional flat spacetime. The stationary string is defined as a world sheet that is tangent to a timelike Killing vector. The Nambu-Goto equation of motion for the stationary string is reduced to the geodesic equation on the orbit space of the isometry group action generated by the Killing vector. We take a linear combination of a time-translation vector and space-rotation vectors as the Killing vector, and explicitly construct general solutions of stationary rotating closed strings in five-dimensional flat spacetime. We show a variety of their configurations and properties.

Bloch-Siegert shift in Dirac-Weyl fermionic systems

Science.gov (United States)

Kumar, Upendra; Kumar, Vipin; Enamullah, Setlur, Girish S.

2018-04-01

The Bloch-Siegert shift is a phenomenon in quantum optics, typically seen in two-level systems, when the driving field is sufficiently strong. The inclusion of frequency doubling effect (counter rotating term) in the conventional rotating wave approximation (RWA) changes the resonance condition thereby producing a rather small shift in the resonance condition, which is known as the Bloch-Siegert shift (BSS). Rabi oscillations in Dirac-Weyl fermionic systems exhibit anomalous behavior far from resonance, called anomalous Rabi oscillations. Therefore, in the present work, we study the phenomenon of the Bloch-Siegert shift in Weyl semimetal and topological insulator (TI) far from resonance, called anomalous Bloch-Siegert shift (ABSS). It is seen that the change in the resonance condition of anomalous Rabi oscillations is drastic in Weyl semimetal and TI. The ABSS in Weyl semimetals is highly anisotropic, whereas it is isotropic in TI. In case of TI, it is the Chern number which plays a crucial role to produce substantial change in the ABSS.

Quasiparticle scattering in type-II Weyl semimetal MoTe2.

Science.gov (United States)

Lin, Chun-Liang; Arafune, Ryuichi; Minamitani, Emi; Kawai, Maki; Takagi, Noriaki

2018-02-15

The electronic structure of type-II Weyl semimetal molybdenum ditelluride (MoTe 2 ) is studied by using scanning tunneling microscopy and density functional theory calculations. Through measuring energy-dependent quasiparticle interference (QPI) patterns with a cryogenic scanning tunneling microscope, several characteristic features are found in the QPI patterns. Two of them arise from the Weyl semimetal nature; one is the topological Fermi arc surface state and the other can be assigned to be a Weyl point. The remaining structures are derived from the scatterings relevant to the bulk electronic states. The findings lead to further understanding of the topological electronic structure of type-II Weyl semimetal MoTe 2 .

Quasiparticle scattering in type-II Weyl semimetal MoTe2

Science.gov (United States)

Lin, Chun-Liang; Arafune, Ryuichi; Minamitani, Emi; Kawai, Maki; Takagi, Noriaki

2018-03-01

The electronic structure of type-II Weyl semimetal molybdenum ditelluride (MoTe2) is studied by using scanning tunneling microscopy and density functional theory calculations. Through measuring energy-dependent quasiparticle interference (QPI) patterns with a cryogenic scanning tunneling microscope, several characteristic features are found in the QPI patterns. Two of them arise from the Weyl semimetal nature; one is the topological Fermi arc surface state and the other can be assigned to be a Weyl point. The remaining structures are derived from the scatterings relevant to the bulk electronic states. The findings lead to further understanding of the topological electronic structure of type-II Weyl semimetal MoTe2.

Spin Hall and Nernst effects of Weyl magnons

Science.gov (United States)

Zyuzin, Vladimir A.; Kovalev, Alexey A.

2018-05-01

In this paper, we present a simple model of a three-dimensional insulating magnetic structure which represents a magnonic analog of the layered electronic system described by A. A. Burkov and L. Balents [Phys. Rev. Lett. 107, 127205 (2011), 10.1103/PhysRevLett.107.127205]. In particular, our model realizes Weyl magnons as well as surface states with a Dirac spectrum. In this model, the Dzyaloshinskii-Moriya interaction is responsible for the separation of opposite Weyl points in momentum space. We calculate the intrinsic (due to the Berry curvature) transport properties of Weyl and so-called anomalous Hall effect magnons. The results are compared with fermionic analogs.

Novel symmetries in Weyl-invariant gravity with massive gauge field

Energy Technology Data Exchange (ETDEWEB)

Abhinav, K. [S.N. Bose National Centre for Basic Sciences, Salt Lake, Kolkata (India); Shukla, A.; Panigrahi, P.K. [Indian Institute of Science Education and Research Kolkata, Mohanpur (India)

2016-11-15

The background field method is used to linearize the Weyl-invariant scalar-tensor gravity, coupled with a Stueckelberg field. For a generic background metric, this action is found not to be invariant, under both a diffeomorphism and generalized Weyl symmetry, the latter being a combination of gauge and Weyl transformations. Interestingly, the quadratic Lagrangian, emerging from a background of Minkowski metric, respects both transformations independently. The Becchi-Rouet-Stora-Tyutin symmetry of scalar-tensor gravity coupled with a Stueckelberg-like massive gauge particle, possessing a diffeomorphism and generalized Weyl symmetry, reveals that in both cases negative-norm states with unphysical degrees of freedom do exist. We then show that, by combining diffeomorphism and generalized Weyl symmetries, all the ghost states decouple, thereby removing the unphysical redundancies of the theory. During this process, the scalar field does not represent any dynamic mode, yet modifies the usual harmonic gauge condition through non-minimal coupling with gravity. (orig.)

On the propagation of Einstein's equations with quasi-Maxwellian equations of gravity

International Nuclear Information System (INIS)

Novello, M.; Salim, J.M.

1985-01-01

It is proved that an affirmation proposed in a recent paper of Lesche and Som in which they argue about the non equivalence in the use of Weyl conformal tensor instead of the fuel curvature tensor in Bianchi identities regarded as the equation of evolution is wrong. (L.C.) [pt

Quasiparticle Scattering in Type-II Weyl semimetal MoTe2.

Science.gov (United States)

Lin, Chun-Liang; Arafune, Ryuichi; Minamitani, Emi; Kawai, Maki; Takagi, Noriaki

2018-01-30

The electronic structure of type-II Weyl semimetal molybdenum ditelluride (MoTe₂) is studied by using scanning tunneling microscopy and density functional theory calculations. Through measuring energy-dependent quasiparticle interference (QPI) patterns with a cryogenic scanning tunneling microscope, several characteristic features are found in the QPI patterns. Two of them arise from the Weyl semimetal nature; one is the topological Fermi arc surface state and the other can be assigned to be a Weyl point. The remaining structures are derived from the scatterings relevant to the bulk electronic states. The findings lead to thorough understanding of the topological electronic structure of type-II Weyl semimetal MoTe₂. © 2018 IOP Publishing Ltd.

Weyl type N solutions with null electromagnetic fields in the Einstein-Maxwell p-form theory

Czech Academy of Sciences Publication Activity Database

Kuchynka, Martin; Pravdová, Alena

2017-01-01

Roč. 49, č. 5 (2017), č. článku 71. ISSN 0001-7701 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : Einstein–Maxwell equations * Weyl type N spacetimes * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.618, year: 2016 https://link.springer.com/article/10.1007/s10714-017-2234-7

Strain-induced chiral magnetic effect in Weyl semimetals

International Nuclear Information System (INIS)

Cortijo, Alberto; Kharzeev, Dmitri; Vozmediano, Maria A. H.

2016-01-01

Here, we argue that strain applied to a time-reversal and inversion breaking Weyl semimetal in a magnetic field can induce an electric current via the chiral magnetic effect. A tight-binding model is used to show that strain generically changes the locations in the Brillouin zone but also the energies of the band touching points (tips of the Weyl cones). Since axial charge in a Weyl semimetal can relax via intervalley scattering processes, the induced current will decay with a time scale given by the lifetime of a chiral quasiparticle. Lastly, we estimate the strength and lifetime of the current for typical material parameters and find that it should be experimentally observable.

Mathematical implications of Einstein-Weyl causality

International Nuclear Information System (INIS)

Borchers, H.J.; Sen, R.N.

2006-01-01

The present work is the first systematic attempt at answering the following fundamental question: what mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The authors propose an axiomatization of Einstein-Weyl causality (inspired by physics), and investigate the topological and uniform structures that it implies. Their final result is that a causal space is densely embedded in one that is locally a differentiable manifold. The mathematical level required of the reader is that of the graduate student in mathematical physics. (orig.)

Majorana and Majorana-Weyl fermions in lattice gauge theory

International Nuclear Information System (INIS)

Inagaki, Teruaki; Suzuki, Hiroshi

2004-01-01

In various dimensional Euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1 + 8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factorized form of the Dirac determinant. Similarly, in 2 + 8n dimensions, there is a difficulty to decompose a classical lattice action of the Weyl fermion into a system of the Majorana-Weyl fermion and thus to obtain a factorized form of the Weyl determinant. Prescriptions based on the overlap formalism do not remove these difficulties. We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in 8n dimensions. For this reason (besides other well-known reasons), a lattice formulation of the N = 1 super Yang-Mills theory in these dimensions is expected to be extremely difficult to find. (author)

Stability of the Weyl-semimetal phase on the pyrochlore lattice

Science.gov (United States)

Berke, Christoph; Michetti, Paolo; Timm, Carsten

2018-04-01

Motivated by the proposal of a Weyl-semimetal phase in pyrochlore iridates, we consider a Hubbard-type model on the pyrochlore lattice. To shed light on the question as to why such a state has not been observed experimentally, its robustness is analyzed. On the one hand, we study the possible phases when the system is doped. Magnetic frustration favors several phases with magnetic and charge order that do not occur at half filling, including additional Weyl-semimetal states close to quarter filling. On the other hand, we search for density waves that break translational symmetry and destroy the Weyl-semimetal phase close to half filling. The uniform Weyl semimetal is found to be stable, which we attribute to the low density of states close to the Fermi energy.

The Cauchy problem for the Pavlov equation with large data

Science.gov (United States)

Wu, Derchyi

2017-08-01

We prove a local solvability of the Cauchy problem for the Pavlov equation with large initial data by the inverse scattering method. The Pavlov equation arises in studies Einstein-Weyl geometries and dispersionless integrable models. Our theory yields a local solvability of Cauchy problems for a quasi-linear wave equation with a characteristic initial hypersurface.

The Weyl non-Abelian gauge field and the Thomas precession

International Nuclear Information System (INIS)

Barbashov, B.M.; Pestov, A.B.

1998-01-01

The connection between the Fermi-Walker transport and the Weyl non-Abelian gauge field is established. A theoretical possibility of detecting the Weyl gauge field caused by the Thomas precession of a gyroscope is discussed

Simple recipe for holographic Weyl anomaly

Energy Technology Data Exchange (ETDEWEB)

Bugini, F. [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción,Casilla 160-C, Concepción (Chile); Diaz, D.E. [Departamento de Ciencias Físicas, Facultad de Ciencias Exactas, Universidad Andres Bello,Autopista Concepción-Talcahuano 7100, Talcahuano (Chile)

2017-04-20

We propose a recipe — arguably the simplest — to compute the holographic type-B Weyl anomaly for general higher-derivative gravity in asymptotically AdS spacetimes. In 5 and 7 dimensions we identify a suitable basis of curvature invariants that allows to read off easily, without any further computation, the Weyl anomaly coefficients of the dual CFT. We tabulate the contributions from quadratic, cubic and quartic purely algebraic curvature invariants and also from terms involving derivatives of the curvature. We provide few examples, where the anomaly coefficients have been obtained by other means, to illustrate the effectiveness of our prescription.

Universal scattering response across the type-II Weyl semimetal phase diagram

Science.gov (United States)

Rüßmann, P.; Weber, A. P.; Glott, F.; Xu, N.; Fanciulli, M.; Muff, S.; Magrez, A.; Bugnon, P.; Berger, H.; Bode, M.; Dil, J. H.; Blügel, S.; Mavropoulos, P.; Sessi, P.

2018-02-01

The discovery of Weyl semimetals represents a significant advance in topological band theory. They paradigmatically enlarged the classification of topological materials to gapless systems while simultaneously providing experimental evidence for the long-sought Weyl fermions. Beyond fundamental relevance, their high mobility, strong magnetoresistance, and the possible existence of even more exotic effects, such as the chiral anomaly, make Weyl semimetals a promising platform to develop radically new technology. Fully exploiting their potential requires going beyond the mere identification of materials and calls for a detailed characterization of their functional response, which is severely complicated by the coexistence of surface- and bulk-derived topologically protected quasiparticles, i.e., Fermi arcs and Weyl points, respectively. Here, we focus on the type-II Weyl semimetal class in which we find a stoichiometry-dependent phase transition from a trivial to a nontrivial regime. By exploring the two extreme cases of the phase diagram, we demonstrate the existence of a universal response of both surface and bulk states to perturbations. We show that quasiparticle interference patterns originate from scattering events among surface arcs. Analysis reveals that topologically nontrivial contributions are strongly suppressed by spin texture. We also show that scattering at localized impurities can generate defect-induced quasiparticles sitting close to the Weyl point energy. These give rise to strong peaks in the local density of states, which lift the Weyl node, significantly altering the pristine low-energy spectrum. Remarkably, by comparing the WTe2 and the MoTe2 cases we found that scattering response and topological transition are not directly linked. Visualizing the existence of a universal microscopic response to scattering has important consequences for understanding the unusual transport properties of this class of materials. Overall, our observations provide

Weyl magnons in pyrochlore antiferromagnets with an all-in-all-out order

Science.gov (United States)

Jian, Shao-Kai; Nie, Wenxing

2018-03-01

We investigate topological magnon band crossings of pyrochlore antiferromagnets with all-in-all-out (AIAO) magnetic order. By general symmetry analysis and spin-wave theory, we show that pyrochlore materials with AIAO orders can host Weyl magnons under external magnetic fields or uniaxial strains. Under a small magnetic field, the magnon bands of the pyrochlore with AIAO background can feature two opposite-charged Weyl points, which is the minimal number of Weyl points realizable in quantum materials, and has not been experimentally observed so far. We further show that breathing pyrochlores with AIAO orders can exhibit Weyl magnons upon uniaxial strains. These findings apply to any pyrochlore material supporting AIAO orders, irrespective of the forms of interactions. Specifically, we show that the Weyl magnons are robust against direct (positive) Dzyaloshinskii-Moriya interactions. Because of the ubiquitous AIAO orders in pyrochlore magnets including R2Ir2O7 , and experimentally achievable external strain and magnetic field, our predictions provide a promising arena to witness the Weyl magnons in quantum magnets.

Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective

Science.gov (United States)

Bernard, Julien

2018-02-01

I reconstruct Riemann's and Helmholtz-Lie's problems of space, from some perspectives that allow for a fruitful comparison with Weyl. In Part II. of his inaugural lecture, Riemann justifies that the infinitesimal metric is the square root of a quadratic form. Thanks to Finsler geometry, I clarify both the implicit and explicit hypotheses used for this justification. I explain that Riemann-Finsler's kind of method is also appropriate to deal with indefinite metrics. Nevertheless, Weyl shares with Helmholtz a strong commitment to the idea that the notion of group should be at the center of the foundations of geometry. Riemann missed this point, and that is why, according to Weyl, he dealt with the problem of space in a "too formal" way. As a consequence, to solve the problem of space, Weyl abandoned Riemann-Finsler's methods for group-theoretical ones. However, from a philosophical point of view, I show that Weyl and Helmholtz are in strong opposition. The meditation on Riemann's inaugural lecture, and its clear methodological separation between the infinitesimal and the finite parts of the problem of space, must have been crucial for Weyl, while searching for strong epistemological foundations for the group-theoretical methods, avoiding Helmholtz's unjustified transition from the finite to the infinitesimal.

Boundary Layers for the Navier-Stokes Equations Linearized Around a Stationary Euler Flow

Science.gov (United States)

Gie, Gung-Min; Kelliher, James P.; Mazzucato, Anna L.

2018-03-01

We study the viscous boundary layer that forms at small viscosity near a rigid wall for the solution to the Navier-Stokes equations linearized around a smooth and stationary Euler flow (LNSE for short) in a smooth bounded domain Ω \\subset R^3 under no-slip boundary conditions. LNSE is supplemented with smooth initial data and smooth external forcing, assumed ill-prepared, that is, not compatible with the no-slip boundary condition. We construct an approximate solution to LNSE on the time interval [0, T], 0Math J 45(3):863-916, 1996), Xin and Yanagisawa (Commun Pure Appl Math 52(4):479-541, 1999), and Gie (Commun Math Sci 12(2):383-400, 2014).

Two-dimensional Lorentz-Weyl anomaly and gravitational Chern-Simons theory

International Nuclear Information System (INIS)

Chamseddine, A.H.; Froehlich, J.

1992-01-01

Two-dimensional chiral fermions and bosons, more generally conformal blocks of two-dimensional conformal field theories, exhibit Weyl-, Lorentz- and mixed Lorentz-Weyl anomalies. A novel way of computing these anomalies for a system of chiral bosons of arbitrary conformal spin j is sketched. It is shown that the Lorentz- and mixed Lorentz-Weyl anomalies of these theories can be cancelled by the anomalies of a three-dimensional classical Chern-Simons action for the spin connection, expressed in terms of the dreibein field. Some tentative applications of this result to string theory are indicated. (orig.)

Propagation of Boundary-Induced Discontinuity in Stationary Radiative Transfer

Science.gov (United States)

Kawagoe, Daisuke; Chen, I.-Kun

2018-01-01

We consider the boundary value problem of the stationary transport equation in the slab domain of general dimensions. In this paper, we discuss the relation between discontinuity of the incoming boundary data and that of the solution to the stationary transport equation. We introduce two conditions posed on the boundary data so that discontinuity of the boundary data propagates along positive characteristic lines as that of the solution to the stationary transport equation. Our analysis does not depend on the celebrated velocity averaging lemma, which is different from previous works. We also introduce an example in two dimensional case which shows that piecewise continuity of the boundary data is not a sufficient condition for the main result.

Exact and analytic solutions of the Ernst equation governing axially symmetric stationary vacuum gravitational fields

International Nuclear Information System (INIS)

Baxter, Mathew; Van Gorder, Robert A

2013-01-01

We obtain solutions to a transformation of the axially symmetric Ernst equation, which governs a class of exact solutions of Einstein's field equations. Physically, the equation serves as a model of axially symmetric stationary vacuum gravitational fields. By an application of the method of homotopy analysis, we are able to construct approximate analytic solutions to the relevant boundary value problem in the case where exact solutions are not possible. The results presented constitute a solution for a complicated nonlinear and singular initial value problem. Through appropriate selection of the auxiliary linear operator and convergence control parameter, we are able to obtain low order approximations which minimize residual error over the problem domain. The benefit to such approach is that we obtain very accurate approximations after computing very few terms, hence the computational efficiency is high. Finally, an exact solution is provided in a special case, and this corresponds to the analytical solutions obtained in the more general case. The approximate solutions agree qualitatively with the exact solutions. (paper)

Local couplings, double insertions and the Weyl consistency condition

International Nuclear Information System (INIS)

Kraus, E.; Sibold, K.

1992-05-01

Within massless φ 4 4 -theory we set up the formalism which is needed, when the coupling λ is permitted to become an external field, i.e. a function of space-time. In particular we have worked out the action of the corresponding Callan-Symanzik operator and conformal transformations on the vertex functions, and furthermore how the Weyl transformations act on the theory with the energy-momentum tensor invariantly coupled. With the help of the Weyl consistency condition we have shown that in the limit of constant coupling the Weyl braking can entirely be written in terms of differential operators, but that otherwise, for truely local coupling, new breaking terms survive. (orig.)

Probing the Chiral Anomaly via Nonlocal Transport in Weyl Semimetals

Science.gov (United States)

Parameswaran, Siddharth; Grover, Tarun; Vishwanath, Ashvin

2013-03-01

Weyl semimetals are three-dimensional analogs of graphene in which a pair of bands touch at points in momentum space, known as Weyl nodes. Electrons originating from a single Weyl node possess a definite topological charge, the chirality. Consequently, they exhibit the Adler-Jackiw-Bell anomaly, which in this condensed matter realization implies that application of parallel electric (E) and magnetic fields (B) pumps electrons between nodes of opposite chirality at a rate proportional to E . B . We argue that this pumping is measurable via transport experiments, in the limit of weak internode scattering. Specifically, we show that injecting a current in a Weyl semimetal subject to an E . B term leads to nonlocal features in transport. We acknowledge support of the Simons Foundation, NSF Grant PHY-1066293 and the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231

How fast can a black hole eat. [Equation stationary spherically symmetric solutions, Thompson scattering, mass flow

Energy Technology Data Exchange (ETDEWEB)

Kafka, P; Meszaros, P [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany, F.R.)

1976-11-01

Stationary spherically symmetric solutions of the equations for accretion of large mass flows onto a black hole, including the interaction of matter and radiation due to Thomson scattering in diffusion approximation are constructed. The relevance of these solutions is discussed with respect to the question of whether the limitation of the luminosity (Eddington limit) also implies an upper bound to the possible rate of mass flow. The question remains open until all instabilities have been studied. At the moment a negative answer is favoured.

Remarks on interior transmission eigenvalues, Weyl formula and branching billiards

International Nuclear Information System (INIS)

Lakshtanov, E; Vainberg, B

2012-01-01

This paper contains the Weyl formula for the counting function of the interior transmission problem when the latter is parameter elliptic. Branching billiard trajectories are constructed, and the second term of the Weyl asymptotics is estimated from above under some conditions on the set of periodic billiard trajectories. (paper)

Classical probabilities for Majorana and Weyl spinors

International Nuclear Information System (INIS)

Wetterich, C.

2011-01-01

Highlights: → Map of classical statistical Ising model to fermionic quantum field theory. → Lattice-regularized real Grassmann functional integral for single Weyl spinor. → Emerging complex structure characteristic for quantum physics. → A classical statistical ensemble describes a quantum theory. - Abstract: We construct a map between the quantum field theory of free Weyl or Majorana fermions and the probability distribution of a classical statistical ensemble for Ising spins or discrete bits. More precisely, a Grassmann functional integral based on a real Grassmann algebra specifies the time evolution of the real wave function q τ (t) for the Ising states τ. The time dependent probability distribution of a generalized Ising model obtains as p τ (t)=q τ 2 (t). The functional integral employs a lattice regularization for single Weyl or Majorana spinors. We further introduce the complex structure characteristic for quantum mechanics. Probability distributions of the Ising model which correspond to one or many propagating fermions are discussed explicitly. Expectation values of observables can be computed equivalently in the classical statistical Ising model or in the quantum field theory for fermions.

Projective Fourier duality and Weyl quantization

International Nuclear Information System (INIS)

Aldrovandi, R.; Saeger, L.A.

1996-08-01

The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs

Weyl corrections to diffusion and chaos in holography

Science.gov (United States)

Li, Wei-Jia; Liu, Peng; Wu, Jian-Pin

2018-04-01

Using holographic methods in the Einstein-Maxwell-dilaton-axion (EMDA) theory, it was conjectured that the thermal diffusion in a strongly coupled metal without quasi-particles saturates an universal lower bound that is associated with the chaotic property of the system at infrared (IR) fixed points [1]. In this paper, we investigate the thermal transport and quantum chaos in the EMDA theory with a small Weyl coupling term. It is found that the Weyl coupling correct the thermal diffusion constant D Q and butterfly velocity v B in different ways, hence resulting in a modified relation between the two at IR fixed points. Unlike that in the EMDA case, our results show that the ratio D Q /( v B 2 τ L ) always contains a non-universal Weyl correction which depends also on the bulk fields as long as the U(1) current is marginally relevant in the IR.

Magnetic and noncentrosymmetric Weyl fermion semimetals in the R AlGe family of compounds (R =rare earth )

Science.gov (United States)

Chang, Guoqing; Singh, Bahadur; Xu, Su-Yang; Bian, Guang; Huang, Shin-Ming; Hsu, Chuang-Han; Belopolski, Ilya; Alidoust, Nasser; Sanchez, Daniel S.; Zheng, Hao; Lu, Hong; Zhang, Xiao; Bian, Yi; Chang, Tay-Rong; Jeng, Horng-Tay; Bansil, Arun; Hsu, Han; Jia, Shuang; Neupert, Titus; Lin, Hsin; Hasan, M. Zahid

2018-01-01

Weyl semimetals are novel topological conductors that host Weyl fermions as emergent quasiparticles. In this Rapid Communication, we propose a new type of Weyl semimetal state that breaks both time-reversal symmetry and inversion symmetry in the R AlGe (R =rare -earth ) family. Compared to previous predictions of magnetic Weyl semimetal candidates, the prediction of Weyl nodes in R AlGe is more robust and less dependent on the details of the magnetism because the Weyl nodes are generated already by the inversion breaking and the ferromagnetism acts as a simple Zeeman coupling that shifts the Weyl nodes in k space. Moreover, R AlGe offers remarkable tunability, which covers all varieties of Weyl semimetals including type I, type II, inversion breaking, and time-reversal breaking, depending on a suitable choice of the rare-earth elements. Furthermore, the unique noncentrosymmetric and ferromagnetic Weyl semimetal state in R AlGe enables the generation of spin currents.

Non-Weyl asymptotics for quantum graphs with general coupling conditions

International Nuclear Information System (INIS)

Davies, E Brian; Exner, Pavel; Lipovsky, JirI

2010-01-01

Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in the case of Kirchhoff or anti-Kirchhoff conditions. While for graphs without permutation symmetry numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight into what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with unequal edge weights.

Weyl Ordering Operator Formula Derived by IWOP Technique and Its Application for Fresnel Operator

International Nuclear Information System (INIS)

Fan Hongyi; Hu Liyun

2009-01-01

Based on the technique of integration within an ordered product of operators, the Weyl ordering operator formula is derived and the Fresnel operators' Weyl ordering is also obtained, which together with the Weyl transformation can immediately lead to Fresnel transformation kernel in classical optics. (general)

Anisotropic Weyl fermions from the quasiparticle excitation spectrum of a 3D Fulde-Ferrell superfluid.

Science.gov (United States)

Xu, Yong; Chu, Rui-Lin; Zhang, Chuanwei

2014-04-04

Weyl fermions, first proposed for describing massless chiral Dirac fermions in particle physics, have not been observed yet in experiments. Recently, much effort has been devoted to explore Weyl fermions around band touching points of single-particle energy dispersions in certain solid state materials (named Weyl semimetals), similar as graphene for Dirac fermions. Here we show that such Weyl semimetals also exist in the quasiparticle excitation spectrum of a three-dimensional spin-orbit-coupled Fulde-Ferrell superfluid. By varying Zeeman fields, the properties of Weyl fermions, such as their creation and annihilation, number and position, as well as anisotropic linear dispersions around band touching points, can be tuned. We study the manifestation of anisotropic Weyl fermions in sound speeds of Fulde-Ferrell fermionic superfluids, which are detectable in experiments.

Introduction to the special issue Hermann Weyl and the philosophy of the 'New Physics'

Science.gov (United States)

De Bianchi, Silvia; Catren, Gabriel

2018-02-01

This Special Issue Hermann Weyl and the Philosophy of the 'New Physics' has two main objectives: first, to shed fresh light on the relevance of Weyl's work for modern physics and, second, to evaluate the importance of Weyl's work and ideas for contemporary philosophy of physics. Regarding the first objective, this Special Issue emphasizes aspects of Weyl's work (e.g. his work on spinors in n dimensions) whose importance has recently been emerging in research fields across both mathematical and experimental physics, as well as in the history and philosophy of physics. Regarding the second objective, this Special Issue addresses the relevance of Weyl's ideas regarding important open problems in the philosophy of physics, such as the problem of characterizing scientific objectivity and the problem of providing a satisfactory interpretation of fundamental symmetries in gauge theories and quantum mechanics. In this Introduction, we sketch the state of the art in Weyl studies and we summarize the content of the contributions to the present volume.

Stationary shear flows in CGL anisotropic toroidal plasmas

International Nuclear Information System (INIS)

Pastukhov, V.P.; Ilgisonis, V.I.

1996-01-01

Recently a general structure of stationary shear flows in toroidal plasmas was obtained in the frame of ideal isotropic-pressure MHD model. The structure of the stationary plasma flows was shown to be determined by a hidden symmetry of MHD equations inherent in the toroidal systems with nested magnetic surfaces. However, the characteristic frequencies of the stationary plasma motion can considerably exceed the collisional frequencies in real plasma experiments. In this case the CGL collisionless MHD model seems to be more adequate than the simplified isotropic-pressure MHD model to describe the stationary plasma flows. In this paper we have generalized our approach to analyze the stationary plasma flows in the frame of the collisionless CGL model. We have found again that the hidden symmetry inherent in the toroidal topology results in two integral invariants which depend on two independent surface functions. The structure of stationary flows for CGL model is still the same as for isotropic MHD, however, the pressure tensor components satisfy a appreciably modifies the steady state force-balance equation. These results are applied to analyze the generalized equilibrium in axisymmetric (tokamak-like) magnetic confinement systems

Hermann Weyl and Representation Theory

Indian Academy of Sciences (India)

told us to hear the volume of a drum but, about the shape, ... resentation theory of Lie groups which solved fundamental problems, and ..... Cartan's classification of simple Lie algebras depended ..... age of 27 due to general sepsis. Weyl was ...

Nonlocality, no-signalling, and Bellʼs theorem investigated by Weyl conformal differential geometry

Science.gov (United States)

De Martini, Francesco; Santamato, Enrico

2014-12-01

The principles and methods of conformal quantum geometrodynamics based on Weyl differential geometry are presented. The theory applied to the case of the relativistic single quantum spin-\\frac{1}{2} leads to a novel and unconventional derivation of the Dirac equation. The further extension of the theory to the case of two-spins-\\frac{1}{2} in the EPR entangled state and to the related violation of Bell inequalities leads, by an exact non-relativistic analysis, to an insightful resolution of all paradoxes implied by quantum nonlocality.

Nonlocality, no-signalling, and Bell's theorem investigated by Weyl conformal differential geometry

International Nuclear Information System (INIS)

Martini, Francesco De; Santamato, Enrico

2014-01-01

The principles and methods of conformal quantum geometrodynamics based on Weyl differential geometry are presented. The theory applied to the case of the relativistic single quantum spin-(1/2) leads to a novel and unconventional derivation of the Dirac equation. The further extension of the theory to the case of two-spins-(1/2) in the EPR entangled state and to the related violation of Bell inequalities leads, by an exact non-relativistic analysis, to an insightful resolution of all paradoxes implied by quantum nonlocality. (paper)

The cosmological constant and Pioneer anomaly from Weyl spacetimes and Mach's principle

International Nuclear Information System (INIS)

Castro, Carlos

2009-01-01

It is shown how Weyl's geometry and Mach's holographic principle furnishes both the magnitude and sign (towards the sun) of the Pioneer anomalous acceleration a P ∼-c 2 /R Hubble firstly observed by Anderson et al. Weyl's geometry can account for both the origins and the value of the observed vacuum energy density (dark energy). The source of dark energy is just the dilaton-like Jordan-Brans-Dicke scalar field that is required to implement Weyl invariance of the most simple of all possible actions. A nonvanishing value of the vacuum energy density of the order of 10 -123 M Planck 4 is found consistent with observations. Weyl's geometry accounts also for the phantom scalar field in modern Cosmology in a very natural fashion.

Discrete systems related to the sixth Painleve equation

International Nuclear Information System (INIS)

Ramani, A; Ohta, Y; Grammaticos, B

2006-01-01

We present discrete Painleve equations which can be obtained as contiguity relations of the solutions of the continuous Painleve VI. The derivation is based on the geometry of the affine Weyl group D (1) 4 associated with the bilinear formalism. As an offshoot we also present the contiguity relations of the solutions of the Bureau-Ablowitz-Fokas equation, which is a Miura transformed, 'modified', P VI

The Holographic Weyl anomaly

CERN Document Server

Henningson, M; Henningson, Mans; Skenderis, Kostas

1998-01-01

We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general covariance. Up to a constant, the anomaly only depends on the dimension d of the manifold on which the conformal field theory is defined. We present concrete expressions for the anomaly in the physically relevant cases d = 2, 4 and 6. In d = 2 we find for the central charge c = 3 l/ 2 G_N in agreement with considerations based on the asymptotic symmetry algebra of adS_3. In d = 4 the anomaly agrees precisely with that of the corresponding N = 4 superconformal SU(N) gauge theory. The result in d = 6 provides new information for the (0, 2) theory, since its Weyl anomaly has not been computed previously. The anomaly in this case grows as N^3, where N is the number of coincident M5 branes, and it vanishes for a Ricci-flat background.

Concurrence of superconductivity and structure transition in Weyl semimetal TaP under pressure

Energy Technology Data Exchange (ETDEWEB)

Li, Yufeng; Zhou, Yonghui; Guo, Zhaopeng; Han, Fei; Chen, Xuliang; Lu, Pengchao; Wang, Xuefei; An, Chao; Zhou, Ying; Xing, Jie; Du, Guan; Zhu, Xiyu; Yang, Huan; Sun, Jian; Yang, Zhaorong; Yang, Wenge; Mao, Ho-Kwang; Zhang, Yuheng; Wen, Hai-Hu

2017-12-01

Weyl semimetal defines a material with three-dimensional Dirac cones, which appear in pair due to the breaking of spatial inversion or time reversal symmetry. Superconductivity is the state of quantum condensation of paired electrons. Turning a Weyl semimetal into superconducting state is very important in having some unprecedented discoveries. In this work, by doing resistive measurements on a recently recognized Weyl semimetal TaP under pressures up to about 100 GPa, we show the concurrence of superconductivity and a structure transition at about 70 GPa. It is found that the superconductivity becomes more pronounced when decreasing pressure and retains when the pressure is completely released. High-pressure x-ray diffraction measurements also confirm the structure phase transition from I41md to P-6m2 at about 70 GPa. More importantly, ab-initial calculations reveal that the P-6m2 phase is a new Weyl semimetal phase and has only one set of Weyl points at the same energy level. Our discovery of superconductivity in TaP by high pressure will stimulate investigations on superconductivity and Majorana fermions in Weyl semimetals.

A note on a generalisation of Weyl's theory of gravitation

International Nuclear Information System (INIS)

Dereli, T.; Tucker, R.W.

1982-01-01

A scale-invariant gravitational theory due to Bach and Weyl is generalised by the inclusion of space-time torsion. The difference between the arbitrary and zero torsion constrained variations of the Weyl action is elucidated. Conformal rescaling properties of the gravitational fields are discussed. A new class of classical solutions with torsion is presented. (author)

Theoretical construction in physics - The role of Leibniz for Weyl's 'Philosophie der Mathematik und Naturwissenschaft'

Science.gov (United States)

Sieroka, Norman

2018-02-01

This paper aims at closing a gap in recent Weyl research by investigating the role played by Leibniz for the development and consolidation of Weyl's notion of theoretical (symbolic) construction. For Weyl, just as for Leibniz, mathematics was not simply an accompanying tool when doing physics-for him it meant the ability to engage in well-guided speculations about a general framework of reality and experience. The paper first introduces some of the background of Weyl's notion of theoretical construction and then discusses particular Leibnizian inheritances in Weyl's 'Philosophie der Mathematik und Naturwissenschaft', such as the general appreciation of the principles of sufficient reason and of continuity. Afterwards the paper focuses on three themes: first, Leibniz's primary quality phenomenalism, which according to Weyl marked the decisive step in realizing that physical qualities are never apprehended directly; second, the conceptual relation between continuity and freedom; and third, Leibniz's notion of 'expression', which allows for a certain type of (surrogative) reasoning by structural analogy and which gave rise to Weyl's optimism regarding the scope of theoretical construction.

Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence

Science.gov (United States)

Kassandrov, Vladimir V.; Rizcallah, Joseph A.

We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, ℂ) Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges (“elementary” for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding “particle-like” field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit nontrivial collective dynamics simulating physical interactions.

Spaces of positive and negative frequency solutions of field equations in curved space--times. I. The Klein--Gordon equation in stationary space--times

International Nuclear Information System (INIS)

Moreno, C.

1977-01-01

In stationary space--times V/sub n/ x R with compact space-section manifold without boundary V/sub n/, the Klein--Gordon equation is solved by the one-parameter group of unitary operators generated by the energy operator i -1 T -1 in the Sobolev spaces H/sup l/(V/sub n/) x H/sup l/(V/sub n/). The canonical symplectic and complex structures of the associated dynamical system are calculated. The existence and the uniqueness of the Lichnerowicz kernel are established. The Hilbert spaces of positive and negative frequency-part solutions defined by means of this kernel are constructed

Anomalous Nernst effect in type-II Weyl semimetals

Science.gov (United States)

Saha, Subhodip; Tewari, Sumanta

2018-01-01

Topological Weyl semimetals (WSM), a new state of quantum matter with gapless nodal bulk spectrum and open Fermi arc surface states, have recently sparked enormous interest in condensed matter physics. Based on the symmetry and fermiology, it has been proposed that WSMs can be broadly classified into two types, type-I and type-II Weyl semimetals. While the undoped, conventional, type-I WSMs have point like Fermi surface and vanishing density of states (DOS) at the Fermi energy, the type-II Weyl semimetals break Lorentz symmetry explicitly and have tilted conical spectra with electron and hole pockets producing finite DOS at the Fermi level. The tilted conical spectrum and finite DOS at Fermi level in type-II WSMs have recently been shown to produce interesting effects such as a chiral anomaly induced longitudinal magnetoresistance that is strongly anisotropic in direction and a novel anomalous Hall effect. In this work, we consider the anomalous Nernst effect in type-II WSMs in the absence of an external magnetic field using the framework of semi-classical Boltzmann theory. Based on both a linearized model of time-reversal breaking WSM with a higher energy cut-off and a more realistic lattice model, we show that the anomalous Nernst response in these systems is strongly anisotropic in space, and can serve as a reliable signature of type-II Weyl semimetals in a host of magnetic systems with spontaneously broken time reversal symmetry.

AC conductivity for a holographic Weyl semimetal

Energy Technology Data Exchange (ETDEWEB)

Grignani, Gianluca; Marini, Andrea; Peña-Benitez, Francisco; Speziali, Stefano [Dipartimento di Fisica e Geologia, Università di Perugia,I.N.F.N. Sezione di Perugia,Via Pascoli, I-06123 Perugia (Italy)

2017-03-23

We study the AC electrical conductivity at zero temperature in a holographic model for a Weyl semimetal. At small frequencies we observe a linear dependence in the frequency. The model shows a quantum phase transition between a topological semimetal (Weyl semimetal phase) with a non vanishing anomalous Hall conductivity and a trivial semimetal. The AC conductivity has an intermediate scaling due to the presence of a quantum critical region in the phase diagram of the system. The phase diagram is reconstructed using the scaling properties of the conductivity. We compare with the experimental data of https://www.doi.org/10.1103/PhysRevB.93.121110 obtaining qualitative agreement.

The signature triality of Majorana-Weyl spacetimes

International Nuclear Information System (INIS)

Andrade, M.A. de; Rojas, M.; Toppan, F.

2000-05-01

The Higher dimensional Majorana-Weyl spacetimes present space-time dualities which are induced by the Spin (8) triality automorphisms. Different signature versions of theories such as 10-dimensional SYM's superstrings, five-branes, F-theory, are shown to be interconnected via the S 3 permutation group. Bilinear and trilinear invariants under spacetime triality are introduced and their possible relevance in building models possessing a space-versus-time exchange symmetry is discussed. Moreover the Cartan's vector/chiral spinor/antichiral spinor triality of SO (8) and SO(4,4) is analyzed in detail and explicit formulas are produced in a Majorana-Weyl basis. This paper is the extended version of hep-th/9907148. (author)

Hermann Weyl (1885–1955)

Indian Academy of Sciences (India)

In 1930, Weyl left Zürich, and after a three-year position in Göttingen, occupying the chair ... of a particle would depend on its past history; something not supported by physics. However, it turned out to be not ... His papers on representations of ...

Visualizing Type-II Weyl Points in Tungsten Ditelluride by Quasiparticle Interference.

Science.gov (United States)

Lin, Chun-Liang; Arafune, Ryuichi; Liu, Ro-Ya; Yoshimura, Masato; Feng, Baojie; Kawahara, Kazuaki; Ni, Zeyuan; Minamitani, Emi; Watanabe, Satoshi; Shi, Youguo; Kawai, Maki; Chiang, Tai-Chang; Matsuda, Iwao; Takagi, Noriaki

2017-11-28

Weyl semimetals (WSMs) are classified into two types, type I and II, according to the topology of the Weyl point, where the electron and hole pockets touch each other. Tungsten ditelluride (WTe 2 ) has garnered a great deal of attention as a strong candidate to be a type-II WSM. However, the Weyl points for WTe 2 are located above the Fermi level, which has prevented us from identifying the locations and the connection to the Fermi arc surface states by using angle-resolved photoemission spectroscopy. Here, we present experimental proof that WTe 2 is a type-II WSM. We measured energy-dependent quasiparticle interference patterns with a cryogenic scanning tunneling microscope, revealing the position of the Weyl point and its connection with the Fermi arc surface states, in agreement with prior theoretical predictions. Our results provide an answer to this crucial question and stimulate further exploration of the characteristics of WSMs.

Resistivity of Weyl semimetals NbP and TaP under pressure

International Nuclear Information System (INIS)

Einaga, M.; Shimizu, K.; Hu, J.; Mao, Z.Q.; Politano, A.

2017-01-01

The resistivity of Weyl semimetals NbP and TaP has been investigated as a function of pressure and temperature. The behaviour of the resistivity as a function of pressure and temperature is closely correlated to the location of the Weyl points compared to the Fermi energy. The rapid increase of the resistivity in TaP and NbP under the application of 4.5 and 8.0 GPa is related with the shift of Weyl points, which affords a finite density of states near the Fermi energy. Specifically, we find that under pressure the Weyl points are situated above the Fermi energy. As regards the temperature behaviour, we detect a nonmonotonous behaviour of resistivity in TaP at 8.7 and 9.8 GPa as a function of temperature, whereas in the case of NbP the behaviour is more complicate. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Resistivity of Weyl semimetals NbP and TaP under pressure

Energy Technology Data Exchange (ETDEWEB)

Einaga, M.; Shimizu, K. [KYOKUGEN, Graduate School of Engineering Science, Osaka University, Toyonaka (Japan); Hu, J.; Mao, Z.Q. [Department of Physics and Engineering Physics, Tulane University, New Orleans, LA (United States); Politano, A. [Fondazione Istituto Italiano di Tecnologia, Graphene Labs, Genova (Italy)

2017-08-15

The resistivity of Weyl semimetals NbP and TaP has been investigated as a function of pressure and temperature. The behaviour of the resistivity as a function of pressure and temperature is closely correlated to the location of the Weyl points compared to the Fermi energy. The rapid increase of the resistivity in TaP and NbP under the application of 4.5 and 8.0 GPa is related with the shift of Weyl points, which affords a finite density of states near the Fermi energy. Specifically, we find that under pressure the Weyl points are situated above the Fermi energy. As regards the temperature behaviour, we detect a nonmonotonous behaviour of resistivity in TaP at 8.7 and 9.8 GPa as a function of temperature, whereas in the case of NbP the behaviour is more complicate. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Irradiated three-dimensional Luttinger semimetal: A factory for engineering Weyl semimetals

Science.gov (United States)

Ghorashi, Sayed Ali Akbar; Hosur, Pavan; Ting, Chin-Sen

2018-05-01

We study the interaction between elliptically polarized light and a three-dimensional Luttinger semimetal with quadratic band touching using Floquet theory. In the absence of light, the touching bands can have the same or the opposite signs of the curvature; in each case, we show that simply tuning the light parameters allows us to create a zoo of Weyl semimetallic phases. In particular, we find that double- and single-Weyl points can coexist at different energies, and they can be tuned to be type I or type II. We also find an unusual phase transition, in which a pair of Weyl nodes form at finite momentum and disappear off to infinity. Considering the broad tunability of light and abundance of materials described by the Luttinger Hamiltonian, such as certain pyrochlore iridates, half-Heuslers, and zinc-blende semiconductors, we believe this work can lay the foundation for creating Weyl semimetals in the laboratory and dynamically tuning between them.

Standard Model Vacuum Stability and Weyl Consistency Conditions

DEFF Research Database (Denmark)

Antipin, Oleg; Gillioz, Marc; Krog, Jens

2013-01-01

At high energy the standard model possesses conformal symmetry at the classical level. This is reflected at the quantum level by relations between the different beta functions of the model. These relations are known as the Weyl consistency conditions. We show that it is possible to satisfy them...... order by order in perturbation theory, provided that a suitable coupling constant counting scheme is used. As a direct phenomenological application, we study the stability of the standard model vacuum at high energies and compare with previous computations violating the Weyl consistency conditions....

Weyl modules, demazure modules, KR-modules, crystals, fusion products and limit constructions

OpenAIRE

Fourier, G.; Littelmann, P.

2007-01-01

We study finite dimensional representations of current algebras, loop algebras and their quantized versions. For the current algebra of a simple Lie algebra of type {\\tt ADE}, we show that Kirillov-Reshetikhin modules and Weyl modules are in fact all Demazure modules. As a consequence one obtains an elementary proof of the dimension formula for Weyl modules for the current and the loop algebra. Further, we show that the crystals of the Weyl and the Demazure module are the same up to some addi...

Elastic Gauge Fields in Weyl Semimetals

Science.gov (United States)

Cortijo, Alberto; Ferreiros, Yago; Landsteiner, Karl; Hernandez Vozmediano, Maria Angeles

We show that, as it happens in graphene, elastic deformations couple to the electronic degrees of freedom as pseudo gauge fields in Weyl semimetals. We derive the form of the elastic gauge fields in a tight-binding model hosting Weyl nodes and see that this vector electron-phonon coupling is chiral, providing an example of axial gauge fields in three dimensions. As an example of the new response functions that arise associated to these elastic gauge fields, we derive a non-zero phonon Hall viscosity for the neutral system at zero temperature. The axial nature of the fields provides a test of the chiral anomaly in high energy with three axial vector couplings. European Union structural funds and the Comunidad de Madrid MAD2D-CM Program (S2013/MIT-3007).

An infinite number of stationary soliton solutions to the five-dimensional vacuum Einstein equation

International Nuclear Information System (INIS)

Azuma, Takahiro; Koikawa, Takao

2006-01-01

We obtain an infinite number of soliton solutions to the five-dimensional stationary Einstein equation with axial symmetry by using the inverse scattering method. We start with the five-dimensional Minkowski space as a seed metric to obtain these solutions. The solutions are characterized by two soliton numbers and a constant appearing in the normalization factor which is related to a coordinate condition. We show that the (2, 0)-soliton solution is identical to the Myers-Perry solution with one angular momentum variable by imposing a condition on the relation between parameters. We also show that the (2, 2)-soliton solution is different from the black ring solution discovered by Emparan and Reall, although one component of the two metrics can be identical. (author)

Studies on the numerical solution of three-dimensional stationary diffusion equations using the finite element method

International Nuclear Information System (INIS)

Franke, H.P.

1976-05-01

The finite element method is applied to the solution of the stationary 3D group diffusion equations. For this, a programme system with the name of FEM3D is established which also includes a module for semi-automatic mesh generation. Tetrahedral finite elements are used. The neutron fluxes are described by complete first- or second-order Lagrangian polynomials. General homogeneous boundary conditions are allowed. The studies show that realistic three-dimensional problems can be solved at less expense by iterative methods, in particular so when especially adapted matrix handling and storage schemes are used efficiently. (orig./RW) [de

Signatures of Fermi Arcs in the Quasiparticle Interferences of the Weyl Semimetals TaAs and NbP.

Science.gov (United States)

Chang, Guoqing; Xu, Su-Yang; Zheng, Hao; Lee, Chi-Cheng; Huang, Shin-Ming; Belopolski, Ilya; Sanchez, Daniel S; Bian, Guang; Alidoust, Nasser; Chang, Tay-Rong; Hsu, Chuang-Han; Jeng, Horng-Tay; Bansil, Arun; Lin, Hsin; Hasan, M Zahid

2016-02-12

The recent discovery of the first Weyl semimetal in TaAs provides the first observation of a Weyl fermion in nature. Such a topological semimetal features a novel type of anomalous surface state, the Fermi arc, which connects a pair of Weyl nodes through the boundary of the crystal. Here, we present theoretical calculations of the quasiparticle interference (QPI) patterns that arise from the surface states including the topological Fermi arcs in the Weyl semimetals TaAs and NbP. Most importantly, we discover that the QPI exhibits termination points that are fingerprints of the Weyl nodes in the interference pattern. Our results, for the first time, propose a universal interference signature of the topological Fermi arcs in TaAs, which is fundamental for scanning tunneling microscope (STM) measurements on this prototypical Weyl semimetal compound. More generally, our work provides critical guideline and methodology for STM studies on new Weyl semimetals. Further, the scattering channels revealed by our QPIs are broadly relevant to surface transport and device applications based on Weyl semimetals.

Topological Weyl semimetals in Bi1 -xSbx alloys

Science.gov (United States)

Su, Yu-Hsin; Shi, Wujun; Felser, Claudia; Sun, Yan

2018-04-01

We investigated Weyl semimetal (WSM) phases in bismuth antimony (Bi1 -xSbx ) alloys by combination of atomic composition and arrangement. Via first-principles calculations, we found two WSM states with Sb concentrations of x =0.5 and 0.83 with specific inversion-symmetry-broken elemental arrangement. The Weyl points are close to the Fermi level in both of these two WSM states. Therefore, it is likely to obtain Weyl points in Bi-Sb alloy. The WSM phase provides a reasonable explanation for the current transport study of Bi-Sb alloy with the violation of Ohm's law [D. Shin, Y. Lee, M. Sasaki, Y. H. Jeong, F. Weickert, J. B. Betts, H.-J. Kim, K.-S. Kim, and J. Kim, Nat. Mater. 16, 1096 (2017), 10.1038/nmat4965]. This paper shows that the topological phases in Bi-Sb alloys depend on both elemental composition and their specific arrangement.

Spin in stationary gravitational fields and rotating frames

International Nuclear Information System (INIS)

Obukhov, Yuri N.; Silenko, Alexander J.; Teryaev, Oleg V.

2010-01-01

A spin motion of particles in stationary spacetimes is investigated in the framework of the classical gravity and relativistic quantum mechanics. We bring the Dirac equation for relativistic particles in nonstatic spacetimes to the Hamiltonian form and perform the Foldy-Wouthuysen transformation. We show the importance of the choice of tetrads for description of spin dynamics in the classical gravity. We derive classical and quantum mechanical equations of motion of the spin for relativistic particles in stationary gravitational fields and rotating frames and establish the full agreement between the classical and quantum mechanical approaches.

Magnetic Weyl Semimetal in Quasi Two-dimensional Half Metallic Co$_3$Sn$_2$Se$_2$

OpenAIRE

Xu, Qiunan; Liu, Enke; Shi, Wujun; Muechler, Lukas; Felser, Claudia; Sun, Yan

2017-01-01

We have found a ferromagnetic Weyl semimetal (WSM) in half metallic Co$_3$Sn$_2$Se$_2$. The three pairs of Weyl points near Fermi level (E$_F$) are derived from nodal lines gapped by spin-orbit coupling (SOC). Though the Weyl points are 0.11 eV above the charge neutral point, Fermi arc related states in the cleaved surface can range from E$_F$ -0.15 to E$_F$ +0.11 eV in energy space, due to the surface bands dispersion. Hence, Weyl points related physics should be detected by surface measurem...

Disorder effect on chiral edge modes and anomalous Hall conductance in Weyl semimetals

International Nuclear Information System (INIS)

Takane, Yositake

2016-01-01

Typical Weyl semimetals host chiral surface states and hence show an anomalous Hall response. Although a Weyl semimetal phase is known to be robust against weak disorder, the effect of disorder on chiral states has not been fully clarified so far. We study the behavior of such chiral states in the presence of disorder and its consequences on an anomalous Hall response, focusing on a thin slab of Weyl semimetal with chiral surface states along its edge. It is shown that weak disorder does not disrupt chiral edge states but crucially affects them owing to the renormalization of a mass parameter: the number of chiral edge states changes depending on the strength of disorder. It is also shown that the Hall conductance is quantized when the Fermi level is located near Weyl nodes within a finite-size gap. This quantization of the Hall conductance collapses once the strength of disorder exceeds a critical value, suggesting that it serves as a probe to distinguish a Weyl semimetal phase from a diffusive anomalous Hall metal phase. (author)

Classification of the Weyl tensor in higher dimensions and applications

International Nuclear Information System (INIS)

Coley, A

2008-01-01

We review the theory of alignment in Lorentzian geometry and apply it to the algebraic classification of the Weyl tensor in higher dimensions. This classification reduces to the well-known Petrov classification of the Weyl tensor in four dimensions. We discuss the algebraic classification of a number of known higher dimensional spacetimes. There are many applications of the Weyl classification scheme, especially when used in conjunction with the higher dimensional frame formalism that has been developed in order to generalize the four-dimensional Newman-Penrose formalism. For example, we discuss higher dimensional generalizations of the Goldberg-Sachs theorem and the peeling theorem. We also discuss the higher dimensional Lorentzian spacetimes with vanishing scalar curvature invariants and constant scalar curvature invariants, which are of interest since they are solutions of supergravity theory. (topical review)

Anomalous thermoelectric phenomena in lattice models of multi-Weyl semimetals

Science.gov (United States)

Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.; Sukhachov, P. O.

2017-10-01

The thermoelectric transport coefficients are calculated in a generic lattice model of multi-Weyl semimetals with a broken time-reversal symmetry by using the Kubo's linear response theory. The contributions connected with the Berry curvature-induced electromagnetic orbital and heat magnetizations are systematically taken into account. It is shown that the thermoelectric transport is profoundly affected by the nontrivial topology of multi-Weyl semimetals. In particular, the calculation reveals a number of thermal coefficients of the topological origin which describe the anomalous Nernst and thermal Hall effects in the absence of background magnetic fields. Similarly to the anomalous Hall effect, all anomalous thermoelectric coefficients are proportional to the integer topological charge of the Weyl nodes. The dependence of the thermoelectric coefficients on the chemical potential and temperature is also studied.

On the trace anomaly of a Weyl fermion

Energy Technology Data Exchange (ETDEWEB)

Bastianelli, Fiorenzo; Martelli, Riccardo [Dipartimento di Fisica e Astronomia, Università di Bologna,via Irnerio 46, I-40126 Bologna (Italy); INFN - Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy)

2016-11-29

We calculate the trace anomaly of a Weyl fermion coupled to gravity by using Fujikawa’s method supplemented by a consistent regulator. The latter is constructed out of Pauli-Villars regulating fields. The motivation for presenting such a calculation stems from recent studies that suggest that the trace anomaly of chiral fermions in four dimensions might contain an imaginary part proportional to the Pontryagin density. We find that the trace anomaly of a Weyl fermion is given by half the trace anomaly of a Dirac fermion, so that no imaginary part proportional to the Pontryagin density is seen to arise.

Critical study of Weyl anomaly calculation in the string by Fujikawa method

International Nuclear Information System (INIS)

Dalmazi, D.

1987-01-01

The Fujikawa's evaluation of Weyl's anomaly in the bosonic string is carefully analyzed, paying special attention to the covariance under conformal transformation. The choice of operators used to calculate the variation of path integral measure under Weyl's transformation is discussed in detail. (author) [pt

Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states

Science.gov (United States)

Chen, Wen-Jie; Xiao, Meng; Chan, C. T.

2016-01-01

Weyl points, as monopoles of Berry curvature in momentum space, have captured much attention recently in various branches of physics. Realizing topological materials that exhibit such nodal points is challenging and indeed, Weyl points have been found experimentally in transition metal arsenide and phosphide and gyroid photonic crystal whose structure is complex. If realizing even the simplest type of single Weyl nodes with a topological charge of 1 is difficult, then making a real crystal carrying higher topological charges may seem more challenging. Here we design, and fabricate using planar fabrication technology, a photonic crystal possessing single Weyl points (including type-II nodes) and multiple Weyl points with topological charges of 2 and 3. We characterize this photonic crystal and find nontrivial 2D bulk band gaps for a fixed kz and the associated surface modes. The robustness of these surface states against kz-preserving scattering is experimentally observed for the first time. PMID:27703140

Klein-Weyl's program and the ontology of gauge and quantum systems

Science.gov (United States)

Catren, Gabriel

2018-02-01

We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program-that we call the Klein-Weyl program-for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a "structure-endowed entity" equipped with a "group of automorphisms". First, we analyze what Weyl calls the "problem of relativity" in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures. Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are "indices characterizing representations of groups" ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness.

Stable multiple-layer stationary solutions of a semilinear parabolic equation in two-dimensional domains

Directory of Open Access Journals (Sweden)

Arnaldo Simal do Nascimento

1997-12-01

Full Text Available We use $Gamma$--convergence to prove existence of stable multiple--layer stationary solutions (stable patterns to the reaction--diffusion equation. $$ eqalign{ {partial v_varepsilon over partial t} =& varepsilon^2, hbox{div}, (k_1(xabla v_varepsilon + k_2(x(v_varepsilon -alpha(Beta-v_varepsilon (v_varepsilon -gamma_varepsilon(x,,hbox{ in }Omegaimes{Bbb R}^+ cr &v_varepsilon(x,0 = v_0 quad {partial v_varepsilon over partial widehat{n}} = 0,, quadhbox{ for } xin partialOmega,, t >0,.} $$ Given nested simple closed curves in ${Bbb R}^2$, we give sufficient conditions on their curvature so that the reaction--diffusion problem possesses a family of stable patterns. In particular, we extend to two-dimensional domains and to a spatially inhomogeneous source term, a previous result by Yanagida and Miyata.

Pseudo-Newtonian Equations for Evolution of Particles and Fluids in Stationary Space-times

Energy Technology Data Exchange (ETDEWEB)

Witzany, Vojtěch; Lämmerzahl, Claus, E-mail: vojtech.witzany@zarm.uni-bremen.de, E-mail: claus.laemmerzahl@zarm.uni-bremen.de [ZARM, Universität Bremen, Am Fallturm, D-28359 Bremen (Germany)

2017-06-01

Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism, in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper, we develop a general pseudo-Newtonian formalism, which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and most elegant formulas are obtained in space-times without gravitomagnetic effects, such as the Schwarzschild rather than the Kerr space-time; the quantitative errors are smallest for motion with low binding energy. Included is a ready-to-use set of fluid equations in Schwarzschild space-time in Cartesian and radial coordinates.

Weyl Semimetal to Metal Phase Transitions Driven by Quasiperiodic Potentials

Science.gov (United States)

Pixley, J. H.; Wilson, Justin H.; Huse, David A.; Gopalakrishnan, Sarang

2018-05-01

We explore the stability of three-dimensional Weyl and Dirac semimetals subject to quasiperiodic potentials. We present numerical evidence that the semimetal is stable for weak quasiperiodic potentials, despite being unstable for weak random potentials. As the quasiperiodic potential strength increases, the semimetal transitions to a metal, then to an "inverted" semimetal, and then finally to a metal again. The semimetal and metal are distinguished by the density of states at the Weyl point, as well as by level statistics, transport, and the momentum-space structure of eigenstates near the Weyl point. The critical properties of the transitions in quasiperiodic systems differ from those in random systems: we do not find a clear critical scaling regime in energy; instead, at the quasiperiodic transitions, the density of states appears to jump abruptly (and discontinuously to within our resolution).

Effective action and electromagnetic response of topological superconductors and Majorana-mass Weyl fermions

Science.gov (United States)

Stone, Michael; Lopes, Pedro L. e. S.

2016-05-01

Motivated by an apparent paradox in [X.-L. Qi, E. Witten, and S.-C. Zhang, Phys. Rev. B 87, 134519 (2013), 10.1103/PhysRevB.87.134519], we use the method of gauged Wess-Zumino-Witten functionals to construct an effective action for a Weyl fermion with a Majorana mass that arises from coupling to a charged condensate. We obtain expressions for the current induced by an external gauge field and observe that the topological part of the current is only one-third of that that might have been expected from the gauge anomaly. The anomaly is not changed by the induced mass gap, however. The topological current is supplemented by a conventional supercurrent that provides the remaining two-thirds of the anomaly once the equation of motion for the Goldstone mode is satisfied. We apply our formula for the current to resolve the apparent paradox and also to the chiral magnetic effect (CME), where it predicts a reduction of the CME current to one-third of its value for a free Weyl gas in thermal equilibrium. We attribute this reduction to a partial cancellation of the CME by a chiral vortical effect current arising from the persistent rotation of the fluid induced by the external magnetic field.

Weyl consistency conditions in non-relativistic quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Pal, Sridip; Grinstein, Benjamín [Department of Physics, University of California,San Diego, 9500 Gilman Drive, La Jolla, CA 92093 (United States)

2016-12-05

Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme ambiguities for generic non-relativistic theories in 2+1 dimensions with anisotropic scaling exponent z=2; the extension to other values of z are discussed as well. We give the consistency conditions among these anomalies. As an application we find several candidates for a C-theorem. We comment on possible candidates for a C-theorem in higher dimensions.

Quasiparticle interference of the Fermi arcs and surface-bulk connectivity of a Weyl semimetal.

Science.gov (United States)

Inoue, Hiroyuki; Gyenis, András; Wang, Zhijun; Li, Jian; Oh, Seong Woo; Jiang, Shan; Ni, Ni; Bernevig, B Andrei; Yazdani, Ali

2016-03-11

Weyl semimetals host topologically protected surface states, with arced Fermi surface contours that are predicted to propagate through the bulk when their momentum matches that of the surface projections of the bulk's Weyl nodes. We used spectroscopic mapping with a scanning tunneling microscope to visualize quasiparticle scattering and interference at the surface of the Weyl semimetal TaAs. Our measurements reveal 10 different scattering wave vectors, which can be understood and precisely reproduced with a theory that takes into account the shape, spin texture, and momentum-dependent propagation of the Fermi arc surface states into the bulk. Our findings provide evidence that Weyl nodes act as sinks for electron transport on the surface of these materials. Copyright © 2016, American Association for the Advancement of Science.

Spectroscopic Visualization of Inversion and Time-Reversal Symmetry Breaking Weyl Semi-metals

Science.gov (United States)

Beidenkopf, Haim

A defining property of a topological material is the existence of surface bands that cannot be realized but as the termination of a topological bulk. In a Weyl semi-metal these surface states are in the form of Fermi-arcs. Their open-contour Fermi-surface curves between pairs of surface projections of bulk Weyl cones. Such Dirac-like bulk bands, as opposed to the gapped bulk of topological insulators, land a unique opportunity to examine the deep notion of bulk to surface correspondence. We study the intricate properties both of inversion symmetry broken and of time-reversal symmetry broken Weyl semimetals using scanning tunneling spectroscopy. We visualize the Fermi arc states on the surface of the non-centrosymmetric Weyl semi-metal TaAs. Using the distinct structure and spatial distribution of the wavefunctions associated with the different topological and trivial bands we detect the scattering processes that involve Fermi arcs. Each of these imaged scattering processes entails information on the unique nature of Fermi arcs and their correspondence to the topological bulk. We further visualize the magnetic response of the candidate magnetic Weyl semimetal GdPtBi in which the magnetic order parameter is coupled to the topological classification. European Research Council (ERC-StG no. 678702, TOPO-NW\\x9D), the Israel Science Foundation (ISF), and the United States-Israel Binational Science Foundation (BSF).

The Weyl Definition of Redshifts

Science.gov (United States)

Harvey, Alex

2012-01-01

In 1923, Weyl published a (not widely known) protocol for the calculation of redshifts. It is completely independent of the origin of the shift and treats it as a pure Doppler shift. The method is comprehensive and depends solely on the relation between the world lines of source and observer. It has the merit of simplicity of statement and…

Stationary localized modes of the quintic nonlinear Schroedinger equation with a periodic potential

International Nuclear Information System (INIS)

Alfimov, G. L.; Konotop, V. V.; Pacciani, P.

2007-01-01

We consider localized modes (bright solitons) of the one-dimensional quintic nonlinear Schroedinger equation with a periodic potential, describing several mean-field models of low-dimensional condensed gases. In the case of attractive nonlinearity we deduce sufficient conditions for collapse. We show that there exist spatially localized modes with arbitrarily large numbers of particles. We study such solutions in the semi-infinite gap (attractive case) and in the first gap (attractive and repulsive cases), and show that a nonzero minimum value of the number of particles is necessary for a localized mode to be created. In the limit of large negative frequencies (attractive case) we observe quantization of the number of particles of the stationary modes. Such solutions can be interpreted as coupled Townes solitons and appear to be stable. The modes in the first gap have numbers of particles infinitely growing with frequencies approaching one of the gap edges, which is explained by the power decay of the modes. Stability of the localized modes is discussed

Structural and Transport Properties of the Weyl Semimetal NbAs at High Pressure

International Nuclear Information System (INIS)

Zhang Jun; Liu Feng-Liang; Dong Jin-Kui; Xu Yang; Li Shi-Yan; Li Na-Na; Yang Wen-Ge

2015-01-01

We perform a series of high-pressure synchrotron x-ray diffraction (XRD) and resistance measurements on the Weyl semimetal NbAs. The crystal structure remains stable up to 26 GPa according to the powder XRD data. The resistance of NbAs single crystal increases monotonically with pressure at low temperature. Up to 20 GPa, no superconducting transition is observed down to 0.3 K. These results show that the Weyl semimetal phase is robust in NbAs, and applying pressure may not be a good way to obtain a topological superconductor from Weyl semimetal NbAs. (paper)

Weyl calculus in QED I. The unitary group

Science.gov (United States)

Amour, L.; Lascar, R.; Nourrigat, J.

2017-01-01

In this work, we consider fixed 1/2 spin particles interacting with the quantized radiation field in the context of quantum electrodynamics. We investigate the time evolution operator in studying the reduced propagator (interaction picture). We first prove that this propagator belongs to the class of infinite dimensional Weyl pseudodifferential operators recently introduced in Amour et al. [J. Funct. Anal. 269(9), 2747-2812 (2015)] on Wiener spaces. We give a semiclassical expansion of the symbol of the reduced propagator up to any order with estimates on the remainder terms. Next, taking into account analyticity properties for the Weyl symbol of the reduced propagator, we derive estimates concerning transition probabilities between coherent states.

Genesis of unified models from Majorana-Weyl fields

International Nuclear Information System (INIS)

Budini, P.; Furlan, P.

1977-07-01

It is proposed that all forms of interaction arise from elementary interactions between Weyl-Majorana fields. Weak interactions due to the high masses of the intermediate bosons are practically identical to the elementary interactions. Strong and electromagnetic interactions arise at larger distance, where dynamic determines both masses and symmetry. In the frame of these ideas, Pati-Salam and Fritzsch-Minkowski type of unified models are constructed starting from eight Weyl-Majorana fields. Fractional charges for quarks, integer charges for lepton and regularization of q.e.d. arise naturally from the model. Unobserved transitions (μ→e + γ, p→ leptons) may be ascribed to properties of the elementary fields (handedness) rather than very high W masses

Low energy electronic scattering processes in the topological Weyl semimetal TaAs

Energy Technology Data Exchange (ETDEWEB)

Muellner, Silvia; Lemmens, Peter [IPKM, TU-BS, Braunschweig (Germany); Gnezdilov, Vladimir [IPKM, TU-BS, Braunschweig (Germany); ILTPE NAS (Ukraine); Sankar, Raman; Chou, Fangcheng [CCMS, National Taiwan Univ., Taipei (China)

2016-07-01

The topological Weyl semimetal TaAs shows Weyl points as well as topological surface states (Fermi arcs) intimately related to symmetry and strong spin orbit interaction. We find evidence for a low energy maximum in the scattering intensity that is compatible with electronic correlations in a collision dominated regime. We compare our observations with topological insulators.

Thermodynamics, phase transition and quasinormal modes with Weyl corrections

Energy Technology Data Exchange (ETDEWEB)

Mahapatra, Subhash [The Institute of Mathematical Sciences,Chennai 600113 (India)

2016-04-21

We study charged black holes in D dimensional AdS space, in the presence of four derivative Weyl correction. We obtain the black hole solution perturbatively up to first as well as second order in the Weyl coupling, and show that first law of black hole thermodynamics is satisfied in all dimensions. We study its thermodynamic phase transition and then calculate the quasinormal frequencies of the massless scalar field perturbation. We find that, here too, the quasinormal frequencies capture the essence of black hole phase transition. Few subtleties near the second order critical point are discussed.

The Finite Heisenberg-Weyl Groups in Radar and Communications

Directory of Open Access Journals (Sweden)

Calderbank AR

2006-01-01

Full Text Available We investigate the theory of the finite Heisenberg-Weyl group in relation to the development of adaptive radar and to the construction of spreading sequences and error-correcting codes in communications. We contend that this group can form the basis for the representation of the radar environment in terms of operators on the space of waveforms. We also demonstrate, following recent developments in the theory of error-correcting codes, that the finite Heisenberg-Weyl groups provide a unified basis for the construction of useful waveforms/sequences for radar, communications, and the theory of error-correcting codes.

Anisotropic Weyl invariance

Energy Technology Data Exchange (ETDEWEB)

Perez-Nadal, Guillem [Universidad de Buenos Aires, Buenos Aires (Argentina)

2017-07-15

We consider a non-relativistic free scalar field theory with a type of anisotropic scale invariance in which the number of coordinates ''scaling like time'' is generically greater than one. We propose the Cartesian product of two curved spaces, the metric of each space being parameterized by the other space, as a notion of curved background to which the theory can be extended. We study this type of geometries, and find a family of extensions of the theory to curved backgrounds in which the anisotropic scale invariance is promoted to a local, Weyl-type symmetry. (orig.)

Pseudo Landau levels and quantum oscillations in strained Weyl semimetals

Science.gov (United States)

Alisultanov, Z. Z.

2018-05-01

The crystal lattice deformation in Weyl materials where the two chiralities are separated in momentum space leads to the appearance of gauge pseudo-fields. We investigated the pseudo-magnetic field induced quantum oscillations in strained Weyl semimetal (WSM). In contrast to all previous works on this problem, we use here a more general tilted Hamiltonian. Such Hamiltonian, seems to be is more suitable for a strained WSMs. We have shown that a pseudo-magnetic field induced magnetization of strained WSM is nonzero due to the fact that electric field (gradient of the deformation potential) is induced simultaneously with the pseudo-magnetic field. This related with fact that the pseudo Landau levels (LLs) in strained WSM are differ in vicinities of different WPs due to the presence of tilt in spectrum. Such violation of the equivalence between Weyl points (WPs) leads to modulation of quantum oscillations. We also showed that magnetization magnitude can be changed by application of an external electric field. In particular, it can be reduced to zero. The possibility of controlling of the magnetization by an electric field is interesting both from a fundamental point of view (a new type of magneto-electric effect) and application point of view (additional possibility to control diamagnetism of deformed WSMs). Finally, a coexistence of type-I and type-II Weyl fermions is possible in the system under investigation. Such phase is absolutely new for physics of topological systems.

Numerical Clifford Analysis for the Non-stationary Schroedinger Equation

International Nuclear Information System (INIS)

Faustino, N.; Vieira, N.

2007-01-01

We construct a discrete fundamental solution for the parabolic Dirac operator which factorizes the non-stationary Schroedinger operator. With such fundamental solution we construct a discrete counterpart for the Teodorescu and Cauchy-Bitsadze operators and the Bergman projectors. We finalize this paper with convergence results regarding the operators and a concrete numerical example

Field-Theoretic Weyl Deformation Quantization of Enlarged Poisson Algebras

Directory of Open Access Journals (Sweden)

Lothar Schlafer

2008-05-01

Full Text Available C*-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is found in the construction of Poisson algebras and non-commutative twisted Banach-*-algebras on the stage of measures on the not locally compact test function space. Already within this frame strict deformation quantization is obtained, but in terms of Banach-*-algebras instead of C*-algebras. Fourier transformation and representation theory of the measure Banach-*-algebras are combined with the theory of continuous projective group representations to arrive at the genuine C*-algebraic strict deformation quantization in the sense of Rieffel and Landsman. Weyl quantization is recognized to depend in the first step functorially on the (in general infinite dimensional, pre-symplectic test function space; but in the second step one has to select a family of representations, indexed by the deformation parameter h. The latter ambiguity is in the present investigation connected with the choice of a folium of states, a structure, which does not necessarily require a Hilbert space representation.

Plasma oscillations in a stationary external magnetic field

Energy Technology Data Exchange (ETDEWEB)

Ciulli, S [Joint Institute for Nuclear Research, Dubna, Moscow (USSR); Micu, M [Institute of Atomic Physics, Bucharest (Romania)

1958-07-01

The stationary distribution function as well as the small deviations from the stationary state of a gas discharge using the Boltzmann equation is studied as a basis for the calculations. The stationary problem which is discussed corresponds to plasma with cylindrical symmetry. It leads to a Maxwell velocity distribution and to a spatial distribution function which has the asymptotic form 1/r{sup 4}. The plasma perturbations are estimated by the deviations of the first order moments from their Maxwell values. A homogeneous system of differential equations is derived for the Fourier amplitudes of the magnetic field and their asymptotic form is studied. The dispersion relation is obtained by joining smoothly a solution regular at the origin with the regular asymptotic one.A number of idealizations and approximations have been made in the present analysis which limit the utility of the formulae obtained. For example, if the collision term is included in the Boltzmann equation additional quantities appear in the final results, i.e., viscosity, thermal and electrical conductivity, etc. Furthermore, the finite dimensions of linear discharge tubes or the toroidal form of some discharges strongly modify the present results. Taking into account these additional effects, exact solutions are to be obtained numerically for different values of the experimental parameters.

Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

International Nuclear Information System (INIS)

Senovilla, Jose M M

2010-01-01

The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)

Floquet Weyl semimetals in light-irradiated type-II and hybrid line-node semimetals

Science.gov (United States)

Chen, Rui; Zhou, Bin; Xu, Dong-Hui

2018-04-01

Type-II Weyl semimetals have recently attracted intensive research interest because they host Lorentz-violating Weyl fermions as quasiparticles. The discovery of type-II Weyl semimetals evokes the study of type-II line-node semimetals (LNSMs) whose linear dispersion is strongly tilted near the nodal ring. We present here a study on the circularly polarized light-induced Floquet states in type-II LNSMs, as well as those in hybrid LNSMs that have a partially overtilted linear dispersion in the vicinity of the nodal ring. We illustrate that two distinct types of Floquet Weyl semimetal (WSM) states can be induced in periodically driven type-II and hybrid LNSMs, and the type of Floquet WSMs can be tuned by the direction and intensity of the incident light. We construct phase diagrams of light-irradiated type-II and hybrid LNSMs which are quite distinct from those of light-irradiated type-I LNSMs. Moreover, we show that photoinduced Floquet type-I and type-II WSMs can be characterized by the emergence of different anomalous Hall conductivities.

Charge-induced spin torque in Weyl semimetals

Science.gov (United States)

Kurebayashi, Daichi; Nomura, Kentaro

In this work, we present phenomenological and microscopic derivations of spin torques in magnetically doped Weyl semimetals. As a result, we obtain the analytical expression of the spin torque generated, without a flowing current, when the chemical potential is modulated. We also find that this spin torque is a direct consequence of the chiral anomaly. Therefore, observing this spin torque in magnetic Weyl semimetals might be an experimental evidence of the chiral anomaly. This spin torque has also a great advantage in application. In contrast to conventional current-induced spin torques such as the spin-transfer torques, this spin torque does not accompany a constant current flow. Thus, devices using this operating principle is free from the Joule heating and possibly have higher efficiency than devices using conventional current-induced spin torques. This work was supported by JSPS KAKENHI Grant Number JP15H05854 and JP26400308.

Stationary stochastic processes theory and applications

CERN Document Server

Lindgren, Georg

2012-01-01

Some Probability and Process BackgroundSample space, sample function, and observablesRandom variables and stochastic processesStationary processes and fieldsGaussian processesFour historical landmarksSample Function PropertiesQuadratic mean propertiesSample function continuityDerivatives, tangents, and other characteristicsStochastic integrationAn ergodic resultExercisesSpectral RepresentationsComplex-valued stochastic processesBochner's theorem and the spectral distributionSpectral representation of a stationary processGaussian processesStationary counting processesExercisesLinear Filters - General PropertiesLinear time invariant filtersLinear filters and differential equationsWhite noise in linear systemsLong range dependence, non-integrable spectra, and unstable systemsThe ARMA-familyLinear Filters - Special TopicsThe Hilbert transform and the envelopeThe sampling theoremKarhunen-Loève expansionClassical Ergodic Theory and MixingThe basic ergodic theorem in L2Stationarity and transformationsThe ergodic th...

Bianchi type I universe in brane world scenario with non-zero Weyl tensor of the bulk

Energy Technology Data Exchange (ETDEWEB)

Chaudhuri, S. [University of Burdwan, Department of Physics, Burdwan (India)

2017-09-15

In the paper, we present exact solutions of gravitational field equations for an anisotropic brane with a Bianchi type I universe with perfect fluid having non-vanishing Weyl tensor of the bulk. It is assumed that the thermodynamic pressure bears a linear relation with the energy density. For a particular non-zero value of the pressure the solutions are obtained in an exact analytic form with and without the cosmological constant for a Bianchi type I universe. The relevant physical quantities associated with the evolution of the universe are also derived in the two cases. (orig.)

Present accelerated expansion of the universe from new Weyl-integrable gravity approach

Energy Technology Data Exchange (ETDEWEB)

Aguila, Ricardo; Madriz Aguilar, Jose Edgar; Moreno, Claudia [Universidad de Guadalajara (UdG), Departamento de Matematicas, Centro Universitario de Ciencias Exactas e ingenierias (CUCEI), Guadalajara, Jalisco (Mexico); Bellini, Mauricio [Universidad Nacional de Mar del Plata (UNMdP), Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Mar del Plata (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Instituto de Investigaciones Fisicas de Mar del Plata (IFIMAR), La Plata (Argentina)

2014-11-15

We investigate if a recently introduced formulation of general relativity on a Weyl-integrable geometry contains cosmological solutions exhibiting acceleration in the present cosmic expansion. We derive the general conditions to have acceleration in the expansion of the universe and obtain a particular solution for the Weyl scalar field describing a cosmological model for the present time in concordance with the data combination Planck + WP + BAO + SN. (orig.)

Stationary strings near a higher-dimensional rotating black hole

International Nuclear Information System (INIS)

Frolov, Valeri P.; Stevens, Kory A.

2004-01-01

We study stationary string configurations in a space-time of a higher-dimensional rotating black hole. We demonstrate that the Nambu-Goto equations for a stationary string in the 5D (five-dimensional) Myers-Perry metric allow a separation of variables. We present these equations in the first-order form and study their properties. We prove that the only stationary string configuration that crosses the infinite redshift surface and remains regular there is a principal Killing string. A worldsheet of such a string is generated by a principal null geodesic and a timelike at infinity Killing vector field. We obtain principal Killing string solutions in the Myers-Perry metrics with an arbitrary number of dimensions. It is shown that due to the interaction of a string with a rotating black hole, there is an angular momentum transfer from the black hole to the string. We calculate the rate of this transfer in a space-time with an arbitrary number of dimensions. This effect slows down the rotation of the black hole. We discuss possible final stationary configurations of a rotating black hole interacting with a string

Expansions of general stationary stochastic optical fields: general formalism

International Nuclear Information System (INIS)

Martinez-Herrero, R.; Mejias, P.M.

1985-01-01

A new expansion of a general stationary stochastic optical field is derived. Each term of the series is seen to represent a recently defined new class of optical fields, the so-called spectrally quasi-factorizable fields. Alternative expansion in terms of nonstationary fields that obey the wave equation is also shown. A relationship between temporal and spatial features of stationary free optical fields is discussed

Surface spectra of Weyl semimetals through self-adjoint extensions

Science.gov (United States)

Seradjeh, Babak; Vennettilli, Michael

2018-02-01

We apply the method of self-adjoint extensions of Hermitian operators to the low-energy, continuum Hamiltonians of Weyl semimetals in bounded geometries and derive the spectrum of the surface states on the boundary. This allows for the full characterization of boundary conditions and the surface spectra on surfaces both normal to the Weyl node separation as well as parallel to it. We show that the boundary conditions for quadratic bulk dispersions are, in general, specified by a U (2 ) matrix relating the wave function and its derivatives normal to the surface. We give a general procedure to obtain the surface spectra from these boundary conditions and derive them in specific cases of bulk dispersion. We consider the role of global symmetries in the boundary conditions and their effect on the surface spectrum. We point out several interesting features of the surface spectra for different choices of boundary conditions, such as a Mexican-hat shaped dispersion on the surface normal to Weyl node separation. We find that the existence of bound states, Fermi arcs, and the shape of their dispersion, depend on the choice of boundary conditions. This illustrates the importance of the physics at and near the boundaries in the general statement of bulk-boundary correspondence.

Extremely high magnetoresistance and conductivity in the type-II Weyl semimetals WP2 and MoP2.

Science.gov (United States)

Kumar, Nitesh; Sun, Yan; Xu, Nan; Manna, Kaustuv; Yao, Mengyu; Süss, Vicky; Leermakers, Inge; Young, Olga; Förster, Tobias; Schmidt, Marcus; Borrmann, Horst; Yan, Binghai; Zeitler, Uli; Shi, Ming; Felser, Claudia; Shekhar, Chandra

2017-11-21

The peculiar band structure of semimetals exhibiting Dirac and Weyl crossings can lead to spectacular electronic properties such as large mobilities accompanied by extremely high magnetoresistance. In particular, two closely neighboring Weyl points of the same chirality are protected from annihilation by structural distortions or defects, thereby significantly reducing the scattering probability between them. Here we present the electronic properties of the transition metal diphosphides, WP 2 and MoP 2 , which are type-II Weyl semimetals with robust Weyl points by transport, angle resolved photoemission spectroscopy and first principles calculations. Our single crystals of WP 2 display an extremely low residual low-temperature resistivity of 3 nΩ cm accompanied by an enormous and highly anisotropic magnetoresistance above 200 million % at 63 T and 2.5 K. We observe a large suppression of charge carrier backscattering in WP 2 from transport measurements. These properties are likely a consequence of the novel Weyl fermions expressed in this compound.

Chiral pair of Fermi arcs, anomaly cancellation, and spin or valley Hall effects in Weyl metals with broken inversion symmetry

Science.gov (United States)

Jang, Iksu; Kim, Ki-Seok

2018-04-01

Anomaly cancellation has been shown to occur in broken time-reversal symmetry Weyl metals, which explains the existence of a Fermi arc. We extend this result in the case of broken inversion symmetry Weyl metals. Constructing a minimal model that takes a double pair of Weyl points, we demonstrate the anomaly cancellation explicitly. This demonstration explains why a chiral pair of Fermi arcs appear in broken inversion symmetry Weyl metals. In particular, we find that this pair of Fermi arcs gives rise to either "quantized" spin Hall or valley Hall effects, which corresponds to the "quantized" version of the charge Hall effect in broken time-reversal symmetry Weyl metals.

Pressure tuning of the electrical transport properties of the Weyl semimetal NbP

Energy Technology Data Exchange (ETDEWEB)

Reis, Ricardo dos; Ajeesh, M.O.; Sun, Yan; Shekhar, Chandra; Schmidt, Marcus; Felser, Claudia; Yan, Binghai; Nicklas, Michael [Max Planck Institute for Chemical Physics of Solids, Dresden (Germany)

2016-07-01

Recently enormous attention has been given to a class of material called Weyl semimetal (WSM) due to the prediction of many exotic phenomena, in particular exceptional transport properties, making these systems not only interesting for fundamental research, but also promising materials for novel applications. WSM can be viewed as the hybrid of 3D graphene and topological insulators. The band crossing point, the so-called Weyl point, acts as a magnetic monopole (a singular point of Berry curvature) in momentum space, which always comes in a pairs. If the time-reversal and inversion symmetries are respected, a pair of Weyl points is degenerate in energy, forming another topological phase called Dirac semimetal. Owing this complex band structure the details of the electronic structure can play a significant role in the electrical transport properties of these materials. In this context, external pressure is an important control parameter to effectively tune lattice structures and the corresponding electronic states in a systematic fashion, avoiding the complexity brought by chemical doping. Here, we present a high pressure study of the magnetotransport properties of the Weyl semimetal NbP, which are particularly important to explore novel phenomena and understand the physics behind.

Topological insulators Dirac equation in condensed matter

CERN Document Server

Shen, Shun-Qing

2017-01-01

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

Weyl and Marchaud derivatives: a forgotten history

OpenAIRE

Ferrari, Fausto

2017-01-01

In this paper, we recall the contribution given by Hermann Weyl and André Marchaud to the notion of fractional derivative. In addition, we discuss some relationships between the fractional Laplace operator and Marchaud derivative in the perspective to generalize these objects to different fields of the mathematics.

On a strong solution of the non-stationary Navier-Stokes equations under slip or leak boundary conditions of friction type

Science.gov (United States)

Kashiwabara, Takahito

Strong solutions of the non-stationary Navier-Stokes equations under non-linearized slip or leak boundary conditions are investigated. We show that the problems are formulated by a variational inequality of parabolic type, to which uniqueness is established. Using Galerkin's method and deriving a priori estimates, we prove global and local existence for 2D and 3D slip problems respectively. For leak problems, under no-leak assumption at t=0 we prove local existence in 2D and 3D cases. Compatibility conditions for initial states play a significant role in the estimates.

Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP.

Science.gov (United States)

Arnold, Frank; Shekhar, Chandra; Wu, Shu-Chun; Sun, Yan; Dos Reis, Ricardo Donizeth; Kumar, Nitesh; Naumann, Marcel; Ajeesh, Mukkattu O; Schmidt, Marcus; Grushin, Adolfo G; Bardarson, Jens H; Baenitz, Michael; Sokolov, Dmitry; Borrmann, Horst; Nicklas, Michael; Felser, Claudia; Hassinger, Elena; Yan, Binghai

2016-05-17

Weyl semimetals (WSMs) are topological quantum states wherein the electronic bands disperse linearly around pairs of nodes with fixed chirality, the Weyl points. In WSMs, nonorthogonal electric and magnetic fields induce an exotic phenomenon known as the chiral anomaly, resulting in an unconventional negative longitudinal magnetoresistance, the chiral-magnetic effect. However, it remains an open question to which extent this effect survives when chirality is not well-defined. Here, we establish the detailed Fermi-surface topology of the recently identified WSM TaP via combined angle-resolved quantum-oscillation spectra and band-structure calculations. The Fermi surface forms banana-shaped electron and hole pockets surrounding pairs of Weyl points. Although this means that chirality is ill-defined in TaP, we observe a large negative longitudinal magnetoresistance. We show that the magnetoresistance can be affected by a magnetic field-induced inhomogeneous current distribution inside the sample.

Liouville equation with boundary conditions derived from classical strings

International Nuclear Information System (INIS)

Marnelius, R.

1983-01-01

It is shown in terms of the classical string theory that a breaking of the Weyl invariance necessarily requires the Liouville equation for the variable phi=1n rho, where rho is the variable that appears in the conformal gauge gsub(α#betta#)=rhoetasub(α#betta#). Appropriate boundary conditions on phi for open and closed strings are then derived. (orig.)

Weyl and Marchaud Derivatives: A Forgotten History

Directory of Open Access Journals (Sweden)

Fausto Ferrari

2018-01-01

Full Text Available In this paper, we recall the contribution given by Hermann Weyl and André Marchaud to the notion of fractional derivative. In addition, we discuss some relationships between the fractional Laplace operator and Marchaud derivative in the perspective to generalize these objects to different fields of the mathematics.

Illuminating the chirality of Weyl fermions

Science.gov (United States)

Ma, Qiong; Xu, Su-Yang; Chan, Ching-Kit; Zhang, Cheng-Long; Chang, Guoqing; Lin, Hsin; Jia, Shuang; Lee, Patrick; Gedik, Nuh; Jarillo-Herrero, Pablo

In particle physics, Weyl fermions (WF) are elementary particles that travel at the speed of light and have a definite chirality. In condensed matter, it has been recently realized that WFs can arise as magnetic monopoles in the momentum space of a novel topological metal, the Weyl semimetal (WSM). Their chirality, given by the sign of the monopole charge, is the defining property of a WSM, since it directly serves as the topological number and gives rise to exotic properties such as Fermi arcs and the chiral anomaly. Moreover, the two chiralities, analogous to the two valleys in 2D materials, lead to a new degree of freedom in a 3D crystal, suggesting novel pathways to store and carry information. By shining circularly polarized light on the WSM TaAs, we illuminate the chirality of the WFs and achieve an electrical current that is highly controllable based on the WFs' chirality. Our results open up a wide range of new possibilities for experimentally studying and controlling the WFs and their associated quantum anomalies by optical and electrical means, which suggest the exciting prospect of ``Weyltronics''.

Plasma equilibria and stationary flows in axisymmetric systems. Pt. 2

International Nuclear Information System (INIS)

Zelazny, R.; Stankiewicz, R.; Potempski, S.

1988-05-01

Part I of this report described the computational problems connected with the bifurcating solutions to static and extended Grad-Shafranov-Schlueter equations (with stationary flows). Part II is a listing of the computer program for solving the extended Grad-Shafranov-Schlueter equations developed in Part I. (author)

Stationary solution of the Fokker-Planck equation for linearly coupled motion in an electron storage ring

International Nuclear Information System (INIS)

Chao, A.W.; Lee, M.J.

1975-09-01

Effects upon longitudinal bunch shape in a storage ring due to linear and nonlinear potential can be calculated by finding the stationary solution to the Fokker-Planck equation for the particle distribution. Effects upon transverse bunch shape of a stored electron beam due to photon emissions and damping can be calculated by this method. It has been found that this method can also be used for a case in which the transverse modes of oscillation are coupled to the energy deviation δ. Examples of lattice elements which produce linear coupling between these oscillations are skew quadrupole magnets and solenoid magnets. For the linearly coupled case the stationary solution has been found to be given by exp (ΣΣA/sub ij/ x/sub i/x/sub j/) with x/sub i/ the canonical variables (x,p/sub x/, y, p/sub y/, δ, p/sub δ/) and A /sub ij/ some constants. The solution for the values of A /sub ij/'s will be described in this report. It will be shown that this solution can be expressed in a compact form. For simple cases, this form of solution leads directly to analytic expressions for the values of A /sub ij/'s and the bunch shape can be calculated by integrating the distribution function over some of the coordinates; for the more complex cases, it can be conveniently adapted as an algorithm for numerical evaluation. 16 refs

The Weyl group of the Cuntz algebra

DEFF Research Database (Denmark)

Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech

2012-01-01

The Weyl group of the Cuntz algebra O_n is investigated. This is (isomorphic to) the group of polynomial automorphisms lambda_u of O_n, namely those induced by unitaries u that can be written as finite sums of words in the canonical generating isometries S_i and their adjoints. A necessary...

Stationary two-variable gravitational vortex fields

International Nuclear Information System (INIS)

Koppel, A.

1974-01-01

Some properties of stationary two-variable solutions of the Einstein equations were studied on the basis of rigorous analysis of the nonrelativistic limit of the relativistic gravitation theory. For this case a particular method was developed of determining so-called vortex gravitational fields described by vortex solutions, which in the nonrelativistic limit transform from → infinity to the nonnewtonian type solutions. The main formulae for such fields are derived and a scheme for their calculation is presented. It is shown that under certain conditions the exact stationary solutions of the Papapetrou type for vacuum relativistic equations are vortical. From this fact, first, the presence of particular exact vortical solutions for the Einstein equations is proved, and secondly, a new possibility of a physical interpretation is proposed for the Papapetrou solutions. It is also shown that the nonrelativistic limit of this class of solutions strongly depends on the structure of solution parameters (under certain conditions these solutions may also have the Newtonian limit). 'Multipole' and 'one-variable' partial solutions of the Papapetrou class solution are derived as particular examples of vortical solutions. It is shown that for a specific parameter structure the known NUT solution is also vortical, since it belongs to the Papapetrou class [ru

Rotating black string and the effective Teukolsky equation in the braneworld

International Nuclear Information System (INIS)

Kanno, Sugumi; Soda, Jiro

2004-01-01

In the Randall-Sundrum two-brane (RS1) model, a large Kerr black hole on the brane can be naturally identified with a section of a rotating black string. To estimate Kaluza-Klein (KK) corrections on gravitational waves emitted by perturbed rotating black strings, we give the effective Teukolsky equation on the brane, which is a separable equation and hence numerically manageable. In this process, we derive the master equation for the electric part of the Weyl tensor, E μν , which is also useful in discussing the transition from black strings to localized black holes triggered by Gregory-Laflamme instability

Spin-1 Dirac-Weyl fermions protected by bipartite symmetry

Energy Technology Data Exchange (ETDEWEB)

Lin, Zeren [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); School of Physics, Peking University, Beijing 100871 (China); Liu, Zhirong, E-mail: LiuZhiRong@pku.edu.cn [College of Chemistry and Molecular Engineering, Peking University, Beijing 100871 (China); Center for Nanochemistry, Beijing National Laboratory for Molecular Sciences (BNLMS), Peking University, Beijing 100871 (China)

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′.

An elementary aspect of the Weyl-Wigner representation

DEFF Research Database (Denmark)

Dahl, Jens Peder; Schleich, W.P.

2003-01-01

It is an elementary aspect of the Weyl-Wigner representation of quantum mechanics that the dynamical phase-space function corresponding to the square of a quantum-mechanical operator is, in general, different from the square of the function representing the operator itself. We call attention...

Stationary magnetohydrodynamic equilibrium of toroidal plasma in rotation

International Nuclear Information System (INIS)

Missiato, O.

1986-01-01

The stationary equations of classical magnetohydrodynamics are utilized to study the toroidal motion of a thermonuclear magnetically - confined plasma with toroidal symmetry (Tokamak). In the present work, we considered a purely toroidal stationary rotation and te problem is reduced to studing a second order partial differencial equation of eliptic type Maschke-Perrin. Assuming that the temperature remains constant on the magnetic surfaces, an analitic solution, valid for low Mach numbers (M ≤ 0 .4), was obtained for the above-mentioned equation by means of a technique developed by Pantuso Sudano. From the solution found, we traced graphs for the quantities which described the equilibrium state of the plasma, namely: mass density, pressure, temperature, electric current density and toroidal magnetic field. Finally we compare this analitical model with others works which utilized differents analitical models and numerical simulations. We conclude that the solutions obtained are in good agreement with the previos results. In addition, however, our model contains the results of Sudano-Goes with the additional advantage of employing much simple analitical expressions. (author) [pt

Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. II. Classification of axisymmetric no-swirl solutions

Science.gov (United States)

Li, Li; Li, YanYan; Yan, Xukai

2018-05-01

We classify all (- 1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south and north poles, parameterizing them as a four dimensional surface with boundary in appropriate function spaces. Then we establish smoothness properties of the solution surface in the four parameters. The smoothness properties will be used in a subsequent paper where we study the existence of (- 1)-homogeneous axisymmetric solutions with non-zero swirl on S2 ∖ { S , N }, emanating from the four dimensional solution surface.

Quasi-Compact Perturbations of the Weyl Essential Spectrum and Application to Singular Transport Operators

Directory of Open Access Journals (Sweden)

Leila Mebarki

2015-11-01

Full Text Available This paper is devoted to the investigation of the stability of the Weyl essential spectrum of closed densely dened linear operator A subjected to additive perturbation K such that (lambda-A-K^{-1}K or K(lambda-A-K^{-1} is a quasi-compact operator. The obtained results are used to describe the Weyl essential spectrum of singular neutron transport operator.

Bianchi type I expanding universe in Weyl-invariant gravity with a quartic interaction term

Energy Technology Data Exchange (ETDEWEB)

Kao, W.F.; Lin, Ing-Chen [National Chiao Tung University, Institute of Physics, Hsinchu (China)

2017-11-15

We will focus on the effect of a Weyl-invariant model with a quadratic interaction term and a free scalar field ψ. A set of analytic solutions will be obtained for this model. This model provides a dynamical alternative to the standard ΛCDM model. In particular, we will show that the quartic Weyl-invariant model prediction is consistent with the Hubble diagram observations. (orig.)

Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring

Science.gov (United States)

Basovník, M.; Semerák, O.

2016-08-01

We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro)vacuum exact solutions of Einstein's equations, we first considered the Majumdar-Papapetrou solution for a binary of extreme black holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric thin ring described by the Bach-Weyl solution. The geometry is again revealed on the simplest invariants determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature (Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time) where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being already distinct on the level of potential and acceleration, this is still more pronounced on the level of curvature: for a sufficiently massive and/or nearby (small) ring, the Kretschmann scalar even becomes negative in certain toroidal regions mostly touching the horizon from inside. Such regions have been interpreted as those where magnetic-type curvature dominates, but here we deal with space-times which do not involve rotation and the negative value is achieved due to the electric-type components of the Riemann/Weyl tensor. The Kretschmann scalar also shapes rather nontrivial landscapes outside the horizon.

Homogeneous Solutions of Stationary Navier-Stokes Equations with Isolated Singularities on the Unit Sphere. I. One Singularity

Science.gov (United States)

Li, Li; Li, YanYan; Yan, Xukai

2018-03-01

We classify all (-1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south pole, parameterize them as a two dimensional surface with boundary, and analyze their pressure profiles near the north pole. Then we prove that there is a curve of (-1)-homogeneous axisymmetric solutions with nonzero swirl, having the same smoothness property, emanating from every point of the interior and one part of the boundary of the solution surface. Moreover we prove that there is no such curve of solutions for any point on the other part of the boundary. We also establish asymptotic expansions for every (-1)-homogeneous axisymmetric solutions in a neighborhood of the singular point on the unit sphere.

Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials.

Science.gov (United States)

Hübener, Hannes; Sentef, Michael A; De Giovannini, Umberto; Kemper, Alexander F; Rubio, Angel

2017-01-17

Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na 3 Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet-Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance.

Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials

Science.gov (United States)

Hübener, Hannes; Sentef, Michael A.; de Giovannini, Umberto; Kemper, Alexander F.; Rubio, Angel

2017-01-01

Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na3Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet-Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance.

Creating stable Floquet–Weyl semimetals by laser-driving of 3D Dirac materials

Science.gov (United States)

Hübener, Hannes; Sentef, Michael A.; De Giovannini, Umberto; Kemper, Alexander F.; Rubio, Angel

2017-01-01

Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na3Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet–Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance. PMID:28094286

On the generation of magnetostatic solutions from gravitational two-soliton solutions of a stationary mass

Energy Technology Data Exchange (ETDEWEB)

Chaudhuri, A. [B.K.C. College, Department of Physics, Kolkata (India); Chaudhuri, S. [University of Burdwan, Department of Physics, Burdwan (India)

2017-11-15

In the paper, magnetostatic solutions of the Einstein-Maxwell field equations are generated from the gravitational two-soliton solutions of a stationary mass. Using the soliton technique of Belinskii and Zakharov (Sov Phys JETP 48:985, 1978, Sov Phys JETP 50:1, 1979), we construct diagonal two-soliton solutions of Einstein's gravitational field equations for an axially symmetric stationary space-time and investigate some properties of the generated stationary gravitational metric. Magnetostatic solutions corresponding to the generated stationary gravitational solutions are then constructed using the transformation technique of Das and Chaudhuri (Pramana J Phys 40:277, 1993). The mass and the dipole moment of the source are evaluated. In our analysis we make use of a second transformation (Chaudhuri in Pramana J Phys 58:449, 2002), probably for the first time in the literature, to generate magnetostatic solutions from the stationary gravitational two-soliton solutions which give us simple and straightforward expressions for the mass and the magnetic dipole moment. (orig.)

On quantization, the generalised Schroedinger equation and classical mechanics

International Nuclear Information System (INIS)

Jones, K.R.W.

1991-01-01

A ψ-dependent linear functional operator, was defined, which solves the problem of quantization in non-relativistic quantum mechanics. Weyl ordering is implemented automatically and permits derivation of many of the quantum to classical correspondences. The parameter λ presents a natural C ∞ deformation of the dynamical structure of quantum mechanics via a non-linear integro-differential 'Generalised Schroedinger Equation', admitting an infinite family of soliton solutions. All these solutions are presented and it is shown that this equation gives an exact dynamic and energetic reproduction of classical mechanics with the correct measurement theoretic limit. 23 refs

Inflation with light Weyl ghost

Directory of Open Access Journals (Sweden)

Tokareva Anna

2016-01-01

Full Text Available Inflationary perturbations are considered in a renormalizable but non-unitary theory of gravity with the additional Weyl term. We obtained that ghost degrees of freedom do not spoil the inflation and the scalar perturbation amplitude at the linear level even in a case of the ghost with mass smaller than Hubble parameter at inflation. The ghost impact to the observables is also estimated to be negligible for the range of masses allowed by the experiment. The non-linear level of the theory and its possible application are also discussed.

Negative magnetoresistance in Weyl semimetals NbAs and NbP: Intrinsic chiral anomaly and extrinsic effects

Science.gov (United States)

Li, Yupeng; Wang, Zhen; Li, Pengshan; Yang, Xiaojun; Shen, Zhixuan; Sheng, Feng; Li, Xiaodong; Lu, Yunhao; Zheng, Yi; Xu, Zhu-An

2017-06-01

Chiral anomaly-induced negative magnetoresistance (NMR) has been widely used as critical transport evidence for the existence of Weyl fermions in topological semimetals. In this mini-review, we discuss the general observation of NMR phenomena in non-centrosymmetric NbP and NbAs. We show that NMR can arise from the intrinsic chiral anomaly of Weyl fermions and/or extrinsic effects, such as the superimposition of Hall signals; field-dependent inhomogeneous current flow in the bulk, i.e., current jetting; and weak localization (WL) of coexistent trivial carriers. The WL-controlled NMR is heavily dependent on sample quality and is characterized by a pronounced crossover from positive to negative MR growth at elevated temperatures, resulting from the competition between the phase coherence time and the spin-orbital scattering constant of the bulk trivial pockets. Thus, the correlation between the NMR and the chiral anomaly need to be scrutinized without the support of complimentary techniques. Because of the lifting of spin degeneracy, the spin orientations of Weyl fermions are either parallel or antiparallel to the momentum, which is a unique physical property known as helicity. The conservation of helicity provides strong protection for the transport of Weyl fermions, which can only be effectively scattered by magnetic impurities. Chemical doping with magnetic and non-magnetic impurities is thus more convincing than the NMR method for detecting the existence of Weyl fermions.

The computation of stationary distributions of Markov chains through perturbations

Directory of Open Access Journals (Sweden)

Jeffery J. Hunter

1991-01-01

Full Text Available An algorithmic procedure for the determination of the stationary distribution of a finite, m-state, irreducible Markov chain, that does not require the use of methods for solving systems of linear equations, is presented. The technique is based upon a succession of m, rank one, perturbations of the trivial doubly stochastic matrix whose known steady state vector is updated at each stage to yield the required stationary probability vector.

Stability of stationary states of non-local equations with singular interaction potentials

KAUST Repository

Fellner, Klemens; Raoul, Gaë l

2011-01-01

repulsive interaction potentials we show the stability of stationary states of uniformly bounded solutions under a convexity condition.Finally, we present numerical simulations to illustrate our results. © 2010 Elsevier Ltd.

q-fractional calculus and equations

CERN Document Server

Annaby, Mahmoud H

2012-01-01

This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson’s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular  q-Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional q-calculi of the types Riemann–Liouville; Grünwald–Letnikov;  Caputo;  Erdélyi–Kober and Weyl are defined analytically. Fractional q-Leibniz rules with applications  in q-series are  also obtained with rigorous proofs of the formal  results of  Al-Salam-Verma, which remained unproved for decades. In working ...

Wave fields in Weyl spaces and conditions for the existence of a preferred pseudo-Riemannian structure

International Nuclear Information System (INIS)

Audretsch, J.; Gaehler, F.; Straumann, N.

1984-01-01

Previous axiomatic approaches to general relativity which led to a Weylian structure of space-time are supplemented by a physical condition which implies the existence of a preferred pseudo-Riemannian structure. It is stipulated that the trajectories of the short wave limit of classical massive fields agree with the geodesics of the Weyl connection and it is shown that this is equivalent to the vanishing of the covariant derivative of a ''mass function'' of nontrivial Weyl type.This in turn is proven to be equivalent to the existence of a preferred metric of the conformal structure such that the Weyl connection is reducible to a connection of the bundle of orthonormal frames belonging to this distinguished metric. (orig.)

A dissipative model of solar system and stability of stationary rotations

Science.gov (United States)

Vilke, V. G.

2009-04-01

receives the equations describing movements of the centers of mass of planets and their own rotations. In the offered model takes place a dissipation of the energy which source are internally viscous forces of each planet. The system supposes the first integral - the law of preservation of the kinetic moment concerning the centre of mass of system. As a result of deformations of planets in the law of the universal gravitation which has been written down for material points, there are small conservative amendments. The equations of motion describe motions of the centers of mass of planets and their rotation around of the centers of mass in view of the tidal phenomena and the dissipative forces. The connected system of the equations consists of 3 the vector equations of the second order representing the theorems of motion of the center of mass of planets, and the vector equations of the first order determining changes of the own kinetic moments of each planet. Stationary values of full mechanical energy on the variety set in integral of the kinetic moment, correspond to stationary motions - to rotations of system as rigid body with constant angular velocity around of the centre of mass of all system. Angular velocity of stationary rotation is directed along a constant vector of the kinetic moment, and the axis of rotation is the principal central axis of inertia of system. We shall notice, that deformations of planets in stationary motion are constant, as in system of coordinates rotating with constant angular velocity centrifugal forces and forces of gravitational interaction of planets are constant. Stationary configurations of system are determined according to Routh`s technique as stationary points of the changed potential energy submitted by the sum potential energies of centrifugal and gravitational forces. The first variation of the changed potential energy addresses in zero on a stationary configuration. The judgment about stability stationary configurations is based

Un-equivalency theorem between deformed and undeformed Heisenberg-Weyl's algebras

International Nuclear Information System (INIS)

Zhang Jianzu

2006-01-01

Two fundamental issues about the relation between the deformed Heisenberg-Weyl algebra in noncommutative space and the undeformed one in commutative space are elucidated. First the un-equivalency theorem between two algebras is proved: the deformed algebra related to the undeformed one by a non-orthogonal similarity transformation is explored; furthermore, non-existence of a unitary similarity transformation which transforms the deformed algebra to the undeformed one is demonstrated. Secondly the uniqueness of realizing the deformed phase space variables via the undeformed ones is elucidated: both the deformed Heisenberg-Weyl algebra and the deformed bosonic algebra should be maintained under a linear transformation between two sets of phase space variables which fixes that such a linear transformation is unique. Elucidation of this un-equivalency theorem has basic meaning both in theory and experiment

Weyl and Riemann-Liouville multifractional Ornstein-Uhlenbeck processes

International Nuclear Information System (INIS)

Lim, S C; Teo, L P

2007-01-01

This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein-Uhlenbeck process and the Riemann-Liouville multifractional Ornstein-Uhlenbeck process. Basic properties of these processes such as locally self-similar property and Hausdorff dimension are studied. The relationship between the multifractional Ornstein-Uhlenbeck processes and the corresponding multifractional Brownian motions is established

Kondo effect in three-dimensional Dirac and Weyl systems

NARCIS (Netherlands)

Mitchell, Andrew K.; Fritz, Lars

2015-01-01

Magnetic impurities in three-dimensional Dirac and Weyl systems are shown to exhibit a fascinatingly diverse range of Kondo physics, with distinctive experimental spectroscopic signatures. When the Fermi level is precisely at the Dirac point, Dirac semimetals are in fact unlikely candidates for a

Topological Nodal Cooper Pairing in Doped Weyl Metals

Science.gov (United States)

Li, Yi; Haldane, F. D. M.

2018-02-01

We generalize the concept of Berry connection of the single-electron band structure to that of a two-particle Cooper pairing state between two Fermi surfaces with opposite Chern numbers. Because of underlying Fermi surface topology, the pairing Berry phase acquires nontrivial monopole structure. Consequently, pairing gap functions have topologically protected nodal structure as vortices in the momentum space with the total vorticity solely determined by the pair monopole charge qp. The nodes of gap function behave as the Weyl-Majorana points of the Bogoliubov-de Gennes pairing Hamiltonian. Their relation with the connection patterns of the surface modes from the Weyl band structure and the Majorana surface modes inside the pairing gap is also discussed. Under the approximation of spherical Fermi surfaces, the pairing symmetry are represented by monopole harmonic functions. The lowest possible pairing channel carries angular momentum number j =|qp|, and the corresponding gap functions are holomorphic or antiholomorphic functions on Fermi surfaces. After projected on the Fermi surfaces with nontrivial topology, all the partial-wave channels of pairing interactions acquire the monopole charge qp independent of concrete pairing mechanism.

Completely integrable operator evolution equations. II

International Nuclear Information System (INIS)

Chudnovsky, D.V.

1979-01-01

The author continues the investigation of operator classical completely integrable systems. The main attention is devoted to the stationary operator non-linear Schroedinger equation. It is shown that this equation can be used for separation of variables for a large class of completely integrable equations. (Auth.)

Completeness in quantum mechanics and the Weyl-Titchmarsh-Kodaira theorem

Energy Technology Data Exchange (ETDEWEB)

Palma, G [Departamento de Fisica, Universidad de Santiago de Chile, Casilla 307, Santiago 2 (Chile); Prado, H; Reyes, E G, E-mail: guillermo.palma@usach.c, E-mail: humberto.prado@usach.c, E-mail: ereyes@fermat.usach.c [Departamento de Matematica y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago (Chile)

2010-06-25

We discuss the completeness of (generalized) eigenfunctions in quantum mechanics using the classical theory developed by Weyl, Titchmarsh, and Kodaira. As applications, we rigorously prove the completeness of generalized eigenfunctions for the step and well potentials.

Inviscid limit of stochastic damped 2D Navier–Stokes equations

International Nuclear Information System (INIS)

Bessaih, Hakima; Ferrario, Benedetta

2014-01-01

We consider the inviscid limit of the stochastic damped 2D Navier–Stokes equations. We prove that, when the viscosity vanishes, the stationary solution of the stochastic damped Navier–Stokes equations converges to a stationary solution of the stochastic damped Euler equation and that the rate of dissipation of enstrophy converges to zero. In particular, this limit obeys an enstrophy balance. The rates are computed with respect to a limit measure of the unique invariant measure of the stochastic damped Navier–Stokes equations. (paper)

A Note on the Problem of Proper Time in Weyl Space-Time

Science.gov (United States)

Avalos, R.; Dahia, F.; Romero, C.

2018-02-01

We discuss the question of whether or not a general Weyl structure is a suitable mathematical model of space-time. This is an issue that has been in debate since Weyl formulated his unified field theory for the first time. We do not present the discussion from the point of view of a particular unification theory, but instead from a more general standpoint, in which the viability of such a structure as a model of space-time is investigated. Our starting point is the well known axiomatic approach to space-time given by Elhers, Pirani and Schild (EPS). In this framework, we carry out an exhaustive analysis of what is required for a consistent definition for proper time and show that such a definition leads to the prediction of the so-called "second clock effect". We take the view that if, based on experience, we were to reject space-time models predicting this effect, this could be incorporated as the last axiom in the EPS approach. Finally, we provide a proof that, in this case, we are led to a Weyl integrable space-time as the most general structure that would be suitable to model space-time.

Remark to the Comment on "New pseudoclassical model for Weyl particles"

OpenAIRE

Gitman, D. M.; Gonçalves, A. E.; Tyutin, I. V.

1996-01-01

We present here our considerations concerning the problem of classical consistency of pseudoclassical models touched upon in a recent comment on our paper "New pseudoclassical model for Weyl particle".

Periodic Solutions and S-Asymptotically Periodic Solutions to Fractional Evolution Equations

Directory of Open Access Journals (Sweden)

Jia Mu

2017-01-01

Full Text Available This paper deals with the existence and uniqueness of periodic solutions, S-asymptotically periodic solutions, and other types of bounded solutions for some fractional evolution equations with the Weyl-Liouville fractional derivative defined for periodic functions. Applying Fourier transform we give reasonable definitions of mild solutions. Then we accurately estimate the spectral radius of resolvent operator and obtain some existence and uniqueness results.

Weyl transforms associated with the Riemann-Liouville operator

Directory of Open Access Journals (Sweden)

N. B. Hamadi

2006-01-01

Full Text Available For the Riemann-Liouville transform ℛα, α∈ℝ+, associated with singular partial differential operators, we define and study the Weyl transforms Wσ connected with ℛα, where σ is a symbol in Sm, m∈ℝ. We give criteria in terms of σ for boundedness and compactness of the transform Wσ.

A new Weyl-like tensor of geometric origin

Science.gov (United States)

Vishwakarma, Ram Gopal

2018-04-01

A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.

Central extensions for the Weyl CCR in Curved space

International Nuclear Information System (INIS)

Emch, G.G.

1993-01-01

For non-necessarily flat homogeneous configuration spaces, we illustrate how the cohomological choices made in the definition a Weyl group of the CCR are reflected in the momentum map for the action of this group on its co-adjoint orbit of maximal dimension. (Author) 8 refs

How to translate a massless particle (the Weyl neutrino)

International Nuclear Information System (INIS)

Berger, S.B.

1979-01-01

Previous work indicated a deep connection between translations and rotations for a Weyl neutrino (a massless particle). In the letter the explicit form of a translation in the z-direction is given assuming a translation operator of the form esup(i anti g.anti x). (author)

New topological theories and conjugacy classes of the Weyl group

International Nuclear Information System (INIS)

Hollowood, T.J.; Miramontes, J.L.

1993-01-01

The problem of interpreting a set of W-algebra constraints constructed in terms of an arbitrarily twisted scalar field as recursion relations of some topological theory is addressed. In this picture, the models of topological gravity coupled to A, D or E topological matter, correspond to taking the scalar field twisted by the Coxeter element of the Weyl group. It turns out that not all conjugacy classes of the Weyl group lead to models which allow for such an interpretation. For example, it is shown that for the A algebras there are two possible choices for the conjugacy class, giving a new set of theories in addition to the conventional ones. Furthermore, it is shown how the new series of theories contains the conventional series as a subsector. A tentative interpretation of this new series in terms of intersection theory is presented. (orig.)

Variance-optimal hedging for processes with stationary independent increments

DEFF Research Database (Denmark)

Hubalek, Friedrich; Kallsen, J.; Krawczyk, L.

We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation, we...

Long time tails in stationary random media. I. Theory

NARCIS (Netherlands)

Ernst, M.H.; Machta, J.; Dorfman, J.R.; Beijeren, H. van

1984-01-01

Diffusion of moving particles in stationary disordered media is studied using a phenomenological mode-coupling theory. The presence of disorder leads to a generalized diffusion equation, with memory kernels having power law long time tails. The velocity autocorrelation function is found to decay

Applications of Affine and Weyl geometry

CERN Document Server

García-Río, Eduardo; Nikcevic, Stana

2013-01-01

Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannia

The Schroedinger equation as a singular perturbation problem

International Nuclear Information System (INIS)

Jager, E.M. de; Kuepper, T.

1978-01-01

Comparisons are made of the eigenvalues and the corresponding eigenfunctions of the eigenvalue problem connected with the one dimensional Schroedinger equation in Hilbert space. The difference of the eigenvalues is estimated by applying Weyl's monotonicity principle and the minimum maximum principle. The difference of the eigenfunctions is estimated in L 2 norm and in maximum norm obtained by using simple tools from operator theory in Hilbert spaces. An application concerning perturbations of the Planck ideal linear oscillator is given. (author)

Study of the stability of the stationary wave of nuclear fission

International Nuclear Information System (INIS)

Khotyanintsev, V.N.; Aksenov, A.V.; Khotyanintseva, E.N.; Pavlovich, V.N.

2014-01-01

Stability of the stationary wave of nuclear burning in fast reactor with uranium-plutonium fuel chain is investigated. The reactor model including 1-D diffusion equation in one-group approximation for neutron flux density and kinetic equations for nuclear densities describes slow evolution of nuclear densities followed by neutron flux. New analytical approach was proposed, which is based on the approximation of small wave velocity of the stationary wave. We obtain so-called wave velocity characteristic of the reactor which is the dependence of wave velocity to the effective absorber concentration. We show that due to instability of long-living 241 Pu a turning point and lower branch of stationary solutions appear. Numerical solution of the time dependent problem proves that the solutions of the lower branch are unstable. Thus, the turning point of the velocity characteristic corresponds to the lower margin of possible wave velocities of nuclear fission waves of the steady shape. At the same time the solutions of the upper branch are stable with respect to slow evolution of nuclear densities

Stationary solutions of multicomponent chiral and gauge models

International Nuclear Information System (INIS)

Chudnovsky, D.V.; Chudnovsky, G.V.

1979-01-01

The authors examine stationary solutions of completely integrable systems in (x, t) dimensions having infinitely many components. Among the cases under investigation are: (1) the infinite-component non-linear Schroedinger equation; (2) infinite component CPsup(Ω) or SU(N) sigma-models; (3) general gauge and chiral completely integrable systems. (Auth.)

New exact solutions of Einstein's field equations: gravitational force can also be repulsive!

International Nuclear Information System (INIS)

Dietz, W.

1988-01-01

This article has not been written for specialists of exact solutions of Einstein's field equations but for physicists who are interested in nontrivial information on this topic. We recall the history and some basic properties of exact solutions of Einstein's vacuum equations. We show that the field equations for stationary axisymmetric vacuum gravitational fields can be expressed by only one nonlinear differential equation for a complex function. This compact form of the field equations allows the generation of almost all stationary axisymmetric vacuum gravitational fields. We present a new stationary two-body solution of Einstein's equations as an application of this generation technique. This new solution proves the existence of a macroscopic, repulsive spin-spin interaction in general relativity. Some estimates that are related to this new two-body solution are given

Vacillations induced by interference of stationary and traveling planetary waves

Science.gov (United States)

Salby, Murry L.; Garcia, Rolando R.

1987-01-01

The interference pattern produced when a traveling planetary wave propagates over a stationary forced wave is explored, examining the interference signature in a variety of diagnostics. The wave field is first restricted to a diatomic spectrum consisting of two components: a single stationary wave and a single monochromatic traveling wave. A simple barotropic normal mode propagating over a simple stationary plane wave is considered, and closed form solutions are obtained. The wave fields are then restricted spatially, providing more realistic structures without sacrificing the advantages of an analytical solution. Both stationary and traveling wave fields are calculated numerically with the linearized Primitive Equations in a realistic basic state. The mean flow reaction to the fluctuating eddy forcing which results from interference is derived. Synoptic geopotential behavior corresponding to the combined wave and mean flow fields is presented, and the synoptic signature in potential vorticity on isentropic surfaces is examined.

On the Weyl character formula for SU(n)

International Nuclear Information System (INIS)

Plymen, R.J.

1976-01-01

A straight line is drawn between the representation theory of SU(3) and the SU(3)-classification schemes in particle physics. The approach is based on that of Weyl (The Theory of Groups and Quantum Mechanics, Dover, New York, p. 381 (1950)). The present formulation brings an important part of particle physics into line with two contemporary accounts of compact Lie groups. (author)

Stochastic reliability analysis using Fokker Planck equations

International Nuclear Information System (INIS)

Hari Prasad, M.; Rami Reddy, G.; Srividya, A.; Verma, A.K.

2011-01-01

The Fokker-Planck equation describes the time evolution of the probability density function of the velocity of a particle, and can be generalized to other observables as well. It is also known as the Kolmogorov forward equation (diffusion). Hence, for any process, which evolves with time, the probability density function as a function of time can be represented with Fokker-Planck equation. In stochastic reliability analysis one is more interested in finding out the reliability or failure probability of the components or structures as a function of time rather than instantaneous failure probabilities. In this analysis the variables are represented with random processes instead of random variables. A random processes can be either stationary or non stationary. If the random process is stationary then the failure probability doesn't change with time where as in the case of non stationary processes the failure probability changes with time. In the present paper Fokker Planck equations have been used to find out the probability density function of the non stationary random processes. In this paper a flow chart has been provided which describes step by step process for carrying out stochastic reliability analysis using Fokker-Planck equations. As a first step one has to identify the failure function as a function of random processes. Then one has to solve the Fokker-Planck equation for each random process. In this paper the Fokker-Planck equation has been solved by using Finite difference method. As a result one gets the probability density values of the random process in the sample space as well as time space. Later at each time step appropriate probability distribution has to be identified based on the available probability density values. For checking the better fitness of the data Kolmogorov-Smirnov Goodness of fit test has been performed. In this way one can find out the distribution of the random process at each time step. Once one has the probability distribution

An Algebraic Construction of the First Integrals of the Stationary KdV Hierarchy

Science.gov (United States)

Matsushima, Masatomo; Ohmiya, Mayumi

2009-09-01

The stationary KdV hierarchy is constructed using a kind of recursion operator called Λ-operator. The notion of the maximal solution of the n-th stationary KdV equation is introduced. Using this maximal solution, a specific differential polynomial with the auxiliary spectral parameter called the spectral M-function is constructed as the quadratic form of the fundamental system of the eigenvalue problem for the 2-nd order linear ordinary differential equation which is related to the linearizing operator of the hierarchy. By calculating a perfect square condition of the quadratic form by an elementary algebraic method, the complete set of first integrals of this hierarchy is constructed.

Convergent Difference Schemes for Hamilton-Jacobi equations

KAUST Repository

Duisembay, Serikbolsyn

2018-01-01

In this thesis, we consider second-order fully nonlinear partial differential equations of elliptic type. Our aim is to develop computational methods using convergent difference schemes for stationary Hamilton-Jacobi equations with Dirichlet

Quantum cosmology and stationary states

International Nuclear Information System (INIS)

Padmanabhan, T.

1983-01-01

A model for quantum gravity, in which the conformal part of the metric is quantized using the path integral formalism, is presented. Einstein's equations can be suitably modified to take into account the effects of quantum conformal fluctuations. A closed Friedman model can be described in terms of well-defined stationary states. The ''ground state'' sets a lower bound (at Planck length) to the scale factor preventing the collapse. A possible explanation for matter creation and quantum nature of matter is suggested. (author)

Topological surface Fermi arcs in magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$

OpenAIRE

Xu, Qiunan; Liu, Enke; Shi, Wujun; Muechler, Lukas; Felser, Claudia; Sun, Yan

2017-01-01

Very recently, the half-metallic compound Co$_3$Sn$_2$S$_2$ was predicted to be a magnetic WSM with Weyl points only 60 meV above the Fermi level ($E_F$). Owing to the low charge carrier density and large Berry curvature induced, Co$_3$Sn$_2$S$_2$ possesses both a large anomalous Hall conductivity (AHC) and a large anomalous Hall angle (AHA), which provide strong evidence for the existence of Weyl points in Co$_3$Sn$_2$S$_2$. In this work, we theoretically studied the surface topological feat...

Uniqueness of solution to a stationary boundary kinetic problem

International Nuclear Information System (INIS)

Zhykharsky, A.V.

1992-01-01

The paper treats the question of uniqueness of solution to the boundary kinetic problem. This analysis is based on the accurate solutions to the stationary one-dimensional boundary kinetic problem for the limited plasma system. In the paper a simplified problem statement is used (no account is taken of the external magnetic field, a simplest form of boundary conditions is accepted) which, however, covers all features of the problem considered. Omitting the details of the conclusion we will write a set of Vlasov stationary kinetic equations for the cases of plane, cylindrical and spherical geometry of the problem. (author) 1 ref

Chiral tunneling in gated inversion symmetric Weyl semimetal

Science.gov (United States)

Bai, Chunxu; Yang, Yanling; Chang, Kai

2016-01-01

Based on the chirality-resolved transfer-matrix method, we evaluate the chiral transport tunneling through Weyl semimetal multi-barrier structures created by periodic gates. It is shown that, in sharp contrast to the cases of three dimensional normal semimetals, the tunneling coefficient as a function of incident angle shows a strong anisotropic behavior. Importantly, the tunneling coefficients display an interesting periodic oscillation as a function of the crystallographic angle of the structures. With the increasement of the barriers, the tunneling current shows a Fabry-Perot type interferences. For superlattice structures, the fancy miniband effect has been revealed. Our results show that the angular dependence of the first bandgap can be reduced into a Lorentz formula. The disorder suppresses the oscillation of the tunneling conductance, but would not affect its average amplitude. This is in sharp contrast to that in multi-barrier conventional semiconductor structures. Moreover, numerical results for the dependence of the angularly averaged conductance on the incident energy and the structure parameters are presented and contrasted with those in two dimensional relativistic materials. Our work suggests that the gated Weyl semimetal opens a possible new route to access to new type nanoelectronic device. PMID:26888491

Topological surface Fermi arcs in the magnetic Weyl semimetal Co3Sn2S2

Science.gov (United States)

Xu, Qiunan; Liu, Enke; Shi, Wujun; Muechler, Lukas; Gayles, Jacob; Felser, Claudia; Sun, Yan

2018-06-01

Very recently, the half-metallic compound Co3Sn2S2 was proposed to be a magnetic Weyl semimetal (WSM) with Weyl points only 60 meV above the Fermi level EF. Owing to the low charge carrier density and large Berry curvature induced, Co3Sn2S2 possesses both a large anomalous Hall conductivity and a large anomalous Hall angle, which provide strong evidence for the existence of Weyl points in Co3Sn2S2 . In this work, we theoretically study the surface topological feature of Co3Sn2S2 and its counterpart Co3Sn2Se2 . By cleaving the sample at the weak Sn-S/Se bonds, one can achieve two different surfaces terminated with Sn and S/Se atoms, respectively. The resulting Fermi-arc-related states can range from the energy of the Weyl points to EF-0.1 eV in the Sn-terminated surface. Therefore, it should be possible to observe the Fermi arcs in angle-resolved photoemission spectroscopy (ARPES) measurements. Furthermore, in order to simulate quasiparticle interference in scanning tunneling microscopy (STM) measurements, we also calculate the joint density of states for both terminals. This work should be helpful for a comprehensive understanding of the topological properties of these two magnetic WSMs and further ARPES and STM measurements.

Stationary drift-Rossby vortices in shear flows

International Nuclear Information System (INIS)

Horihata, Satoshi; Irie, Haruyuki; Sato, Masatomo

1990-01-01

Starting from Hasegawa-Mima equation with the generalized vorticity q which describes both electrostatic drift waves in plasmas and Rossby waves in the atmosphere of rotating planets, the stationary solutions of this equation in the (x, y) plane were considered assuming that the equilibrium density no depends on x and the electron temperature T 0 is constant. The arbitrary function F(φ) yielded from integration of transformed Hasegawa-Mima equation was taken either linear or nonlinear in φ, where φ is the stream function. When F is linear, vortex solutions were obtained by dividing the entire plane into internal and external regions by a closed boundary curve. Imposing the boundary conditions at the boundary curve, the constants in the solutions φ ex and φ in were determined. 4 examples are figured. When F is nonlinear, isolated (localized) vortex was considered. Deriving the equation to determine F, the equation for ψ, the internal vortical motion beyond the boundary was given. 2 examples are shown. (M.T.)

Nonlinear Fokker-Planck Equations Fundamentals and Applications

CERN Document Server

Frank, Till Daniel

2005-01-01

Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, popul...

Asymptotic Value Distribution for Solutions of the Schroedinger Equation

International Nuclear Information System (INIS)

Breimesser, S. V.; Pearson, D. B.

2000-01-01

We consider the Dirichlet Schroedinger operator T=-(d 2 /d x 2 )+V, acting in L 2 (0,∞), where Vis an arbitrary locally integrable potential which gives rise to absolutely continuous spectrum. Without any other restrictive assumptions on the potential V, the description of asymptotics for solutions of the Schroedinger equation is carried out within the context of the theory of value distribution for boundary values of analytic functions. The large x asymptotic behaviour of the solution v(x,λ) of the equation Tf(x,λ)=λf(x,λ), for λ in the support of the absolutely continuous part μ a.c. of the spectral measure μ, is linked to the spectral properties of this measure which are determined by the boundary value of the Weyl-Titchmarsh m-function. Our main result (Theorem 1) shows that the value distribution for v'(N,λ)/v(N,λ) approaches the associated value distribution of the Herglotz function m N (z) in the limit N → ∞, where m N (z) is the Weyl-Titchmarsh m-function for the Schroedinger operator -(d 2 /d x 2 )+Vacting in L 2 (N,∞), with Dirichlet boundary condition at x=N. We will relate the analysis of spectral asymptotics for the absolutely continuous component of Schroedinger operators to geometrical properties of the upper half-plane, viewed as a hyperbolic space

Classical local U(1 gauge invariance in Weyl 2-spinor lenguage and charge quantization from irreducible representations of the gauge group

Directory of Open Access Journals (Sweden)

J. Buitrago

Full Text Available A new classical 2-spinor approach to U(1 gauge theory is presented in which the usual four-potential vector field is replaced by a symmetric second rank spinor. Following a lagrangian formulation, it is shown that the four-rank spinor representing the Maxwell field tensor has a U(1 local gauge invariance in terms of the electric and magnetic field strengths. When applied to the magnetic field of a monopole, this formulation, via the irreducible representation condition for the gauge group, leads to a quantization condition differing by a factor 2 of the one predicted by Dirac without relying on any kind of singular vector potentials. Finally, the U(1 invariant spinor equations, are applied to electron magnetic resonance which has many applications in the study of materials. Keywords: Weyl 2-spinor lenguage, Dirac equation, Gauge theories, Charge quantization

Stationary solutions and self-trapping in discrete quadratic nonlinear systems

DEFF Research Database (Denmark)

Bang, Ole; Christiansen, Peter Leth; Clausen, Carl A. Balslev

1998-01-01

We consider the simplest equations describing coupled quadratic nonlinear (chi((2))) systems, which each consists of a fundamental mode resonantly interacting with its second harmonic. Such discrete equations apply, e.g., to optics, where they can describe arrays of chi((2)) waveguides...... the nonintegrable dimer reduce to the discrete nonlinear Schrodinger (DNLS) equation with two degrees of freedom, which is integrable. We show how the stationary solutions to the two systems correspond to each other and how the self-trapped DNLS solutions gradually develop chaotic dynamics in the chi((2)) system...

Holographic Floquet states I: a strongly coupled Weyl semimetal

International Nuclear Information System (INIS)

Hashimoto, Koji; Kinoshita, Shunichiro; Murata, Keiju; Oka, Takashi

2017-01-01

Floquet states can be realized in quantum systems driven by continuous time-periodic perturbations. It is known that a state known as the Floquet Weyl semimetal can be realized when free Dirac fermions are placed in a rotating electric field. What will happen if strong interaction is introduced to this system? Will the interaction wash out the characteristic features of Weyl semimetals such as the Hall response? Is there a steady state and what is its thermodynamic behavior? We answer these questions using AdS/CFT correspondence in the N=2 supersymmetric massless QCD in a rotating electric field in the large N c limit realizing the first example of a “holographic Floquet state”. In this limit, gluons not only mediate interaction, but also act as an energy reservoir and stabilize the nonequilibrium steady state (NESS). We obtain the electric current induced by a rotating electric field: in the high frequency region, the Ohm’s law is satisfied, while we recover the DC nonlinear conductivity at low frequency, which was obtained holographically in a previous work. The thermodynamic properties of the NESS, e.g., fluctuation-dissipation relation, is characterized by the effective Hawking temperature that is defined from the effective horizon giving a holographic meaning to the “periodic thermodynamic” concept. In addition to the strong (pump) rotating electric field, we apply an additional weak (probe) electric field in the spirit of the pump-probe experiments done in condensed matter experiments. Weak DC and AC probe analysis in the background rotating electric field shows Hall currents as a linear response, therefore the Hall response of Floquet Weyl semimetals survives at the strong coupling limit. We also find frequency mixed response currents, i.e., a heterodyning effect, characteristic to periodically driven Floquet systems.

Holographic Floquet states I: a strongly coupled Weyl semimetal

Energy Technology Data Exchange (ETDEWEB)

Hashimoto, Koji [Department of Physics, Osaka University, Toyonaka, Osaka 560-0043 (Japan); Kinoshita, Shunichiro [Department of Physics, Chuo University, Tokyo 112-8551 (Japan); Murata, Keiju [Keio University, 4-1-1 Hiyoshi, Yokohama 223-8521 (Japan); Oka, Takashi [Max-Planck-Institut für Physik komplexer Systeme (MPI-PKS), Nöthnitzer Straße 38, Dresden 01187 (Germany); Max-Planck-Institut für Chemische Physik fester Stoffe (MPI-CPfS),Nöthnitzer Straße 40, Dresden 01187 (Germany)

2017-05-23

Floquet states can be realized in quantum systems driven by continuous time-periodic perturbations. It is known that a state known as the Floquet Weyl semimetal can be realized when free Dirac fermions are placed in a rotating electric field. What will happen if strong interaction is introduced to this system? Will the interaction wash out the characteristic features of Weyl semimetals such as the Hall response? Is there a steady state and what is its thermodynamic behavior? We answer these questions using AdS/CFT correspondence in the N=2 supersymmetric massless QCD in a rotating electric field in the large N{sub c} limit realizing the first example of a “holographic Floquet state”. In this limit, gluons not only mediate interaction, but also act as an energy reservoir and stabilize the nonequilibrium steady state (NESS). We obtain the electric current induced by a rotating electric field: in the high frequency region, the Ohm’s law is satisfied, while we recover the DC nonlinear conductivity at low frequency, which was obtained holographically in a previous work. The thermodynamic properties of the NESS, e.g., fluctuation-dissipation relation, is characterized by the effective Hawking temperature that is defined from the effective horizon giving a holographic meaning to the “periodic thermodynamic” concept. In addition to the strong (pump) rotating electric field, we apply an additional weak (probe) electric field in the spirit of the pump-probe experiments done in condensed matter experiments. Weak DC and AC probe analysis in the background rotating electric field shows Hall currents as a linear response, therefore the Hall response of Floquet Weyl semimetals survives at the strong coupling limit. We also find frequency mixed response currents, i.e., a heterodyning effect, characteristic to periodically driven Floquet systems.

Holographic Floquet states I: a strongly coupled Weyl semimetal

Science.gov (United States)

Hashimoto, Koji; Kinoshita, Shunichiro; Murata, Keiju; Oka, Takashi

2017-05-01

Floquet states can be realized in quantum systems driven by continuous time-periodic perturbations. It is known that a state known as the Floquet Weyl semimetal can be realized when free Dirac fermions are placed in a rotating electric field. What will happen if strong interaction is introduced to this system? Will the interaction wash out the characteristic features of Weyl semimetals such as the Hall response? Is there a steady state and what is its thermodynamic behavior? We answer these questions using AdS/CFT correspondence in the N = 2 supersymmetric massless QCD in a rotating electric field in the large N c limit realizing the first example of a "holographic Floquet state". In this limit, gluons not only mediate interaction, but also act as an energy reservoir and stabilize the nonequilibrium steady state (NESS). We obtain the electric current induced by a rotating electric field: in the high frequency region, the Ohm's law is satisfied, while we recover the DC nonlinear conductivity at low frequency, which was obtained holographically in a previous work. The thermodynamic properties of the NESS, e.g., fluctuation-dissipation relation, is characterized by the effective Hawking temperature that is defined from the effective horizon giving a holographic meaning to the "periodic thermodynamic" concept. In addition to the strong (pump) rotating electric field, we apply an additional weak (probe) electric field in the spirit of the pump-probe experiments done in condensed matter experiments. Weak DC and AC probe analysis in the background rotating electric field shows Hall currents as a linear response, therefore the Hall response of Floquet Weyl semimetals survives at the strong coupling limit. We also find frequency mixed response currents, i.e., a heterodyning effect, characteristic to periodically driven Floquet systems.

The semi-classical limit of the time dependent Hartree-Fock equation. II. The Wick symbol of the solution

OpenAIRE

Amour, Laurent; Khodja, Mohamed; Nourrigat, Jean

2011-01-01

We study the Wick symbol of a solution of the time dependent Hartree Fock equation, under weaker hypotheses than those needed for the Weyl symbol in the first paper with thesame title. With similar, we prove some kind of Ehrenfest theorem for observables that are not pseudo-differential operators.

Stationary flow near fronts

Directory of Open Access Journals (Sweden)

Reinhold Steinacker

2016-12-01

Full Text Available In 1906, the Austrian scientist Max Margules published a paper on temperature stratification in resting and non-accelerated moving air. The paper derives conditions for stationary slopes of air mass boundaries and was an important forerunner of frontal theories. Its formulation of relations between changes in density and geostrophic wind across the front is basically a discrete version of the thermal wind balance equation. The paper was highly influential and is still being cited to the present day. This paper accompanies an English translation of Margules’ seminal paper. We conclude here our “Classic Papers” series of the Meteorologische Zeitschrift.

Darboux transformations and the symmetric fourth Painleve equation

International Nuclear Information System (INIS)

Sen, A; Hone, A N W; Clarkson, P A

2005-01-01

This paper is concerned with the group symmetries of the fourth Painleve equation P IV , a second-order nonlinear ordinary differential equation. It is well known that the parameter space of P IV admits the action of the extended affine Weyl group A-tilde 2 (1) . As shown by Noumi and Yamada, the action of A-tilde 2 (1) as Baecklund transformations of P IV provides a derivation of its symmetric form SP 4 . The dynamical system SP 4 is also equivalent to the isomonodromic deformation of an associated three-by-three matrix linear system (Lax pair). The action of the generators of A-tilde 2 (1) on this Lax pair is derived using the Darboux transformation for an associated third-order operator

Electronic properties in a quantum well structure of Weyl semimetal

International Nuclear Information System (INIS)

You, Wen-Long; Zhou, Jiao-Jiao; Wang, Xue-Feng; Oleś, Andrzej M.

2016-01-01

We investigate the confined states and transport of three-dimensional Weyl electrons around a one-dimensional external rectangular electrostatic potential. The confined states with finite transverse wave vector exist at energies higher than the half well depth or lower than the half barrier height. The rectangular potential appears completely transparent to the normal incident electrons but not otherwise. The tunneling transmission coefficient is sensitive to their incident angle and shows resonant peaks when their energy coincides with the confined spectra. In addition, for the electrons in the conduction (valence) band through a potential barrier (well), the transmission spectrum has a gap of width increasing with the incident angle. Interestingly, the electron linear zero-temperature conductance over the potential can approach zero when the Fermi energy is aligned to the top and bottom energies of the potential, when only electron beams normal to the potential interfaces can pass through. The considered structure can be used to collimate the Weyl electron beams.

Influence of Stationary Crossflow Modulation on Secondary Instability

Science.gov (United States)

Choudhari, Meelan M.; Li, Fei; Paredes, Pedro

2016-01-01

A likely scenario for swept wing transition on subsonic aircraft with natural laminar flow involves the breakdown of stationary crossflow vortices via high frequency secondary instability. A majority of the prior research on this secondary instability has focused on crossflow vortices with a single dominant spanwise wavelength. This paper investigates the effects of the spanwise modulation of stationary crossflow vortices at a specified wavelength by a subharmonic stationary mode. Secondary instability of the modulated crossflow pattern is studied using planar, partial-differential-equation based eigenvalue analysis. Computations reveal that weak modulation by the first subharmonic of the input stationary mode leads to mode splitting that is particularly obvious for Y-type secondary modes that are driven by the wall-normal shear of the basic state. Thus, for each Y mode corresponding to the fundamental wavelength of results in unmodulated train of crossflow vortices, the modulated flow supports a pair of secondary modes with somewhat different amplification rates. The mode splitting phenomenon suggests that a more complex stationary modulation such as that induced by natural surface roughness would yield a considerably richer spectrum of secondary instability modes. Even modest levels of subharmonic modulation are shown to have a strong effect on the overall amplification of secondary disturbances, particularly the Z-modes driven by the spanwise shear of the basic state. Preliminary computations related to the nonlinear breakdown of these secondary disturbances provide interesting insights into the process of crossflow transition in the presence of the first subharmonic of the dominant stationary vortex.

The Higgs field and the resolution of the Cosmological Constant Paradox in the Weyl-geometrical Universe

Science.gov (United States)

De Martini, Francesco

2017-10-01

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of Weyl's differential geometry: the parallel displacement of vectors in curved space-time. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the SU(2)L⊗U(1)Y as well as on the conformal groups of space-time Weyl's transformations is analysed within the framework of a general-relativistic, conformally covariant scalar-tensor theory that includes the electromagnetic and the Yang-Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An `effective cosmological potential': Veff is expressed in terms of the dark energy potential: via the `mass reduction parameter': , a general property of the Universe. The mass of the Higgs boson, which is considered a `free parameter' by the standard electroweak theory, by our theory is found to be proportional to the mass which accounts for the measured cosmological constant, i.e. the measured content of vacuum-energy in the Universe. The non-integrable application of Weyl's geometry leads to a Proca equation accounting for the dynamics of a φρ-particle, a vector-meson proposed as an an optimum candidate for dark matter. On the basis of previous cosmic microwave background results our theory leads, in the condition of cosmological `critical density', to the assessment of the average energy content of the φρ-excitation. The peculiar mathematical structure of Veff offers a clue towards a very general resolution of a most intriguing puzzle of modern quantum field theory, the `Cosmological Constant Paradox' (here referred to as the `Λ-Paradox'). Indeed, our `universal' theory offers a resolution of the Λ-Paradox for all exponential inflationary potentials: VΛ(T,φ)∝e-nφ, and for all

On a complex differential Riccati equation

International Nuclear Information System (INIS)

Khmelnytskaya, Kira V; Kravchenko, Vladislav V

2008-01-01

We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schroedinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation such as the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical 'one-dimensional' results, we discuss new features of the considered equation including an analogue of the Cauchy integral theorem

Generalized multivariate Fokker-Planck equations derived from kinetic transport theory and linear nonequilibrium thermodynamics

International Nuclear Information System (INIS)

Frank, T.D.

2002-01-01

We study many particle systems in the context of mean field forces, concentration-dependent diffusion coefficients, generalized equilibrium distributions, and quantum statistics. Using kinetic transport theory and linear nonequilibrium thermodynamics we derive for these systems a generalized multivariate Fokker-Planck equation. It is shown that this Fokker-Planck equation describes relaxation processes, has stationary maximum entropy distributions, can have multiple stationary solutions and stationary solutions that differ from Boltzmann distributions

Subroutine MLTGRD: a multigrid algorithm based on multiplicative correction and implicit non-stationary iteration

International Nuclear Information System (INIS)

Barry, J.M.; Pollard, J.P.

1986-11-01

A FORTRAN subroutine MLTGRD is provided to solve efficiently the large systems of linear equations arising from a five-point finite difference discretisation of some elliptic partial differential equations. MLTGRD is a multigrid algorithm which provides multiplicative correction to iterative solution estimates from successively reduced systems of linear equations. It uses the method of implicit non-stationary iteration for all grid levels

Toeplitz quantization and asymptotic expansions : Peter Weyl decomposition

Czech Academy of Sciences Publication Activity Database

Engliš, Miroslav; Upmeier, H.

2010-01-01

Roč. 68, č. 3 (2010), s. 427-449 ISSN 0378-620X R&D Projects: GA ČR GA201/09/0473 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded symmetric domain * real symmetric domain * star product * Toeplitz operator * Peter-Weyl decomposition Subject RIV: BA - General Mathematics Impact factor: 0.521, year: 2010 http://link.springer.com/article/10.1007%2Fs00020-010-1808-5

Weyl-van der Waerden spinor technic for spin-3/2 fermions

International Nuclear Information System (INIS)

Novaes, S.F.; Spehler, D.

1991-09-01

We use the Weyl-van der Waerden spinor technic to construct helicity wave functions for massless and massive spin-3/2 fermions. We apply our formalism to evaluate helicity amplitudes taking into account some phenomenological couplings involving these particles. (author)

From GCM energy kernels to Weyl-Wigner Hamiltonians: a particular mapping

International Nuclear Information System (INIS)

Galetti, D.

1984-01-01

A particular mapping is established which directly connects GCM energy kernels to Weyl-Wigner Hamiltonians, under the assumption of gaussian overlap kernel. As an application of this mapping scheme the collective Hamiltonians for some giant resonances are derived. (Author) [pt

Stationary radiation of objects with scattering media

International Nuclear Information System (INIS)

Vasil'eva, Inna A

2001-01-01

The radiation observed inside or outside a stationary radiator with a scattering medium is a sum of components, each being determined by, first, the primary radiation from some part of the radiator and, second, the probability of this radiation reaching the region where it is observed. In this review, general and rather simple relations between these components are discussed. These relations, unlike the components themselves, are independent of the specific optical characteristics of the object as well as of its geometry, inhomogeneity, etc. In deriving the relations, the situations in which geometrical optics is either applicable or inapplicable to radiation in a scattering medium are considered. For the case where geometrical optics does apply, stationary relations are derived from the probabilistic stationarity condition for radiation passing through the medium, i.e., from the fact that all radiation emitted in a stationary regime disappears with probability unity. Equilibrium relations are derived from the stationary relations in the particular case of a thermal radiator in an isothermal cavity. To derive the stationary relations in the geometrical optics approximation, we obtain general solutions of the linear equation of transfer using the Green function approach. If geometrical optics cannot be applied to a scattering and radiating medium, only relations for the components of outgoing thermal radiation are obtained, and the generalized Kirchhoff law, obtained by Levin and Rytov using statistical radio-physics methods, is employed. In this case, stationary relations are also derived from a probabilistic stationarity condition; the equilibrium relations follow from the stationary ones as well as from the equilibrium condition for radiation in the isothermal cavity. The quantities involved in all the relations obtained are a subject of experimental and computational spectroscopic studies. Examples of current and potential applications are given. The relations

Imaginary Schur-Weyl duality

CERN Document Server

Kleshchev, Alexander

2017-01-01

The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules-one for each real positive root for the corresponding affine root system {\\tt X}_l^{(1)}, as well as irreducible imaginary modules-one for each l-multiplication. The authors study imaginary modules by means of "imaginary Schur-Weyl duality" and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula.

Equations of motion of higher-spin gauge fields as a free differential algebra

International Nuclear Information System (INIS)

Vasil'ev, M.A.

1988-01-01

It is shown that the introduction of auxiliary dynamical variables that generalize the gravitational Weyl tensor permits one to reduce the equations of motion of free massless fields of all spins in the anti-de Sitter O(3,2) space to a form characteristic of free differential algebras. The equations of motion of auxiliary gauge fields introduced previously are modified analogously. Arguments are presented to the effect that the equations of motion of interacting massless fields of all spins should be described in terms of a free differential algebra which is a deformation of a known free differential algebra generated by 1- and 0-forms in the adjoint representation of a nonabelian superalgebra of higher spins and auxiliary fields

From Weyl to Born–Jordan quantization: The Schrödinger representation revisited

Energy Technology Data Exchange (ETDEWEB)

Gosson, Maurice A. de, E-mail: maurice.de.gosson@univie.ac.at

2016-03-30

The ordering problem has been one of the long standing and much discussed questions in quantum mechanics from its very beginning. Nowadays, there is more or less a consensus among physicists that the right prescription is Weyl’s rule, which is closely related to the Moyal–Wigner phase space formalism. We propose in this report an alternative approach by replacing Weyl quantization with the less well-known Born–Jordan quantization. This choice is actually natural if we want the Heisenberg and Schrödinger pictures of quantum mechanics to be mathematically equivalent. It turns out that, in addition, Born–Jordan quantization can be recovered from Feynman’s path integral approach provided that one used short-time propagators arising from correct formulas for the short-time action, as observed by Makri and Miller. These observations lead to a slightly different quantum mechanics, exhibiting some unexpected features, and this without affecting the main existing theory; for instance quantizations of physical Hamiltonian functions are the same as in the Weyl correspondence. The differences are in fact of a more subtle nature; for instance, the quantum observables will not correspond in a one-to-one fashion to classical ones, and the dequantization of a Born–Jordan quantum operator is less straightforward than that of the corresponding Weyl operator. The use of Born–Jordan quantization moreover solves the “angular momentum dilemma”, which already puzzled L. Pauling. Born–Jordan quantization has been known for some time (but not fully exploited) by mathematicians working in time–frequency analysis and signal analysis, but ignored by physicists. One of the aims of this report is to collect and synthesize these sporadic discussions, while analyzing the conceptual differences with Weyl quantization, which is also reviewed in detail. Another striking feature is that the Born–Jordan formalism leads to a redefinition of phase space quantum mechanics, where

Quantum critical matter. Quantum phase transitions with multiple dynamics and Weyl superconductors

International Nuclear Information System (INIS)

Meng, Tobias

2012-01-01

In this PhD thesis, the physics of quantum critical matter and exotic quantum state close to quantum phase transitions is investigated. We will focus on three different examples that highlight some of the interesting phenomena related to quantum phase transitions. Firstly, we discuss the physics of quantum phase transitions in quantum wires as a function of an external gate voltage when new subbands are activated. We find that at these transitions, strong correlations lead to the formation of an impenetrable gas of polarons, and identify criteria for possible instabilities in the spin- and charge sectors of the model. Our analysis is based on the combination of exact resummations, renormalization group techniques and Luttinger liquid approaches. Secondly, we turn to the physics of multiple divergent time scales close to a quantum critical point. Using an appropriately generalized renormalization group approach, we identify that the presence of multiple dynamics at a quantum phase transition can lead to the emergence of new critical scaling exponents and thus to the breakdown of the usual scaling schemes. We calculate the critical behavior of various thermodynamic properties and detail how unusual physics can arise. It is hoped that these results might be helpful for the interpretation of experimental scaling puzzles close to quantum critical points. Thirdly, we turn to the physics of topological transitions, and more precisely the physics of Weyl superconductors. The latter are the superconducting variant of the topologically non-trivial Weyl semimetals, and emerge at the quantum phase transition between a topological superconductor and a normal insulator upon perturbing the transition with a time reversal symmetry breaking perturbation, such as magnetism. We characterize the topological properties of Weyl superconductors and establish a topological phase diagram for a particular realization in heterostructures. We discuss the physics of vortices in Weyl

From Weyl to Born–Jordan quantization: The Schrödinger representation revisited

International Nuclear Information System (INIS)

Gosson, Maurice A. de

2016-01-01

The ordering problem has been one of the long standing and much discussed questions in quantum mechanics from its very beginning. Nowadays, there is more or less a consensus among physicists that the right prescription is Weyl’s rule, which is closely related to the Moyal–Wigner phase space formalism. We propose in this report an alternative approach by replacing Weyl quantization with the less well-known Born–Jordan quantization. This choice is actually natural if we want the Heisenberg and Schrödinger pictures of quantum mechanics to be mathematically equivalent. It turns out that, in addition, Born–Jordan quantization can be recovered from Feynman’s path integral approach provided that one used short-time propagators arising from correct formulas for the short-time action, as observed by Makri and Miller. These observations lead to a slightly different quantum mechanics, exhibiting some unexpected features, and this without affecting the main existing theory; for instance quantizations of physical Hamiltonian functions are the same as in the Weyl correspondence. The differences are in fact of a more subtle nature; for instance, the quantum observables will not correspond in a one-to-one fashion to classical ones, and the dequantization of a Born–Jordan quantum operator is less straightforward than that of the corresponding Weyl operator. The use of Born–Jordan quantization moreover solves the “angular momentum dilemma”, which already puzzled L. Pauling. Born–Jordan quantization has been known for some time (but not fully exploited) by mathematicians working in time–frequency analysis and signal analysis, but ignored by physicists. One of the aims of this report is to collect and synthesize these sporadic discussions, while analyzing the conceptual differences with Weyl quantization, which is also reviewed in detail. Another striking feature is that the Born–Jordan formalism leads to a redefinition of phase space quantum mechanics, where

Existence of stationary solutions in the coronal loop problem

Energy Technology Data Exchange (ETDEWEB)

Hulshof, J; Terman, D; Verhulst, F

1988-01-01

The study of a hot plasma confined to a magnetic loop in the sun's corona leads to a singularly perturbed nonlinear reaction-diffusion equation with rather unusual side conditions. Monotone solutions of the stationary problem appear as fixed points of an iteration map which is contractive if the perturbation parameter is sufficiently small.

Large anomalous magnetic moment in three-dimensional Dirac and Weyl semimetals

NARCIS (Netherlands)

Van Der Wurff, E. C I; Stoof, H. T C

2016-01-01

We investigate the effect of Coulomb interactions on the electromagnetic response of three-dimensional Dirac and Weyl semimetals. In a calculation reminiscent of Schwinger's seminal work on quantum electrodynamics, we find three physically distinct effects for the anomalous magnetic moment of the

Weakly nonparallel and curvature effects on stationary crossflow instability: Comparison of results from multiple-scales analysis and parabolized stability equations

Science.gov (United States)

Singer, Bart A.; Choudhari, Meelan; Li, Fei

1995-01-01

A multiple-scales approach is used to approximate the effects of nonparallelism and streamwise surface curvature on the growth of stationary crossflow vortices in incompressible, three-dimesional boundary layers. The results agree with results predicted by solving the parabolized stability equations in regions where the nonparallelism is sufficiently weak. As the nonparallelism increases, the agreement between the two approaches worsens. An attempt has been made to quantify the nonparallelism on flow stability in terms of a nondimensional number that describes the rate of change of the mean flow relative to the disturbance wavelength. We find that the above nondimensional number provides useful information about the adequacy of the multiple-scales approximation for different disturbances for a given flow geometry, but the number does not collapse data for different flow geometries onto a single curve.

Magneto-optical conductivity of Weyl semimetals with quadratic term in momentum

Directory of Open Access Journals (Sweden)

J. M. Shao

2016-02-01

Full Text Available Weyl semimetal is a three-dimensional Dirac material whose low energy dispersion is linear in momentum. Adding a quadratic (Schrödinger term to the Weyl node breaks the original particle-hole symmetry and also breaks the mirror symmetry between the positive and negative Landau levels in present of magnetic field. This asymmetry splits the absorption line of the longitudinal magneto-optical conductivity into a two peaks structure. It also results in an oscillation pattern in the absorption part of the Hall conductivity. The two split peaks in Reσxx (or the positive and negative oscillation in Imσxy just correspond to the absorptions of left-handed (σ− and right-handed (σ+ polarization light, respectively. The split in Reσxx and the displacement between the absorption of σ+ and σ− are decided by the magnitude of the quadratic term and the magnetic field.

Vortices and polynomials: non-uniqueness of the Adler–Moser polynomials for the Tkachenko equation

International Nuclear Information System (INIS)

Demina, Maria V; Kudryashov, Nikolai A

2012-01-01

Stationary and translating relative equilibria of point vortices in the plane are studied. It is shown that stationary equilibria of any system containing point vortices with arbitrary choice of circulations can be described with the help of the Tkachenko equation. It is also obtained that translating relative equilibria of point vortices with arbitrary circulations can be constructed using a generalization of the Tkachenko equation. Roots of any pair of polynomials solving the Tkachenko equation and the generalized Tkachenko equation are proved to give positions of point vortices in stationary and translating relative equilibria accordingly. These results are valid even if the polynomials in a pair have multiple or common roots. It is obtained that the Adler–Moser polynomial provides non-unique polynomial solutions of the Tkachenko equation. It is shown that the generalized Tkachenko equation possesses polynomial solutions with degrees that are not triangular numbers. (paper)

Smooth vectors and Weyl-Pedersen calculus for representations of nilpotent Lie groups

OpenAIRE

Beltita, Ingrid; Beltita, Daniel

2009-01-01

We present some recent results on smooth vectors for unitary irreducible representations of nilpotent Lie groups. Applications to the Weyl-Pedersen calculus of pseudo-differential operators with symbols on the coadjoint orbits are also discussed.

Studies of Dirac and Weyl fermions by angle resolved photoemission spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Huang, Lunan [Iowa State Univ., Ames, IA (United States)

2016-01-01

This dissertation consists of three parts. First, we study magnetic domains in Nd₂Fe₁₄B single crystals using high resolution magnetic force microscopy (MFM). In addition to the elongated, wavy nano-domains reported by a previous MFM study, we found that the micrometer size, star-shaped fractal pattern is constructed of an elongated network of nano-domains about 20 nm in width, with resolution-limited domain walls thinner than 2 nm. Second, we studied extra Dirac cones of multilayer graphene on SiC surface by ARPES and SPA-LEED. We discovered extra Dirac cones on Fermi surface due to SiC 6 x 6 and graphene 6√ 3 6√ 3 coincidence lattice on both single-layer and three-layer graphene sheets. We interpreted the position and intensity of the Dirac cone replicas, based on the scattering vectors from LEED patterns. We found the positions of replica Dirac cones are determined mostly by the 6 6 SiC superlattice even graphene layers grown thicker. Finally, we studied the electronic structure of MoTe₂ by ARPES and experimentally con rmed the prediction of type II Weyl state in this material. By combining the result of Density Functional Theory calculations and Berry curvature calculations with out experimental data, we identi ed Fermi arcs, track states and Weyl points, all features predicted to exist in a type II Weyl semimetal. This material is an excellent playground for studies of exotic Fermions.

Stationary Magnetohydrodynamic Models of Three-Dimensional Rigidly Rotating Magnetized Coronae

International Nuclear Information System (INIS)

Al-Salti, Nasser; Neukirch, Thomas

2009-01-01

Example solutions of a theory for stationary 3D non-potential solutions of the MHD equations (in the co-rotating frame of reference) are presented. As a first step we present solutions for the mathematically simpler case of a massive central cylinder, but the theory can also be applied to spherical bodies. The fundamental equation of the theory is linear and in the cylindrical case it can be solved using standard methods. Possible application is the structure of coronae of (fast) rotating stars.

A simple stationary semi-analytical wake model

DEFF Research Database (Denmark)

Larsen, Gunner Chr.

We present an idealized simple, but fast, semi-analytical algorithm for computation of stationary wind farm wind fields with a possible potential within a multi-fidelity strategy for wind farm topology optimization. Basically, the model considers wakes as linear perturbations on the ambient non......-linear. With each of these approached, a parabolic system are described, which is initiated by first considering the most upwind located turbines and subsequently successively solved in the downstream direction. Algorithms for the resulting wind farm flow fields are proposed, and it is shown that in the limit......-uniform mean wind field, although the modelling of the individual stationary wake flow fields includes non-linear terms. The simulation of the individual wake contributions are based on an analytical solution of the thin shear layer approximation of the NS equations. The wake flow fields are assumed...

New and old symmetries of the Maxwell and Dirac equations

International Nuclear Information System (INIS)

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

1983-01-01

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

From LHC physics to Dirac-Weyl materials

International Nuclear Information System (INIS)

Raya, Alfredo

2016-01-01

The quantum field theoretical description of particle physics under extreme conditions, namely, at finite temperature, density and in the presence of external magnetic fields, can naturally be extended to describe phenomenology in other branches of physics. In this contribution, I review some aspects of particle physics in the realm of condensed matter physics, particularly graphene and other Dirac-Weyl materials carried out in Mexico. I explore several features of the dynamics of fermions in (2+1)-dimensions which are relevant to heavy ion experiments, but that can be tested in table top experiments. (paper)

Doping and tilting on optics in noncentrosymmetric multi-Weyl semimetals

Science.gov (United States)

Mukherjee, S. P.; Carbotte, J. P.

2018-01-01

We calculate the absorptive part of the ac optical conductivity of a multi-Weyl semimetal with winding number J in both the direction of the tilt σz z(Ω ) and perpendicular to it σx x(Ω ) as a function of photon energy Ω , tilt C, and chemical potential μ (doping). For zero tilt there is a discontinuous rise in the conductivity at twice the value of the chemical potential Ω =2 μ . Below 2 μ , both σx x(Ω ) and σz z(Ω ) are zero and above 2 μ they merge with their value at charge neutrality and display a linear in Ω dependence for J =1 while for J =2 , σx x(Ω ) remains linear but σz z(Ω ) is instead constant. For finite tilt the sharp jump at Ω =2 μ is lost and the onset of absorption starts instead from zero at a lower photon energy Ω =2 μ /(1 +C ) after which it acquires a quasilinear rise to merge with the undoped untilted interband background at Ω =2 μ /(1 -C ) for type I Weyl while for type II the undoped untilted background is never recovered. For noncentrosymmetric materials the energies of a pair of opposite chirality Weyl nodes become shifted by ±Q0 and this leads to two separate absorption edges corresponding to the effective chemical potential of each of the two nodes at 2 (μ +χ Q0) depending on chirality χ =± . We provide analytic expressions for the conductivity in this case which depend only on the ratio Q0/μ and tilt when plotted against Ω /μ . The signature of finite energy shift Q0 is more pronounced for σz z and J =2 than for the other cases.

Aspects of Weyl Supergravity arXiv

CERN Document Server

Ferrara, Sergio; Lust, Dieter

In this paper we study the spectrum of all conformal, ${\\cal N}$-extended supergravities (${\\cal N}=1,2,3,4$) in four space-time dimensions. When these theories are obtained as massless limit of Einstein plus Weyl$^2$supergravity, the appropriate counting of the enhanced gauge symmetries allow us to derive the massless spectrum which consist of a dipole ghost graviton multiplet, a ${\\cal N}$-fold tripole ghost gravitino, the third state belonging to a spin 3/2 multiplet and a residual vector multiplet present for non-maximal ${\\cal N}<4$ theories. These theories are not expected to have a standard gravity holographic dual in five dimensions.

Mathematical analysis of partial differential equations modeling electrostatic MEMS

CERN Document Server

Esposito, Pierpaolo; Guo, Yujin

2010-01-01

Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing "electrostatically actuated" MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems-where the stationary MEMS models fit-are a well-developed

Differential equations inverse and direct problems

CERN Document Server

Favini, Angelo

2006-01-01

DEGENERATE FIRST ORDER IDENTIFICATION PROBLEMS IN BANACH SPACES A NONISOTHERMAL DYNAMICAL GINZBURG-LANDAU MODEL OF SUPERCONDUCTIVITY. EXISTENCE AND UNIQUENESS THEOREMSSOME GLOBAL IN TIME RESULTS FOR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEMSFOURTH ORDER ORDINARY DIFFERENTIAL OPERATORS WITH GENERAL WENTZELL BOUNDARY CONDITIONSTUDY OF ELLIPTIC DIFFERENTIAL EQUATIONS IN UMD SPACESDEGENERATE INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE EXPONENTIAL ATTRACTORS FOR SEMICONDUCTOR EQUATIONSCONVERGENCE TO STATIONARY STATES OF SOLUTIONS TO THE SEMILINEAR EQUATION OF VISCOELASTICITY ASYMPTOTIC BEHA

Magnetic resonance as a local probe for linear bands in the Weyl semimetals NbP and TaP

Energy Technology Data Exchange (ETDEWEB)

Baenitz, Michael; Yasuoka, Hiroshi; Majumder, Mayukh; Shekhar, Chandra; Yan, Binghai; Felser, Claudia; Schmidt, Marcus [MPI for Chemical Physics of Solids, Dresden (Germany)

2016-07-01

Some compensated d-electron semimetals, for example the monophosphites NbP and TaP, with non centrosymmetric structure and with sizable spin orbit coupling (SOC) form a new class of material: the Weyl semimetals (WSM). A unique linear crossing of valence- and conduction- band in a single point in reciprocal space defines the so called Weyl point where the fermion mass vanishes theoretically. In real materials the Fermi level E{sub F} does not exactly match the Weyl node and as a consequence residual very light fermions are found. Due to the SOC these Weyl fermions have a chirality (handedness) on their linear dispersive (E ∝k) bands and frequently a linear density of states (DOS) at the Fermi level E{sub F}. We use NMR as a probe for this linear d- electron bands. The shift provides the s- and d- electron contributions to the DOS at E{sub F}, whereas the spin lattice relaxation is governed by low energy excitations around E{sub F}. {sup 31}P (I = 1/2) - Fourier - transform - and {sup 95}Nb (I = 9/2) - broadline - sweep - NMR studies are performed. We investigated powder samples as well as single crystals on both systems. The angular dependence of the {sup 95}Nb- and {sup 31}P - NMR lines is discussed.

Spacetimes of Weyl and Ricci type N in higher dimensions

Czech Academy of Sciences Publication Activity Database

Kuchynka, M.; Pravdová, Alena

2016-01-01

Roč. 33, č. 11 (2016), s. 115006 ISSN 0264-9381 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : Weyl type N * Ricci type N * higher dimensions Subject RIV: BA - General Mathematics Impact factor: 3.119, year: 2016 http://iopscience.iop.org/article/10.1088/0264-9381/33/11/115006

Determination of Gravitational Counterterms Near Four Dimensions from RG Equations

OpenAIRE

Hamada, Ken-ji

2014-01-01

The finiteness condition of renormalization gives a restriction on the form of the gravitational action. By reconsidering the Hathrell's RG equations for massless QED in curved space, we determine the gravitational counterterms and the conformal anomalies as well near four dimensions. As conjectured for conformal couplings in 1970s, we show that at all orders of the perturbation they can be combined into two forms only: the square of the Weyl tensor in $D$ dimensions and $E_D=G_4 +(D-4)\\chi(D...

Nonlinear scalar field equations. Pt. 1

International Nuclear Information System (INIS)

Berestycki, H.; Lions, P.L.

1983-01-01

This paper as well as a subsequent one is concerned with the existence of nontrivial solutions for some semi-linear elliptic equations in Rsup(N). Such problems are motivated in particular by the search for certain kinds of solitary waves (stationary states) in nonlinear equations of the Klein-Gordon or Schroedinger type. (orig./HSI)

On progress of the solution of the stationary 2-dimensional neutron diffusion equation: a polynomial approximation method with error analysis

International Nuclear Information System (INIS)

Ceolin, C.; Schramm, M.; Bodmann, B.E.J.; Vilhena, M.T.

2015-01-01

Recently the stationary neutron diffusion equation in heterogeneous rectangular geometry was solved by the expansion of the scalar fluxes in polynomials in terms of the spatial variables (x; y), considering the two-group energy model. The focus of the present discussion consists in the study of an error analysis of the aforementioned solution. More specifically we show how the spatial subdomain segmentation is related to the degree of the polynomial and the Lipschitz constant. This relation allows to solve the 2-D neutron diffusion problem for second degree polynomials in each subdomain. This solution is exact at the knots where the Lipschitz cone is centered. Moreover, the solution has an analytical representation in each subdomain with supremum and infimum functions that shows the convergence of the solution. We illustrate the analysis with a selection of numerical case studies. (author)

On progress of the solution of the stationary 2-dimensional neutron diffusion equation: a polynomial approximation method with error analysis

Energy Technology Data Exchange (ETDEWEB)

Ceolin, C., E-mail: celina.ceolin@gmail.com [Universidade Federal de Santa Maria (UFSM), Frederico Westphalen, RS (Brazil). Centro de Educacao Superior Norte; Schramm, M.; Bodmann, B.E.J.; Vilhena, M.T., E-mail: celina.ceolin@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica

2015-07-01

Recently the stationary neutron diffusion equation in heterogeneous rectangular geometry was solved by the expansion of the scalar fluxes in polynomials in terms of the spatial variables (x; y), considering the two-group energy model. The focus of the present discussion consists in the study of an error analysis of the aforementioned solution. More specifically we show how the spatial subdomain segmentation is related to the degree of the polynomial and the Lipschitz constant. This relation allows to solve the 2-D neutron diffusion problem for second degree polynomials in each subdomain. This solution is exact at the knots where the Lipschitz cone is centered. Moreover, the solution has an analytical representation in each subdomain with supremum and infimum functions that shows the convergence of the solution. We illustrate the analysis with a selection of numerical case studies. (author)

Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models

International Nuclear Information System (INIS)

Steinacker, Harold

2009-01-01

The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.

Stationary spiral flow in polytropic stellar models

Science.gov (United States)

Pekeris, C. L.

1980-01-01

It is shown that, in addition to the static Emden solution, a self-gravitating polytropic gas has a dynamic option in which there is stationary flow along spiral trajectories wound around the surfaces of concentric tori. The motion is obtained as a solution of a partial differential equation which is satisfied by the meridional stream function, coupled with Poisson's equation and a Bernoulli-type equation for the pressure (density). The pressure is affected by the whole of the Bernoulli term rather than by the centrifugal part only, which acts for a rotating model, and it may be reduced down to zero at the center. The spiral type of flow is illustrated for an incompressible fluid (n = 0), for which an exact solution is obtained. The features of the dynamic constant-density model are discussed as a basis for future comparison with the solution for compressible models. PMID:16592825

The holographic Weyl semi-metal

Directory of Open Access Journals (Sweden)

Karl Landsteiner

2016-02-01

Full Text Available We present a holographic model of a Weyl semi-metal. We show the evidences that upon varying a mass parameter the model undergoes a sharp crossover at small temperature from a topologically non-trivial state to a trivial one. The order parameter is the anomalous Hall effect (AHE and we find that it is very strongly suppressed above a critical value of the mass parameter. This can be taken as a hint for an underlying topological quantum phase transition. We give an interpretation of the results in terms of a holographic RG flow and compare to a weakly coupled field theoretical model. Since there are no fermionic quasiparticle excitations in the strongly coupled holographic model the presence of an anomalous Hall effect cannot be bound to notions of topology in momentum spaces.

The holographic Weyl semi-metal

Energy Technology Data Exchange (ETDEWEB)

Landsteiner, Karl, E-mail: karl.landsteiner@csic.es; Liu, Yan, E-mail: yan.liu@csic.es

2016-02-10

We present a holographic model of a Weyl semi-metal. We show the evidences that upon varying a mass parameter the model undergoes a sharp crossover at small temperature from a topologically non-trivial state to a trivial one. The order parameter is the anomalous Hall effect (AHE) and we find that it is very strongly suppressed above a critical value of the mass parameter. This can be taken as a hint for an underlying topological quantum phase transition. We give an interpretation of the results in terms of a holographic RG flow and compare to a weakly coupled field theoretical model. Since there are no fermionic quasiparticle excitations in the strongly coupled holographic model the presence of an anomalous Hall effect cannot be bound to notions of topology in momentum spaces.

Structural Equation Modeling of Multivariate Time Series

Science.gov (United States)

du Toit, Stephen H. C.; Browne, Michael W.

2007-01-01

The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be…

A conformal gauge invariant functional for Weyl structures and the first variation formula

OpenAIRE

Ichiyama, Toshiyuki; Furuhata, Hitoshi; Urakawa, Hajime

1999-01-01

We consider a new conformal gauge invariant functional which is a natural curvature functional on the space of Weyl structures. We derive the first variation formula of its functional and characterize its critical points.

The Cauchy problem for the Bogolyubov hierarchy of equations. The BCS model

International Nuclear Information System (INIS)

Vidybida, A.K.

1975-01-01

A chain of Bogolyubov's kinetic equations for an infinite quantum system of particles distributed in space with the mean density 1/V and interacting with the BCS model operator is considered as a single abstract equation in some countable normalized space bsup(v) of sequences of integral operators. In this case an unique solution of the Cauchy problem has been obtained at arbitrary initial conditions from bsup(v), stationary solutions of the equation have been derived, and the class of the initial conditions which approach to stationary ones is indicated

A one-to-one correspondence between the static Einstein-Maxwell and stationary Einstein-vacuum space-times

International Nuclear Information System (INIS)

Chandrasekhar, Subrahmanyan

1989-01-01

A one-to-one correspondence is established between the static solutions of the Einstein-Maxwell equations and the stationary solutions of the Einstein-vacuum equations, that enables one to directly write down a solution for the one from a known solution of the other, and conversely, by a simple transcription. The directness of the correspondence is achieved by writing the metric for static Einstein-Maxwell space-times in a coordinate system and a gauge adapted to the two-centre problem and the metric for stationary Einstein-vacuum space-times in a coordinate system and a gauge adapted to black holes with event horizons. (author)

Semiclassical Weyl Formula for a Class of Weakly Regular Elliptic Operators

Energy Technology Data Exchange (ETDEWEB)

Zielinski, Lech [Universite du Littoral, LMPA, Centre Mi-Voix (France)], E-mail: Lech.Zielinski@lmpa.univ-littoral.fr

2006-02-15

We investigate the semiclassical Weyl formula describing the asymptotic behaviour of the counting function for the number of eigenvalues in the case of self-adjoint elliptic differential operators satisfying weak regularity hypotheses. We consider symbols with possible critical points and with coefficients which have Hoelder continuous derivatives of first order.

Semiclassical Weyl Formula for a Class of Weakly Regular Elliptic Operators

International Nuclear Information System (INIS)

Zielinski, Lech

2006-01-01

We investigate the semiclassical Weyl formula describing the asymptotic behaviour of the counting function for the number of eigenvalues in the case of self-adjoint elliptic differential operators satisfying weak regularity hypotheses. We consider symbols with possible critical points and with coefficients which have Hoelder continuous derivatives of first order

On new and old symmetries of Maxwell and Dirac equations

International Nuclear Information System (INIS)

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

1983-01-01

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

From quantum stochastic differential equations to Gisin-Percival state diffusion

Science.gov (United States)

Parthasarathy, K. R.; Usha Devi, A. R.

2017-08-01

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy [Commun. Math. Phys. 93, 301 (1984)] and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space Γ (L2(R+ ) ⊗(Cn⊕Cn ) ) and the Hilbert space L2(μ ) , where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B (t ) ,t ≥0 } , we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation [N. Gisin and J. Percival, J. Phys. A 167, 315 (1992)]. This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

The Higgs field and the resolution of the Cosmological Constant Paradox in the Weyl-geometrical Universe.

Science.gov (United States)

De Martini, Francesco

2017-11-13

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of Weyl's differential geometry: the parallel displacement of vectors in curved space-time. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the SU (2) L ⊗ U (1) Y as well as on the conformal groups of space-time Weyl's transformations is analysed within the framework of a general-relativistic, conformally covariant scalar-tensor theory that includes the electromagnetic and the Yang-Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An 'effective cosmological potential': V eff is expressed in terms of the dark energy potential: [Formula: see text] via the 'mass reduction parameter': [Formula: see text], a general property of the Universe. The mass of the Higgs boson, which is considered a 'free parameter' by the standard electroweak theory, by our theory is found to be proportional to the mass [Formula: see text] which accounts for the measured cosmological constant, i.e. the measured content of vacuum-energy in the Universe. The non-integrable application of Weyl's geometry leads to a Proca equation accounting for the dynamics of a ϕ ρ -particle, a vector-meson proposed as an an optimum candidate for dark matter. On the basis of previous cosmic microwave background results our theory leads, in the condition of cosmological 'critical density', to the assessment of the average energy content of the ϕ ρ -excitation. The peculiar mathematical structure of V eff offers a clue towards a very general resolution of a most intriguing puzzle of modern quantum field theory, the 'Cosmological Constant Paradox' (here referred to as the ' Λ -Paradox'). Indeed, our 'universal' theory offers a resolution of the Λ -Paradox

Extended Weyl-Heisenberg algebra and Rubakov-Spiridonov superalgebra: Anyonic realizations

International Nuclear Information System (INIS)

Daoud, M.; Douari, J.

2001-09-01

We give the realizations of the extended Weyl-Heisenberg (WH) algebra and the Rubakov-Spiridonov (RS) superalgebra in terms of anyons, characterized by the statistical parameter ν is an element of [0,1], on two-dimensional lattice. The construction uses anyons defined from usual fermionic oscillators (Lerda-Sciuto construction). The anyonic realization of the superalgebra sl(1/1) is also presented. (author)

Optimized waveform relaxation domain decomposition method for discrete finite volume non stationary convection diffusion equation

International Nuclear Information System (INIS)

Berthe, P.M.

2013-01-01

In the context of nuclear waste repositories, we consider the numerical discretization of the non stationary convection diffusion equation. Discontinuous physical parameters and heterogeneous space and time scales lead us to use different space and time discretizations in different parts of the domain. In this work, we choose the discrete duality finite volume (DDFV) scheme and the discontinuous Galerkin scheme in time, coupled by an optimized Schwarz waveform relaxation (OSWR) domain decomposition method, because this allows the use of non-conforming space-time meshes. The main difficulty lies in finding an upwind discretization of the convective flux which remains local to a sub-domain and such that the multi domain scheme is equivalent to the mono domain one. These difficulties are first dealt with in the one-dimensional context, where different discretizations are studied. The chosen scheme introduces a hybrid unknown on the cell interfaces. The idea of up winding with respect to this hybrid unknown is extended to the DDFV scheme in the two-dimensional setting. The well-posedness of the scheme and of an equivalent multi domain scheme is shown. The latter is solved by an OSWR algorithm, the convergence of which is proved. The optimized parameters in the Robin transmission conditions are obtained by studying the continuous or discrete convergence rates. Several test-cases, one of which inspired by nuclear waste repositories, illustrate these results. (author) [fr

Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

Science.gov (United States)

Martirosyan, A; Saakian, David B

2011-08-01

We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

Equation for disentangling time-ordered exponentials with arbitrary quadratic generators

International Nuclear Information System (INIS)

Budanov, V.G.

1987-01-01

In many quantum-mechanical constructions, it is necessary to disentangle an operator-valued time-ordered exponential with time-dependent generators quadratic in the creation and annihilation operators. By disentangling, one understands the finding of the matrix elements of the time-ordered exponential or, in a more general formulation. The solution of the problem can also be reduced to calculation of a matrix time-ordered exponential that solves the corresponding classical problem. However, in either case the evolution equations in their usual form do not enable one to take into account explicitly the symmetry of the system. In this paper the methods of Weyl analysis are used to find an ordinary differential equation on a matrix Lie algebra that is invariant with respect to the adjoint action of the dynamical symmetry group of a quadratic Hamiltonian and replaces the operator evolution equation for the Green's function

Dirac and Weyl fermion dynamics on two-dimensional surface

International Nuclear Information System (INIS)

Kavalov, A.R.; Sedrakyan, A.G.; Kostov, I.K.

1986-01-01

Fermions on 2-dimensional surface, embedded into a 3-dimensional space are investigated. The determinant of induced Dirac operator for the Dirac and Weyl fermions is calculated. The reparametrization-invariant effective action is determined by conformal anomaly (giving Liouville action) and also by Lorentz anomaly leading to Wess-Zumino term, the structure of which at d=3 is determined by the Hopf topological invariant of the S 3 → S 2 map

Inhomogeneous Weyl and Dirac Semimetals: Transport in Axial Magnetic Fields and Fermi Arc Surface States from Pseudo-Landau Levels

Science.gov (United States)

Grushin, Adolfo G.; Venderbos, Jörn W. F.; Vishwanath, Ashvin; Ilan, Roni

2016-10-01

Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work, we study the effect of a space-dependent Weyl node separation, which we interpret as an emergent background axial-vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or nonuniform magnetization and can also be engineered in cold atomic systems. Using a semiclassical approach, we show that the resulting axial magnetic field B5 is observable through an enhancement of the conductivity as σ ˜B52 due to an underlying chiral pseudomagnetic effect. We then use two lattice models to analyze the effect of B5 on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau-level structure for different spatial profiles of B5, revealing that (i) the celebrated surface states of Weyl semimetals, the Fermi arcs, can be reinterpreted as n =0 pseudo-Landau levels resulting from a B5 confined to the surface, (ii) as a consequence of position-momentum locking, a bulk B5 creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces, and (iii) there are equilibrium bound currents proportional to B5 that average to zero over the sample, which are the analogs of bound currents in magnetic materials. We conclude by discussing how our findings can be probed experimentally.

Stationary and non-stationary occurrences of miniature end plate potentials are well described as stationary and non-stationary Poisson processes in the mollusc Navanax inermis.

Science.gov (United States)

Cappell, M S; Spray, D C; Bennett, M V

1988-06-28

Protractor muscles in the gastropod mollusc Navanax inermis exhibit typical spontaneous miniature end plate potentials with mean amplitude 1.71 +/- 1.19 (standard deviation) mV. The evoked end plate potential is quantized, with a quantum equal to the miniature end plate potential amplitude. When their rate is stationary, occurrence of miniature end plate potentials is a random, Poisson process. When non-stationary, spontaneous miniature end plate potential occurrence is a non-stationary Poisson process, a Poisson process with the mean frequency changing with time. This extends the random Poisson model for miniature end plate potentials to the frequently observed non-stationary occurrence. Reported deviations from a Poisson process can sometimes be accounted for by the non-stationary Poisson process and more complex models, such as clustered release, are not always needed.

Equations of motion for massive spin 2 field coupled to gravity

International Nuclear Information System (INIS)

Buchbinder, I.L.; Gitman, D.M.; Krykhtin, V.A.; Pershin, V.D.

2000-01-01

We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in α' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory

Equations of motion for massive spin 2 field coupled to gravity

Energy Technology Data Exchange (ETDEWEB)

Buchbinder, I.L. E-mail: ilb@mail.tomsknet.ru; Gitman, D.M. E-mail: gitman@fma.if.usp.br; Krykhtin, V.A. E-mail: krykhtin@phys.dfe.tpu.edu.ru; Pershin, V.D. E-mail: pershin@ic.tsu.ru

2000-09-18

We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in {alpha}' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.

Comparison of stationary and oscillatory dynamics described by differential equations and Boolean maps in transcriptional regulatory circuits

Science.gov (United States)

Ye, Weiming; Li, Pengfei; Huang, Xuhui; Xia, Qinzhi; Mi, Yuanyuan; Chen, Runsheng; Hu, Gang

2010-10-01

Exploring the principle and relationship of gene transcriptional regulations (TR) has been becoming a generally researched issue. So far, two major mathematical methods, ordinary differential equation (ODE) method and Boolean map (BM) method have been widely used for these purposes. It is commonly believed that simplified BMs are reasonable approximations of more realistic ODEs, and both methods may reveal qualitatively the same essential features though the dynamical details of both systems may show some differences. In this Letter we exhaustively enumerated all the 3-gene networks and many autonomous randomly constructed TR networks with more genes by using both the ODE and BM methods. In comparison we found that both methods provide practically identical results in most of cases of steady solutions. However, to our great surprise, most of network structures showing periodic cycles with the BM method possess only stationary states in ODE descriptions. These observations strongly suggest that many periodic oscillations and other complicated oscillatory states revealed by the BM rule may be related to the computational errors of variable and time discretizations and rarely have correspondence in realistic biology transcriptional regulatory circuits.

Why do we live in 3+1 dimensions?

International Nuclear Information System (INIS)

Nielsen, H.B.; Rugh, S.E.

1993-01-01

Noticing that really the fermions of the Standard Model are best thought of a Weyl - rather than Dirac - particles (relative to fundamental scales located at some presumably very high energies) it becomes interesting that the experimental space-time dimension is singled out by the Weyl equation: It is observed that precisely in the experimentally true space-time dimensionality 4=3+1 the number of linearly independent matrices n 2 Weyl dimensionized as the matrices in the Weyl equation equals the dimension d. So just in this dimension (in fact, also in a trivial case d = 1) do the sigma-matrices of the Weyl-equation form a basis. It is also characteristic for this dimension that there is no degeneracy of helicity states of the Weyl spinor for all nonzero momenta. We would like to interpret these features to signal a special 'form stability' of the Weyl equation in the phenomenologically true dimension of space-time. In an attempt of making this stability to occur in an as large as possible basin of allowed modifications we discuss whether it is possible to define what we could possibly mean by 'stability of Natural laws'. (orig.)

On Stationary Navier-Stokes Flows Around a Rotating Obstacle in Two-Dimensions

Science.gov (United States)

Higaki, Mitsuo; Maekawa, Yasunori; Nakahara, Yuu

2018-05-01

We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of the obstacle and the given exterior force are sufficiently small.

A new multiplicity formula for the Weyl modules of type A

International Nuclear Information System (INIS)

Ye Jiachen; Zhou Zhongguo

2003-08-01

A monomial basis and a filtration of subalgebras for the universal enveloping algebra U(g) of a complex simple Lie algebra g l of type A I is given in this note. In particular, a new multiplicity formula for the Weyl module V(λ) of U(g l ) is obtained in this note. (author)

Semi-classical propagation of wavepackets for the phase space Schroedinger equation: interpretation in terms of the Feichtinger algebra

International Nuclear Information System (INIS)

Gosson, Maurice A de

2008-01-01

The nearby orbit method is a powerful tool for constructing semi-classical solutions of Schroedinger's equation when the initial datum is a coherent state. In this paper, we first extend this method to arbitrary squeezed states and thereafter apply our results to the Schroedinger equation in phase space. This adaptation requires the phase-space Weyl calculus developed in previous work of ours. We also study the regularity of the semi-classical solutions from the point of view of the Feichtinger algebra familiar from the theory of modulation spaces

Phase transition with trivial quantum criticality in an anisotropic Weyl semimetal

Science.gov (United States)

Li, Xin; Wang, Jing-Rong; Liu, Guo-Zhu

2018-05-01

When a metal undergoes continuous quantum phase transition, the correlation length diverges at the critical point and the quantum fluctuation of order parameter behaves as a gapless bosonic mode. Generically, the coupling of this boson to fermions induces a variety of unusual quantum critical phenomena, such as non-Fermi liquid behavior and various emergent symmetries. Here, we perform a renormalization group analysis of the semimetal-superconductor quantum criticality in a three-dimensional anisotropic Weyl semimetal. Surprisingly, distinct from previously studied quantum critical systems, the anomalous dimension of anisotropic Weyl fermions flows to zero very quickly with decreasing energy, and the quasiparticle residue takes a nonzero value. These results indicate that the quantum fluctuation of superconducting order parameter is irrelevant at low energies, and a simple mean-field calculation suffices to capture the essential physics of the superconducting transition. We thus obtain a phase transition that exhibits trivial quantum criticality, which is unique comparing to other invariably nontrivial quantum critical systems. Our theoretical prediction can be experimentally verified by measuring the fermion spectral function and specific heat.

The Coleman-Weinberg mechanism in a conformal (Weyl) invariant theory: application to a magnetic monopole

International Nuclear Information System (INIS)

Edery, Ariel; Graham, Noah

2015-01-01

We consider a massless conformally (Weyl) invariant classical action consisting of a magnetic monopole coupled to gravity in an anti-de Sitter background spacetime. We implement quantum corrections and this breaks the conformal (Weyl) symmetry, introduces a length scale via the process of renormalization and leads to the trace anomaly. We calculate the one-loop effective potential and determine from it the vacuum expectation value (VEV). Spontaneous symmetry breaking is radiatively induced a la Coleman-Weinberg and the scalar coupling constant is exchanged for the dimensionful VEV via dimensional transmutation. An important result is that the Ricci scalar of the AdS background spacetimeis determined entirely by the value of the VEV. (paper)

FAST TRACK COMMUNICATION: Weyl law for fat fractals

Science.gov (United States)

Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos

2010-10-01

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.

Characterizing the selectivity of stationary phases and organic modifiers in reversed-phase high-performance liquid chromatographic systems by a general solvation equation using gradient elution.

Science.gov (United States)

Du, C M; Valko, K; Bevan, C; Reynolds, D; Abraham, M H

2000-11-01

Retention data for a set of 69 compounds using rapid gradient elution are obtained on a wide range of reversed-phase stationary phases and organic modifiers. The chromatographic stationary phases studied are Inertsil (IN)-ODS, pentafluorophenyl, fluoro-octyl, n-propylcyano, Polymer (PLRP-S 100), and hexylphenyl. The organic solvent modifiers are 2,2,2-trifluoroethanol (TFE); 1,1,1,3,3,3-hexafluoropropan-2-ol (HFIP); isopropanol; methanol (MeOH); acetonitrile (AcN); tetrahydrofuran; 1,4-dioxane; N,N-dimethylformamide; and mixed solvents of dimethylsulfoxide (DMSO) with AcN and DMSO with MeOH (1:1). A total of 25 chromatographic systems are analyzed using a solvation equation. In general, most of the systems give reasonable statistics. The selectivity of the reversed phase-high-performance liquid chromatographic (HPLC) systems with respect to the solute's dipolarity-polarity, hydrogen-bond acidity, and basicity are reflected in correspondingly large coefficients in the solvation equation. We wanted to find the most orthogonal HPLC systems, showing the highest possible selectivity difference in order to derive molecular descriptors using the gradient retention times of a compound. We selected eight chromatographic systems that have a large range of coefficients of interest (s, a, and b) similar to those found in water-solvent partitions used previously to derive molecular descriptors. The systems selected are IN-ODS phases with AcN, MeOH, TFE, and HFIP as mobile phase, PLRP-S 100 phase with AcN, propylcyano phase with AcN and MeOH, and fluorooctyl phase with TFE. Using the retention data obtained for a compound in the selected chromatographic systems, we can estimate the molecular descriptors with the faster and simpler gradient elution method.

Wigner weight functions and Weyl symbols of non-negative definite linear operators

NARCIS (Netherlands)

Janssen, A.J.E.M.

1989-01-01

In this paper we present several necessary and, for radially symmetric functions, necessary and sufficient conditions for a function of two variables to be a Wigner weight function (Weyl symbol of a non-negative definite linear operator of L2(R)). These necessary conditions are in terms of spread

Equilibrium initial data for moving puncture simulations: the stationary 1 + log slicing

International Nuclear Information System (INIS)

Baumgarte, T W; Matera, K; Etienne, Z B; Liu, Y T; Shapiro, S L; Taniguchi, K; Murchadha, N O

2009-01-01

We discuss a 'stationary 1 + log' slicing condition for the construction of solutions to Einstein's constraint equations. For stationary spacetimes, these initial data give a stationary foliation when evolved with 'moving puncture' gauge conditions that are often used in black hole evolutions. The resulting slicing is time independent and agrees with the slicing generated by being dragged along a timelike Killing vector of the spacetime. When these initial data are evolved with moving puncture gauge conditions, numerical errors arising from coordinate evolution should be minimized. While these properties appear very promising, suggesting that this slicing condition should be an attractive alternative to, for example, maximal slicing, we demonstrate in this paper that solutions can be constructed only for a small class of problems. For binary black hole initial data, in particular, it is often assumed that there exists an approximate helical Killing vector that generates the binary's orbit. We show that 1 + log slices that are stationary with respect to such a helical Killing vector cannot be asymptotically flat, unless the spacetime possesses an additional axial Killing vector.

Stationary Black Holes: Uniqueness and Beyond

Directory of Open Access Journals (Sweden)

Heusler Markus

1998-01-01

Full Text Available The spectrum of known black hole solutions to the stationary Einstein equations has increased in an unexpected way during the last decade. In particular, it has turned out that not all black hole equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black hole space-times ceases to exist in self-gravitating non-linear field theories. This text aims to review some of the recent developments and to discuss them in the light of the uniqueness theorem for the Einstein-Maxwell system.

Stationary Black Holes: Uniqueness and Beyond

Directory of Open Access Journals (Sweden)

Piotr T. Chruściel

2012-05-01

Full Text Available The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.

Stable Weyl points, trivial surface states, and particle-hole compensation in WP2

Science.gov (United States)

Razzoli, E.; Zwartsenberg, B.; Michiardi, M.; Boschini, F.; Day, R. P.; Elfimov, I. S.; Denlinger, J. D.; Süss, V.; Felser, C.; Damascelli, A.

2018-05-01

A possible connection between extremely large magnetoresistance and the presence of Weyl points has garnered much attention in the study of topological semimetals. Exploration of these concepts in transition-metal diphosphides WP2 has been complicated by conflicting experimental reports. Here we combine angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations to disentangle surface and bulk contributions to the ARPES intensity, the superposition of which has plagued the determination of the band structure in WP2. Our results show that while the hole- and electronlike Fermi surface sheets originating from surface states have different areas, the bulk-band structure of WP2 is electron-hole compensated in agreement with DFT. Furthermore, the ARPES band structure is compatible with the presence of at least four temperature-independent Weyl points, confirming the topological nature of WP2 and its stability against lattice distortions.

Concentration and limit behaviors of stationary measures

Science.gov (United States)

Huang, Wen; Ji, Min; Liu, Zhenxin; Yi, Yingfei

2018-04-01

In this paper, we study limit behaviors of stationary measures of the Fokker-Planck equations associated with a system of ordinary differential equations perturbed by a class of multiplicative noise including additive white noise case. As the noises are vanishing, various results on the invariance and concentration of the limit measures are obtained. In particular, we show that if the noise perturbed systems admit a uniform Lyapunov function, then the stationary measures form a relatively sequentially compact set whose weak∗-limits are invariant measures of the unperturbed system concentrated on its global attractor. In the case that the global attractor contains a strong local attractor, we further show that there exists a family of admissible multiplicative noises with respect to which all limit measures are actually concentrated on the local attractor; and on the contrary, in the presence of a strong local repeller in the global attractor, there exists a family of admissible multiplicative noises with respect to which no limit measure can be concentrated on the local repeller. Moreover, we show that if there is a strongly repelling equilibrium in the global attractor, then limit measures with respect to typical families of multiplicative noises are always concentrated away from the equilibrium. As applications of these results, an example of stochastic Hopf bifurcation and an example with non-decomposable ω-limit sets are provided. Our study is closely related to the problem of noise stability of compact invariant sets and invariant measures of the unperturbed system.

Ionic diffusion through confined geometries: from Langevin equations to partial differential equations

International Nuclear Information System (INIS)

Nadler, Boaz; Schuss, Zeev; Singer, Amit; Eisenberg, R S

2004-01-01

Ionic diffusion through and near small domains is of considerable importance in molecular biophysics in applications such as permeation through protein channels and diffusion near the charged active sites of macromolecules. The motion of the ions in these settings depends on the specific nanoscale geometry and charge distribution in and near the domain, so standard continuum type approaches have obvious limitations. The standard machinery of equilibrium statistical mechanics includes microscopic details, but is also not applicable, because these systems are usually not in equilibrium due to concentration gradients and to the presence of an external applied potential, which drive a non-vanishing stationary current through the system. We present a stochastic molecular model for the diffusive motion of interacting particles in an external field of force and a derivation of effective partial differential equations and their boundary conditions that describe the stationary non-equilibrium system. The interactions can include electrostatic, Lennard-Jones and other pairwise forces. The analysis yields a new type of Poisson-Nernst-Planck equations, that involves conditional and unconditional charge densities and potentials. The conditional charge densities are the non-equilibrium analogues of the well studied pair correlation functions of equilibrium statistical physics. Our proposed theory is an extension of equilibrium statistical mechanics of simple fluids to stationary non-equilibrium problems. The proposed system of equations differs from the standard Poisson-Nernst-Planck system in two important aspects. First, the force term depends on conditional densities and thus on the finite size of ions, and second, it contains the dielectric boundary force on a discrete ion near dielectric interfaces. Recently, various authors have shown that both of these terms are important for diffusion through confined geometries in the context of ion channels

Stationary Response of Lotka—Volterra System with Real Noises

International Nuclear Information System (INIS)

Qi Lu-Yuan; Xu Wei; Gao Wei-Ting

2013-01-01

A stochastic version of Lotka—Volterra model subjected to real noises is proposed and investigated. The approximate stationary probability densities for both predator and prey are obtained analytically. The original system is firstly transformed to a pair of Itô stochastic differential equations. The Itô formula is then carried out to obtain the Itô stochastic differential equation for the period orbit function. The orbit function is considered as slowly varying process under reasonable assumptions. By applying the stochastic averaging method to the orbit function in one period, the averaged Itô stochastic differential equation of the motion orbit and the corresponding Fokker—Planck equation are derived. The probability density functions of the two species are thus formulated. Finally, a classical real noise model is given as an example to show the proposed approximate method. The accuracy of the proposed procedure is verified by Monte Carlo simulation. (interdisciplinary physics and related areas of science and technology)

Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions

OpenAIRE

Wang, Qi; Xu, Yuanfeng; Lou, Rui; Liu, Zhonghao; Li, Man; Huang, Yaobo; Shen, Dawei; Weng, Hongming; Wang, Shancai; Lei, Hechang

2017-01-01

The origin of anomalous Hall effect (AHE) in magnetic materials is one of the most intriguing aspect in condensed matter physics and has been controversial for a long time. Recent studies indicate that the intrinsic AHE is closely related to the Berry curvature of occupied electronic states. In a magnetic Weyl semimetal with broken time-reversal symmetry, there are significant contributions on Berry curvature around Weyl nodes, which would lead to a large intrinsic AHE. Here, we report the la...

Discrete symmetries in the Weyl expansion for quantum billiards

International Nuclear Information System (INIS)

Pavloff, N.

1994-01-01

2 and 3 dimensional quantum billiards with discrete symmetries are considered. The boundary condition is either Dirichlet or Neumann. The first terms of the Weyl expansion are derived for the level density projected onto the irreducible representations of the symmetry group. The formulae require only the knowledge of the character table of the group and the geometrical properties (such as surface, perimeter etc.) of sub-parts of the billiard invariant under a group transformation. (author). 17 refs., 1 fig., 1 tab

Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities

DEFF Research Database (Denmark)

Khare, A.; Rasmussen, Kim Ø; Salerno, M.

2006-01-01

-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.......A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz...

Fitting ARMA Time Series by Structural Equation Models.

Science.gov (United States)

van Buuren, Stef

1997-01-01

This paper outlines how the stationary ARMA (p,q) model (G. Box and G. Jenkins, 1976) can be specified as a structural equation model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. The method is applied to three problem types. (SLD)

Generation of an intense stationary wave in modulated beam-plasma systems

International Nuclear Information System (INIS)

Jungwirth, K.; Krlin, L.

1974-03-01

Basic equations and numerical results describing nonlinear interaction of a weakly modulated electron beam with a single stationary one-dimensional wave excited in a cold plasma without the magnetic field, are presented and discussed. The effect of all possible irreversible processes (e.g., plasma turbulence) accompanying this interaction is simulated by the constant effective collision frequency νsub(eff) of plasma electrons. Starting from the nonlinear Poisson equation, the expression for the amplitude and the phase of the beam-excited wave are derived and solved numerically together with the equations of the beam electron motion. The results are compared with those of a time model. Significant, experimentally detectable differences are established. (author)

Basic properties of a stationary accretion disk surrounding a black hole

International Nuclear Information System (INIS)

Hoshi, Reiun

1977-01-01

The structure of a stationary accretion disk surrounding a black hole is studied by means of newly developed basic equations. The basic equations are derived under the assumption that the vertical distribution of disk matter is given by a polytrope. For a Keplerian accretion disk, basic equations reduce to a differential equation of the first order. We have found that solutions of an optically thick accretion disk converge to a limiting value, irrespective of the outer boundary condition. This gives the happy consequence that the inner structure of an optically thick accretion disk is determined irrespective of the outer boundary condition. On the contrary, an optically thin accretion disk shows bimodal behavior, that is, two physically distinct states exist depending on the outer boundary condition imposed at the outer edge of the accretion disk. (auth.)

An analytical solution for stationary distribution of photon density in traveling-wave and reflective SOAs

International Nuclear Information System (INIS)

Totović, A R; Crnjanski, J V; Krstić, M M; Gvozdić, D M

2014-01-01

In this paper, we analyze two semiconductor optical amplifier (SOA) structures, traveling-wave and reflective, with the active region made of the bulk material. The model is based on the stationary traveling-wave equations for forward and backward propagating photon densities of the signal and the amplified spontaneous emission, along with the stationary carrier rate equation. We start by introducing linear approximation of the carrier density spatial distribution, which enables us to find solutions for the photon densities in a closed analytical form. An analytical approach ensures a low computational resource occupation and an easy analysis of the parameters influencing the SOA’s response. The comparison of the analytical and numerical results shows high agreement for a wide range of the input optical powers and bias currents. (paper)

Weyl geometry and the nonlinear mechanics of distributed point defects

KAUST Repository

Yavari, A.

2012-09-05

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects-where the body is stress-free-is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan\\'s moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby\\'s celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid. © 2012 The Royal Society.

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

International Nuclear Information System (INIS)

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

1995-01-01

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

On the quantum-mechanical Fokker-Planck and Kramers-Chandrasekhar equation

International Nuclear Information System (INIS)

Balazs, N.L.

1978-01-01

In the classical theory of Brownian motion the Langevin equation can be considered as an infinitesimal transformation between the coordinates and momenta of a Brownian particle, given probabilistically, since the impulse appearing is characterized by a Gaussian random process. This probabilistic infinitesimal transformation generates a streaming on the distribution function, expressed by the classical Fokker-Planck and Kramers-Chandrasekhar equations. If the laws obeyed by the Brownian particle are quantum mechanical, the Langevin equation can be reinterpreted as an operator relation expressing an infinitesimal transformation of these operators. Since the impulses are independent of the coordinates and momenta one can think of them as c numbers described by a Gaussian random process. The so resulting infinitesimal operator transformation induces a streaming on the density matrix. One may associate, according to Weyl, functions with operators. The function associated with the density matrix is the Wigner function. Expressing, then, these operator relations in terms of these functions the streaming can be expressed as a continuity equation of the Wigner function. It is found that in this parametrization the extra terms which appear are the same as in the classical theory, augmenting the usual Wigner equation. (Auth.)

The matrix nonlinear Schrodinger equation in dimension 2

DEFF Research Database (Denmark)

Zuhan, L; Pedersen, Michael

2001-01-01

In this paper we study the existence of global solutions to the Cauchy problem for the matrix nonlinear Schrodinger equation (MNLS) in 2 space dimensions. A sharp condition for the global existence is obtained for this equation. This condition is in terms of an exact stationary solution...... of a semilinear elliptic equation. In the scalar case, the MNLS reduces to the well-known cubic nonlinear Schrodinger equation for which existence of solutions has been studied by many authors. (C) 2001 Academic Press....

On the Affine Weyl group of type A˜n−1

Directory of Open Access Journals (Sweden)

Muhammad A. Albar

1987-01-01

Full Text Available We study in this paper the affine Weyl group of type A˜n−1, [1]. Coxeter [1] showed that this group is infinite. We see in Bourbaki [2] that A˜n−1 is a split extension of Sn, the symmetric group of degree n, by a group of translations and of lattice of weights. A˜n−1 is one of the crystallographic Coxeter groups considered by Maxwell [3], [4].

On Optimal Feedback Control for Stationary Linear Systems

International Nuclear Information System (INIS)

Russell, David L.

2010-01-01

We study linear-quadratic optimal control problems for finite dimensional stationary linear systems AX+BU=Z with output Y=CX+DU from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.

Spinning Kerr black holes with stationary massive scalar clouds: the large-coupling regime

Energy Technology Data Exchange (ETDEWEB)

Hod, Shahar [Marine sciences, The Ruppin Academic Center,Ruppin, Emeq Hefer 40250 (Israel); Biotechnology, The Hadassah Academic College,37 Hanevi’im St., Jerusalem 9101001 (Israel)

2017-01-09

We study analytically the Klein-Gordon wave equation for stationary massive scalar fields linearly coupled to spinning Kerr black holes. In particular, using the WKB approximation, we derive a compact formula for the discrete spectrum of scalar field masses which characterize the stationary composed Kerr-black-hole-massive-scalar-field configurations in the large-coupling regime Mμ≫1 (here M and μ are respectively the mass of the central black hole and the proper mass of the scalar field). We confirm our analytically derived formula for the Kerr-scalar-field mass spectrum with numerical data that recently appeared in the literature.

Shot noise and electronic properties in the inversion-symmetric Weyl semimetal resonant structure

Science.gov (United States)

Yang, Yanling; Bai, Chunxu; Xu, Xiaoguang; Jiang, Yong

2018-02-01

Using the transfer matrix method, the authors combine the analytical formula with numerical calculation to explore the shot noise and conductance of massless Weyl fermions in the Weyl semimetal resonant junction. By varying the barrier strength, the structure of the junction, the Fermi energy, and the crystallographic angle, the shot noise and conductance can be tuned efficiently. For a quasiperiodic superlattice, in complete contrast to the conventional junction case, the effect of the disorder strength on the shot noise and conductance depends on the competition of classical tunneling and Klein tunneling. Moreover, the delta barrier structure is also vital in determining the shot noise and conductance. In particular, a universal Fano factor has been found in a single delta potential case, whereas the resonant structure of the Fano factor perfectly matches with the number of barriers in a delta potential superlattice. These results are crucial for engineering nanoelectronic devices based on this topological semimetal material.

Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks

International Nuclear Information System (INIS)

Hasan, M Zahid; Xu, Su-Yang; Bian, Guang

2015-01-01

Unlike string theory, topological physics in lower dimensional condensed matter systems is an experimental reality since the bulk-boundary correspondence can be probed experimentally in lower dimensions. In addition, recent experimental discoveries of non-quantum-Hall-like topological insulators, topological superconductors, Weyl semimetals and other topological states of matter also signal a clear departure from the quantum-Hall-effect-like transport paradigm that has dominated the field since the 1980s. It is these new forms of matter that enabled realizations of topological-Dirac, Weyl cones, helical-Cooper-pairs, Fermi-arc-quasiparticles and other emergent phenomena in fine-tuned photoemission (ARPES) experiments since ARPES experiments directly allow the study of bulk-boundary (topological) correspondence. In this proceeding we provide a brief overview of the key experiments and discuss our perspectives regarding the new research frontiers enabled by these experiments. Taken collectively, we argue in favor of the emergence of ‘topological-condensed-matter-physics’ in laboratory experiments for which a variety of theoretical concepts over the last 80 years paved the way. (review)

Competition between the inter-valley scattering and the intra-valley scattering on magnetoconductivity induced by screened Coulomb disorder in Weyl semimetals

Directory of Open Access Journals (Sweden)

Xuan-Ting Ji

2017-10-01

Full Text Available Recent experiments on Weyl semimetals reveal that charged impurities may play an important role. We use a screened Coulomb disorder to model the charged impurities, and study the magneto-transport in a two-node Weyl semimetal. It is found that when the external magnetic field is applied parallel to the electric field, the calculated longitudinal magnetoconductivity shows positive in the magnetic field, which is just the negative longitudinal magnetoresistivity (LMR observed in experiments. When the two fields are perpendicular to each other, the transverse magnetoconductivities are measured. It is found that the longitudinal (transverse magnetoconductivity is suppressed (enhanced sensitively with increasing the screening length. This feature makes it hardly to observe the negative LMR in Weyl semimetals experimentally owing to a small screening length. Our findings gain insight into further understanding on recently actively debated magneto-transport behaviors in Weyl semimetals. Furthermore we studied the relative weight of the inter-valley scattering and the intra-valley scattering. It shows that the former is as important as the latter and even dominates in the case of strong magnetic fields and small screening length. We emphasize that the discussions on inter-valley scattering is out of the realm of one-node model which has been studied.

Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods

International Nuclear Information System (INIS)

Ernst, Frederick J

2007-01-01

Shortly after Einstein published his general theory of relativity, the spherically symmetric solution of the vacuum field equations was discovered by Karl Schwarzschild, while Hermann Weyl showed that from any axisymmetric solution ψ of the Laplace equation ∇ 2 ψ = 0 (satisfying appropriate boundary conditions) the metric tensor of a static axisymmetric vacuum spacetime can be constructed. In particular, the Schwarzschild solution corresponds to a rather trivial solution of Laplace's equation expressed in terms of prolate spheroidal coordinates. It took about 45 years before Roy Kerr discovered what he called the 'rotating Schwarzschild solution', and an additional five years before I established that from any complex axisymmetric solution E of the nonlinear equation E∇ 2 E = ∇E·∇E (satisfying appropriate boundary conditions) the metric tensor of a stationary axisymmetric vacuum spacetime can be constructed. In particular, the Kerr solution corresponds to an extremely simple solution of this equation expressed in terms of prolate spheroidal coordinates. Ever more complicated solutions of this equation (using prolate spheroidal coordinates) were discovered by Tomimatsu and Sato, but for none of the associated spacetimes has a reasonable material source been suggested. What the present book describes are some of the heroic efforts that have been undertaken to construct physically significant spacetimes by solving the vacuum Ernst equation. Unfortunately, thus far, no one has made much progress extending the Ernst equation approach to facilitate the investigation of spacetime within a stationary axisymmetric material source, where, for example, the stress-energy tensor is that of a perfect fluid. However, in 1994, Meinel and Neugebauer had the novel idea of focusing attention upon global solutions such as the spacetime geometry associated with a rotating infinitely thin disk of dust, where the material source can be represented by discontinuities in the

Generalized boundary conditions in an existence and uniqueness proof for the solution of the non-stationary electron Boltzmann equation by means of operator-semigroups

International Nuclear Information System (INIS)

Bartolomaeus, G.; Wilhelm, J.

1983-01-01

Recently, based on the semigroup approach a new proof was presented of the existence of a unique solution of the non-stationary Boltzmann equation for the electron component of a collision dominated plasma. The proof underlies some restriction which should be overcome to extend the validity range to other problems of physical interest. One of the restrictions is the boundary condition applied. The choice of the boundary condition is essential for the proof because it determines the range of definition of the infinitesimal generator and thus the operator semigroup itself. The paper proves the existence of a unique solution for generalized boundary conditions, this solution takes non-negative values, which is necessary for a distribution function from the physical point of view. (author)

Quantum Gross-Pitaevskii Equation

Directory of Open Access Journals (Sweden)

Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete

2017-07-01

Full Text Available We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

The bicovariant differential calculus on the κ-Poincare and κ-Weyl groups

International Nuclear Information System (INIS)

Przanowski, K.

1997-01-01

The bicovariant differential calculus on four-dimensional κ-Poincare group and corresponding Lie-algebra-like structure for any metric tensor are described. The bicovariant differential calculus on four-dimensional κ-Weyl group and corresponding Lie-algebra-like structure for any metric tensor in the reference frame in which g 00 = 0 are considered. (author). 6 refs

q-deformations of noncompact Lie (super-) algebras: The examples of q-deformed Lorentz, Weyl, Poincare' and (super-) conformal algebras

International Nuclear Information System (INIS)

Dobrev, V.K.

1992-01-01

We review and explain a canonical procedure for the q-deformation of the real forms G of complex Lie (super-) algebras associated with (generalized) Cartan matrices. Our procedure gives different q-deformations for the non-conjugate Cartan subalgebras of G. We give several in detail the q-deformed Lorentz and conformal (super-) algebras. The q-deformed conformal algebra contains as a subalgebra a q-deformed Poincare algebra and as Hopf subalgebras two conjugate 11-generator q-deformed Weyl algebras. The q-deformed Lorentz algebra in Hopf subalgebra of both Weyl algebras. (author). 24 refs

Nonlinear evolution equations having a physical meaning

International Nuclear Information System (INIS)

Nakach, R.

1976-06-01

The non stationary self-similar solutions of the nonlinear evolution equations which can be solved by the inverse scattering method are studied. It turns out, as shown by means of several examples, that when the L linear operator associated with these equations, is of second order and only then, the self-similar solutions can be expressed in terms of the various Painleve's transcendents [fr

Quasiparticle Excitations with Berry Curvature in Insulating Magnets and Weyl Semimetals

Science.gov (United States)

Hirschberger, Maximilian Anton

half-Heusler material GdPtBi. A careful doping study of the negative longitudinal magnetoresistance (LMR) establishes GdPtBi as a new material platform to study the physical properties of a simple Weyl metal with only two Weyl points (for magnetic field along the crystallographic 〈111〉 direction). The negative LMR is associated with the theory of the chiral anomaly in solids, and a direct consequence of the nonzero Berry curvature of the energy band structure of a Weyl semimetal. We compare our results to detailed calculations of the electronic band structure. Moving beyond the negative LMR, we report for the first time the effect of the chiral anomaly on the longitudinal thermopower in a Weyl semimetal.

A class of exact solutions to the Einstein field equations

International Nuclear Information System (INIS)

Goyal, Nisha; Gupta, R K

2012-01-01

The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein-Maxwell equations. (paper)

Explicit free parametrization of the modified tetrahedron equation

CERN Document Server

Gehlen, G V; Sergeev, S

2003-01-01

The modified tetrahedron equation (MTE) with affine Weyl quantum variables at the Nth root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parametrized in terms of eight free parameters and 16 discrete phase choices, thus providing a broad starting point for the construction of three-dimensional integrable lattice models. The Fermat-curve points parametrizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N=2 we write the MTE in full detail.

Explicit free parametrization of the modified tetrahedron equation

International Nuclear Information System (INIS)

Gehlen, G von; Pakuliak, S; Sergeev, S

2003-01-01

The modified tetrahedron equation (MTE) with affine Weyl quantum variables at the Nth root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parametrized in terms of eight free parameters and 16 discrete phase choices, thus providing a broad starting point for the construction of three-dimensional integrable lattice models. The Fermat-curve points parametrizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N=2 we write the MTE in full detail

Twisting null geodesic congruences and the Einstein-Maxwell equations

International Nuclear Information System (INIS)

Newman, Ezra T; Silva-Ortigoza, Gilberto

2006-01-01

In a recent article, we returned to the study of asymptotically flat solutions of the vacuum Einstein equations with a rather unconventional point of view. The essential observation in that work was that from a given asymptotically flat vacuum spacetime with a given Bondi shear, one can find a class of asymptotically shear-free (but, in general, twisting) null geodesic congruences where the class was uniquely given up to the arbitrary choice of a complex analytic 'worldline' in a four-dimensional complex space. By imitating certain terms in the Weyl tensor that are found in the algebraically special type II metrics, this complex worldline could be made unique and given-or assigned-the physical meaning as the complex centre of mass. Equations of motion for this case were found. The purpose of the present work is to extend those results to asymptotically flat solutions of the Einstein-Maxwell equations. Once again, in this case, we get a class of asymptotically shear-free null geodesic congruences depending on a complex worldline in the same four-dimensional complex space. However in this case there will be, in general, two distinct but uniquely chosen worldlines, one of which can be assigned as the complex centre of charge while the other could be called the complex centre of mass. Rather than investigating the situation where there are two distinct complex worldlines, we study instead the special degenerate case where the two worldlines coincide, i.e., where there is a single unique worldline. This mimics the case of algebraically special Einstein-Maxwell fields where the degenerate principle null vector of the Weyl tensor coincides with a Maxwell principle null vector. Again we obtain equations of motion for this worldline-but explicitly found here only in an approximation. Though there are ambiguities in assigning physical meaning to different terms it appears as if reliance on the Kerr and charged Kerr metrics and classical electromagnetic radiation theory helps

Weyl metrics and wormholes

Energy Technology Data Exchange (ETDEWEB)

Gibbons, Gary W. [DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA U.K. (United Kingdom); Volkov, Mikhail S., E-mail: gwg1@cam.ac.uk, E-mail: volkov@lmpt.univ-tours.fr [Laboratoire de Mathématiques et Physique Théorique, LMPT CNRS—UMR 7350, Université de Tours, Parc de Grandmont, Tours, 37200 France (France)

2017-05-01

We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescaling them and extending to complex parameter values yields axially symmetric vacuum solutions containing singularities along circles that can be viewed as singular matter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings literally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality transformations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for example the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts everywhere at the symmetry axes, apart from solutions with locally flat geometry.

A method for computing the stationary points of a function subject to linear equality constraints

International Nuclear Information System (INIS)

Uko, U.L.

1989-09-01

We give a new method for the numerical calculation of stationary points of a function when it is subject to equality constraints. An application to the solution of linear equations is given, together with a numerical example. (author). 5 refs

A Simple Stochastic Differential Equation with Discontinuous Drift

DEFF Research Database (Denmark)

Simonsen, Maria; Leth, John-Josef; Schiøler, Henrik

2013-01-01

In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. We apply two approaches: The Euler-Maruyama method and the Fokker-Planck equation and show that a candidate density function based on the Euler-Maruyama method approximates a candidate density...... function based on the stationary Fokker-Planck equation. Furthermore, we introduce a smooth function which approximates the discontinuous drift and apply the Euler-Maruyama method and the Fokker-Planck equation with this input. The point of departure for this work is a particular SDE with discontinuous...

Electronic transport in torsional strained Weyl semimetals

Science.gov (United States)

Soto-Garrido, Rodrigo; Muñoz, Enrique

2018-05-01

In a recent paper (Muñoz and Soto-Garrido 2017 J. Phys.: Condens. Matter 29 445302) we have studied the effects of mechanical strain and magnetic field on the electronic transport properties in graphene. In this article we extended our work to Weyl semimetals (WSM). We show that although the WSM are 3D materials, most of the analysis done for graphene (2D material) can be carried out. In particular, we studied the electronic transport through a cylindrical region submitted to torsional strain and external magnetic field. We provide exact analytical expressions for the scattering cross section and the transmitted electronic current. In addition, we show the node-polarization effect on the current and propose a recipe to measure the torsion angle from transmission experiments.

On the Field of a Stationary Charged Spherical Source

Directory of Open Access Journals (Sweden)

Stavroulakis N.

2009-04-01

Full Text Available The equations of gravitation related to the field of a spherical charged source imply the existence of an interdependence between gravitation and electricity [5]. The present paper deals with the joint action of gravitation and electricity in the case of a stationary charged spherical source. Let m and " be respectively the mass and the charge of the source, and let k be the gravitational constant. Then the equations of gravitation need specific discussion according as j " j m p k (source strongly charged. In any case the curvature radius of the sphere bounding the matter possesses a strictly positive greatest lower hound, so that the source is necessarily an extended object. Pointwise sources do not exist. In particular, charged black holes do not exist.

The stationary Alfven wave in laboratory and space regimes

Science.gov (United States)

Finnegan, S. M.

In this thesis, a non-linear, collisional, two-fluid model of uniform plasma convection across field-aligned current (FAC) sheets, describing stationary Alfven (StA) waves is developed in support of laboratory experiments performed to test the hypothesis that a stationary inertial Alfven wave pattern forms within a channel of parallel electron current across which plasma is convected. In a previous work, Knudsen (D. J. Knudsen, J. Geophys. Res. 101, 10,761 (1996)) showed that, for cold, collisionless plasma, stationary inertial Alfven (StIA) waves can accelerate electrons parallel to a background magnetic field and cause large, time-independent plasma-density variations having spatial periodicity in the direction of the convective flow over a broad range of spatial scales and energies. Here, Knudsen's model has been generalized for warm, collisional, anisotropic plasma. The inclusion of parallel electron thermal pressure introduces dispersive effects which extend the model to the kinetic (beta > me/mi) regime. The effects of both ion-neutral and electron-ion collisional resistivity on StIA and stationary kinetic Alfven (StKA) wave solutions is studied. Conditions for both periodic and solitary wave solutions are identified. In the small amplitude limit, it is shown that the StA wave equation reduces to the differential equation describing the behavior of a forced harmonic oscillator. Analytical solutions are obtained for both a step and impulse, of finite width, forcing functions. Plasma rotation experiments in the West Virginia University Q-machine (WVUQ) demonstrate that an electron-emitting spiral electrode produces controllable, parabolic radial profile of floating potential, while the space potential showed no such structure. Laser-induced fluorescence measurements confirmed that the azimuthal ion drift velocity is inconsistent with a drift due to a gradient in the space potential. Experiments designed to produce StIA wave signatures were performed in the

Integral equation approach to time-dependent kinematic dynamos in finite domains

International Nuclear Information System (INIS)

Xu Mingtian; Stefani, Frank; Gerbeth, Gunter

2004-01-01

The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The present paper tries to facilitate the use of integral equations in dynamo research. Apart from the pedagogical value to illustrate dynamo action within the well-known picture of the Biot-Savart law, the integral equation approach has a number of practical advantages. The first advantage is its proven numerical robustness and stability. The second and perhaps most important advantage is its applicability to dynamos in arbitrary geometries. The third advantage is its intimate connection to inverse problems relevant not only for dynamos but also for technical applications of magnetohydrodynamics. The paper provides the first general formulation and application of the integral equation approach to time-dependent kinematic dynamos, with stationary dynamo sources, in finite domains. The time dependence is restricted to the magnetic field, whereas the velocity or corresponding mean-field sources of dynamo action are supposed to be stationary. For the spherically symmetric α 2 dynamo model it is shown how the general formulation is reduced to a coupled system of two radial integral equations for the defining scalars of the poloidal and toroidal field components. The integral equation formulation for spherical dynamos with general stationary velocity fields is also derived. Two numerical examples - the α 2 dynamo model with radially varying α and the Bullard-Gellman model - illustrate the equivalence of the approach with the usual differential equation method. The main advantage of the method is exemplified by the treatment of an α 2 dynamo in rectangular domains

Effect of multiplicative noise on stationary stochastic process

Science.gov (United States)

Kargovsky, A. V.; Chikishev, A. Yu.; Chichigina, O. A.

2018-03-01

An open system that can be analyzed using the Langevin equation with multiplicative noise is considered. The stationary state of the system results from a balance of deterministic damping and random pumping simulated as noise with controlled periodicity. The dependence of statistical moments of the variable that characterizes the system on parameters of the problem is studied. A nontrivial decrease in the mean value of the main variable with an increase in noise stochasticity is revealed. Applications of the results in several physical, chemical, biological, and technical problems of natural and humanitarian sciences are discussed.

A Result on the Existence and Uniqueness of Stationary Solutions for a Bioconvective Flow Model

Directory of Open Access Journals (Sweden)

Aníbal Coronel

2018-01-01

Full Text Available In this note, we prove the existence and uniqueness of weak solutions for the boundary value problem modelling the stationary case of the bioconvective flow problem. The bioconvective model is a boundary value problem for a system of four equations: the nonlinear Stokes equation, the incompressibility equation, and two transport equations. The unknowns of the model are the velocity of the fluid, the pressure of the fluid, the local concentration of microorganisms, and the oxygen concentration. We derive some appropriate a priori estimates for the weak solution, which implies the existence, by application of Gossez theorem, and the uniqueness by standard methodology of comparison of two arbitrary solutions.

Fingering patterns in magnetic fluids: Perturbative solutions and the stability of exact stationary shapes

Science.gov (United States)

Anjos, Pedro H. A.; Lira, Sérgio A.; Miranda, José A.

2018-04-01

We examine the formation of interfacial patterns when a magnetic liquid droplet (ferrofluid, or a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. By using a vortex-sheet formalism, we find exact stationary solutions for the fluid-fluid interface in the form of n -fold polygonal shapes. A weakly nonlinear, mode-coupling method is then utilized to find time-evolving perturbative solutions for the interfacial patterns. The stability of such nonzero surface tension exact solutions is checked and discussed, by trying to systematically approach the exact stationary shapes through perturbative solutions containing an increasingly larger number of participating Fourier modes. Our results indicate that the exact stationary solutions of the problem are stable, and that a good matching between exact and perturbative shape solutions is achieved just by using a few Fourier modes. The stability of such solutions is substantiated by a linearization process close to the stationary shape, where a system of mode-coupling equations is diagonalized, determining the eigenvalues which dictate the stability of a fixed point.

Solutions without phase-slip for the Ginsburg-Landau equation

International Nuclear Information System (INIS)

Collet, P.; Eckmann, J.P.

1992-01-01

We consider the Ginsburg-Landau equation for a complex scalar field in one dimension and consider initial data which have two different stationary solutions as their limits in space as x→±∞. If these solutions are not very different, then we show that the initial data will evolve to a stationary solution by a 'phase melting' process which avoids 'phase slips,' i.e., which does not go through zero amplitude. (orig.)

Experimental Observation of Anisotropic Adler-Bell-Jackiw Anomaly in Type-II Weyl Semimetal WTe1.98 Crystals at the Quasiclassical Regime

Science.gov (United States)

Lv, Yang-Yang; Li, Xiao; Zhang, Bin-Bin; Deng, W. Y.; Yao, Shu-Hua; Chen, Y. B.; Zhou, Jian; Zhang, Shan-Tao; Lu, Ming-Hui; Zhang, Lei; Tian, Mingliang; Sheng, L.; Chen, Yan-Feng

2017-03-01

The asymmetric electron dispersion in type-II Weyl semimetal theoretically hosts anisotropic transport properties. Here, we observe the significant anisotropic Adler-Bell-Jackiw (ABJ) anomaly in the Fermi-level delicately adjusted WTe1.98 crystals. Quantitatively, CW , a coefficient representing the intensity of the ABJ anomaly along the a and b axis of WTe1.98 are 0.030 and 0.051 T-2 at 2 K, respectively. We found that the temperature-sensitive ABJ anomaly is attributed to a topological phase transition from a type-II Weyl semimetal to a trivial semimetal, which is verified by a first-principles calculation using experimentally determined lattice parameters at different temperatures. Theoretical electrical transport study reveals that the observation of an anisotropic ABJ along both the a and b axes in WTe1.98 is attributed to electrical transport in the quasiclassical regime. Our work may suggest that electron-doped WTe2 is an ideal playground to explore the novel properties in type-II Weyl semimetals.

Exact vacuum solution to conformal Weyl gravity and galactic rotation curves

International Nuclear Information System (INIS)

Mannheim, P.D.; Kazanas, D.

1989-01-01

The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology. 9 refs

z -Weyl gravity in higher dimensions

Energy Technology Data Exchange (ETDEWEB)

Moon, Taeyoon; Oh, Phillial, E-mail: dpproject@skku.edu, E-mail: ploh@skku.edu [Department of Physics and Institute of Basic Science, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of)

2017-09-01

We consider higher dimensional gravity in which the four dimensional spacetime and extra dimensions are not treated on an equal footing. The anisotropy is implemented in the ADM decomposition of higher dimensional metric by requiring the foliation preserving diffeomorphism invariance adapted to the extra dimensions, thus keeping the general covariance only for the four dimensional spacetime. The conformally invariant gravity can be constructed with an extra (Weyl) scalar field and a real parameter z which describes the degree of anisotropy of conformal transformation between the spacetime and extra dimensional metrics. In the zero mode effective 4D action, it reduces to four-dimensional scalar-tensor theory coupled with nonlinear sigma model described by extra dimensional metrics. There are no restrictions on the value of z at the classical level and possible applications to the cosmological constant problem with a specific choice of z are discussed.

Darboux Transformations for Energy-Dependent Potentials and the Klein–Gordon Equation

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2013-01-01

We construct explicit Darboux transformations for a generalized Schrödinger-type equation with energy-dependent potential, a special case of which is the stationary Klein–Gordon equation. Our results complement and generalize former findings (Lin et al., Phys Lett A 362:212–214, 2007).

Subspace gaps and Weyl's theorem for an elementary operator

Directory of Open Access Journals (Sweden)

B. P. Duggal

2005-01-01

Full Text Available A range-kernal orthogonality property is established for the elementary operators ℰ(X=∑i=1nAiXBi and ℰ*(X=∑i=1nAi*XBi*, where A=(A1,A2,…,An and B=(B1,B2,…,Bn are n-tuples of mutually commuting scalar operators (in the sense of Dunford in the algebra B(H of operators on a Hilbert space H. It is proved that the operator ℰ satisfies Weyl's theorem in the case in which A and B are n-tuples of mutually commuting generalized scalar operators.

Generalized master equations for non-Poisson dynamics on networks.

Science.gov (United States)

Hoffmann, Till; Porter, Mason A; Lambiotte, Renaud

2012-10-01

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

Raman Signatures of Broken Inversion Symmetry and In-Plane Anisotropy in Type-II Weyl Semimetal Candidate TaIrTe4.

Science.gov (United States)

Liu, Yinan; Gu, Qiangqiang; Peng, Yu; Qi, Shaomian; Zhang, Na; Zhang, Yinong; Ma, Xiumei; Zhu, Rui; Tong, Lianming; Feng, Ji; Liu, Zheng; Chen, Jian-Hao

2018-05-07

The layered ternary compound TaIrTe 4 is an important candidate to host the recently predicted type-II Weyl fermions. However, a direct and definitive proof of the absence of inversion symmetry in this material, a prerequisite for the existence of Weyl Fermions, has so far remained evasive. Herein, an unambiguous identification of the broken inversion symmetry in TaIrTe 4 is established using angle-resolved polarized Raman spectroscopy. Combining with high-resolution transmission electron microscopy, an efficient and nondestructive recipe to determine the exact crystallographic orientation of TaIrTe 4 crystals is demonstrated. Such technique could be extended to the fast identification and characterization of other type-II Weyl fermions candidates. A surprisingly strong in-plane electrical anisotropy in TaIrTe 4 thin flakes is also revealed, up to 200% at 10 K, which is the strongest known electrical anisotropy for materials with comparable carrier density, notably in such good metals as copper and silver. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Calculation of control rod oscillations in a hexagonal flow channel by means of the non-stationary pressure distribution around the rods

International Nuclear Information System (INIS)

Grunwald, G.; Mueller, E.

1983-08-01

For the computation of control rod oscillations in a flow channel we set up the differential equations for the non-stationary pressure distribution around the control elements which are coupled with the motion equations of the rods. The equation system is solved by means of a finite difference method. An example shows the efficiency of the numerical calculation procedure. (author)

Stationary bound-state massive scalar field configurations supported by spherically symmetric compact reflecting stars

Energy Technology Data Exchange (ETDEWEB)

Hod, Shahar [The Ruppin Academic Center, Emeq Hefer (Israel); The Hadassah Academic College, Jerusalem (Israel)

2017-12-15

It has recently been demonstrated that asymptotically flat neutral reflecting stars are characterized by an intriguing no-hair property. In particular, it has been proved that these horizonless compact objects cannot support spatially regular static matter configurations made of scalar (spin-0) fields, vector (spin-1) fields and tensor (spin-2) fields. In the present paper we shall explicitly prove that spherically symmetric compact reflecting stars can support stationary (rather than static) bound-state massive scalar fields in their exterior spacetime regions. To this end, we solve analytically the Klein-Gordon wave equation for a linearized scalar field of mass μ and proper frequency ω in the curved background of a spherically symmetric compact reflecting star of mass M and radius R{sub s}. It is proved that the regime of existence of these stationary composed star-field configurations is characterized by the simple inequalities 1 - 2M/R{sub s} < (ω/μ){sup 2} < 1. Interestingly, in the regime M/R{sub s} << 1 of weakly self-gravitating stars we derive a remarkably compact analytical equation for the discrete spectrum {ω(M,R_s, μ)}{sup n=∞}{sub n=1} of resonant oscillation frequencies which characterize the stationary composed compact-reflecting-star-linearized-massive-scalar-field configurations. Finally, we verify the accuracy of the analytically derived resonance formula of the composed star-field configurations with direct numerical computations. (orig.)

Prolongation structure and linear eigenvalue equations for Einstein-Maxwell fields

International Nuclear Information System (INIS)

Kramer, D.; Neugebauer, G.

1981-01-01

The Einstein-Maxwell equations for stationary axisymmetric exterior fields are shown to be the integrability conditions of a set of linear eigenvalue equations for pseudopotentials. Using the method of Wahlquist and Estabrook (J. Math Phys.; 16:1 (1975)) it is shown that the prolongation structure of the Einstein-Maxwell equations contains the SU(2,1) Lie algebra. A new mapping of known solutions to other solutions has been found. (author)

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

International Nuclear Information System (INIS)

Dubrovsky, V. G.; Topovsky, A. V.

2013-01-01

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u (n) , n= 1, …, N are constructed via Zakharov and Manakov ∂-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u (n) and calculated by ∂-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u (n) . It is shown that the sums u=u (k 1 ) +...+u (k m ) , 1 ⩽k 1 2 m ⩽N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas

International Nuclear Information System (INIS)

Bettelheim, Eldad; Abanov, Alexander G; Wiegmann, Paul B

2008-01-01

We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain are integrable equations. They generalize known nonlinear differential equations for correlation functions at equilibrium [1-4] and provide vital tools for studying non-equilibrium dynamics of electronic systems. The method we developed is based only on Wick's theorem and the hydrodynamic description of the Fermi gas. Differential equations appear directly in bilinear form. (fast track communication)

Realization of quantum anomalous Hall effect from a magnetic Weyl semimetal

OpenAIRE

Muechler, Lukas; Liu, Enke; Xu, Qiunan; Felser, Claudia; Sun, Yan

2017-01-01

The quantum anomalous Hall effect (QAHE) and magnetic Weyl semimetals (WSMs) are topological states induced by intrinsic magnetic moments and spin-orbital coupling. Their similarity suggests the possibility of achieving the QAHE by dimensional confinement of a magnetic WSM along one direction. In this study, we investigate the emergence of the QAHE in the two dimensional (2D) limit of magnetic WSMs due to finite size effects. We demonstrate the feasibility of this approach with effective mode...

Classes of general axisymmetric solutions of Einstein-Maxwell equations

International Nuclear Information System (INIS)

Krori, K.D.; Choudhury, T.

1981-01-01

An exact solution of the Einstein equations for a stationary axially symmetric distribution of mass composed of all types of multipoles is obtained. Following Ernst (1968), from this vacuum solution the corresponding solution of the coupled Einstein-Maxwell equations is derived. A solution of Einstein-Maxwell fields for a static axially symmetric system composed of all types of multipoles is also obtained. (author)

Localized solutions of non-linear Klein--Gordon equations

International Nuclear Information System (INIS)

Werle, J.

1977-05-01

Nondissipative, stationary solutions for a class of nonlinear Klein-Gordon equations for a scalar field were found explicitly. Since the field is different from zero only inside a sphere of definite radius, the solutions are called quantum droplets

Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

Science.gov (United States)

Saveliev, V L; Gorokhovski, M A

2005-07-01

On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

On gauge fields with sources

International Nuclear Information System (INIS)

Torres del Castillo, G.F.; Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN, Apartado Postal 14-740, 07000 Mexico, D. F., Mexico)

1987-01-01

It is shown that in an algebraically special space-time that admits a congruence of null strings, the Yang--Mills equations with sources reduce to a pair of nonlinear first-order differential equations for two matrices, provided that the gauge field is aligned with the congruence. In the case where the current is tangent to the null strings, the gauge field is determined by a matrix potential that has to satisfy a second-order differential equation with quadratic nonlinearities. As an example of this case, the Yang--Mills--Weyl equations are reduced, assuming that the multiplet of Weyl neutrino fields are also aligned with the congruence, and a reduced form of the Einstein--Yang--Mills--Weyl equations is also given

Entanglement Equilibrium and the Einstein Equation.

Science.gov (United States)

Jacobson, Ted

2016-05-20

A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies the validity of the hypothesis. A more precise argument shows that, for first-order variations of the local vacuum state of conformal quantum fields, the vacuum entanglement is stationary if and only if the Einstein equation holds. For nonconformal fields, the same conclusion follows modulo a conjecture about the variation of entanglement entropy.

Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Science.gov (United States)

Muruganandam, P.; Adhikari, S. K.

2009-10-01

Here we develop simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation describing the properties of Bose-Einstein condensates at ultra low temperatures. In particular, we consider algorithms involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. In a one-space-variable form of the GP equation we consider the one-dimensional, two-dimensional circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. Numerical results for the chemical potential and root-mean-square size of stationary states are reported using imaginary-time propagation programs for all the cases and compared with previously obtained results. Also presented are numerical results of non-stationary oscillation for different trap symmetries using real-time propagation programs. A set of convenient working codes developed in Fortran 77 are also provided for all these cases (twelve programs in all). In the case of two or three space variables, Fortran 90/95 versions provide some simplification over the Fortran 77 programs, and these programs are also included (six programs in all). Program summaryProgram title: (i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial Catalogue identifier: AEDU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDU_v1_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

Radio-Oxidation in Polyolefins: Non-Stationary Kinetic Conditions

International Nuclear Information System (INIS)

Dely, N.

2006-01-01

In the last fifty years, many authors have been interested in the radio-oxidation processes occurring in polymers. The polymer degradation under ionising radiations in presence of dioxygen is well described by a radical chemistry. The radio-oxidation process occurs in three steps: the first one is the production of radicals P degree by interaction between the polymer and the ionising radiations; then radicals P degree react spontaneously with O 2 solved in the polymer giving a peroxy radical POO degree which attacks the polymer forming a hydroperoxide POOH and a new radical P degree (propagation). The third step corresponds to the termination step, that is bimolecular reactions between radicals. It is generally assumed that the stationary state is rapidly reached and consequently that the oxidation induced during the built-up period of the radical concentration can be neglected. However, to our best knowledge, the temporal evolution of radical concentrations before reaching the steady state regime has never been studied in details. We recently performed a complete study of oxygen consumption under electron irradiation for an EPDM elastomer. An analysis, as function of dose rate and oxygen pressure, and assuming steady state conditions, allowed extracting all the kinetic constants. Starting for these experimental data, we calculated the build-up of the radical concentration by solving numerically the differential equations with help of the Minichem code. We conclude that, in fact, the oxidation induced during the built-up period is negligible. In this paper we show that [P degree] could present a quasi-stationary plateau before reaching its stationary level. Consequently, the full radical time evolution is essentially determined by two characteristic times for reaching the quasi and stationary levels and three concentrations: [P degree] and [POO degree] at the stationary level and [P degree] at the quasi-stationary plateau. We show that realistic approximations can

Invariant and partially-invariant solutions of the equations describing a non-stationary and isentropic flow for an ideal and compressible fluid in (3 + 1) dimensions

Science.gov (United States)

Grundland, A. M.; Lalague, L.

1996-04-01

This paper presents a new method of constructing, certain classes of solutions of a system of partial differential equations (PDEs) describing the non-stationary and isentropic flow for an ideal compressible fluid. A generalization of the symmetry reduction method to the case of partially-invariant solutions (PISs) has been formulated. We present a new algorithm for constructing PISs and discuss in detail the necessary conditions for the existence of non-reducible PISs. All these solutions have the defect structure 0305-4470/29/8/019/img1 and are computed from four-dimensional symmetric subalgebras. These theoretical considerations are illustrated by several examples. Finally, some new classes of invariant solutions obtained by the symmetry reduction method are included. These solutions represent central, conical, rational, spherical, cylindrical and non-scattering double waves.

Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients

International Nuclear Information System (INIS)

Zielinski, Lech

1999-01-01

The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hoermander''s type for the spectral function of pseudo differential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients

Dynamics of Inhomogeneous Shell Systems Under Non-Stationary Loading (Survey)

Science.gov (United States)

Lugovoi, P. Z.; Meish, V. F.

2017-09-01

Experimental works on the determination of dynamics of smooth and stiffened cylindrical shells contacting with a soil medium under various non-stationary loading are reviewed. The results of studying three-layer shells of revolution whose motion equations are obtained within the framework of the hypotheses of the Timoshenko geometrically nonlinear theory are stated. The numerical results for shells with a piecewise or discrete filler enable the analysis of estimation of the influence of geometrical and physical-mechanical parameters of structures on their dynamics and reveal new mechanical effects. Basing on the classical theory of shells and rods, the effect of the discrete arrangement of ribs and coefficients of the Winkler or Pasternak elastic foundation on the normal frequencies and modes of rectangular planar cylindrical and spherical shells is studied. The number and shape of dispersion curves for longitudinal harmonic waves in a stiffened cylindrical shell are determined. The equations of vibrations of ribbed shells of revolution on Winkler or Pasternak elastic foundation are obtained using the geometrically nonlinear theory and the Timoshenko hypotheses. On applying the integral-interpolational method, numerical algorithms are developed and the corresponding non-stationary problems are solved. The special attention is paid to the statement and solution of coupled problems on the dynamical interaction of cylindrical or spherical shells with the soil water-saturated medium of different structure.

Projection-iteration methods for solving nonlinear operator equations

International Nuclear Information System (INIS)

Nguyen Minh Chuong; Tran thi Lan Anh; Tran Quoc Binh

1989-09-01

In this paper, the authors investigate a nonlinear operator equation in uniformly convex Banach spaces as in metric spaces by using stationary and nonstationary generalized projection-iteration methods. Convergence theorems in the strong and weak sense were established. (author). 7 refs

Double shadow of a regular phantom black hole as photons couple to the Weyl tensor

Energy Technology Data Exchange (ETDEWEB)

Huang, Yang; Chen, Songbai; Jing, Jiliang [Hunan Normal University, Institute of Physics and Department of Physics, Changsha, Hunan (China); Hunan Normal University, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha, Hunan (China); Hunan Normal University, Synergetic Innovation Center for Quantum Effects and Applications, Changsha, Hunan (China)

2016-11-15

We have studied the shadow of a regular phantom black hole as photons couple to the Weyl tensor. We find that due to the coupling photons with different polarization directions propagate along different paths in the spacetime so that there exists a double shadow for a black hole, which is quite different from that in the non-coupling case where only a single shadow emerges. The overlap region of the double shadow, the umbra, of the black hole increases with the phantom charge and decreases with the coupling strength. The dependence of the penumbra on the phantom charge and the coupling strength is converse to that of the umbra. Combining with the supermassive central object in our Galaxy, we estimated the shadow of the black hole as the photons couple to the Weyl tensor. Our results show that the coupling brings about richer behaviors of the propagation of coupled photon and the shadow of the black hole in the regular phantom black hole spacetime. (orig.)

Renormalization theory of stationary homogeneous strong turbulence in a collisionless plasma

International Nuclear Information System (INIS)

Zhang, Y.Z.

1984-01-01

A renormalization procedure for the perturbation expansion of the Vlasov-Poisson equation is presented to describe stationary homogeneous turbulence. By using the diagramatic scheme the theory is shown to be renormalizable to any order. The expressions for the renormalized propagator, the renormalized dielectric function, and the intrinsically incoherent source are given. The renormalization leads to a complete separation of the fluctuating distribution function f/sub k/ into two parts, the coherent part, which is proved to represent the dielectric effect of the medium, and the intrinsically incoherent part, which represents the effect of nonlinear source. The turbulent collisional operator in the transport equation is proved equal to GAMMA 0 , the frequency broadening when k = 0

Kinetic equations with pairing correlations

International Nuclear Information System (INIS)

Fauser, R.

1995-12-01

The Gorkov equations are derived for a general non-equilibrium system. The Gorkov factorization is generalized by the cumulant expansion of the 2-particle correlation and by a generalized Wick theorem in the case of a perturbation expansion. A stationary solution for the Green functions in the Schwinger-Keldysh formalism is presented taking into account pairing correlations. Especially the effects of collisional broadening on the spectral functions and Green functions is discussed. Kinetic equations are derived in the quasi-particle approximation and in the case of particles with width. Explicit expressions for the self-energies are given. (orig.)

High-frequency instabilities of stationary crossflow vortices in a hypersonic boundary layer

Science.gov (United States)

Li, Fei; Choudhari, Meelan; Paredes, Pedro; Duan, Lian

2016-09-01

Hypersonic boundary layer flows over a circular cone at moderate incidence angle can support strong crossflow instability in between the windward and leeward rays on the plane of symmetry. Due to more efficient excitation of stationary crossflow vortices by surface roughness, such boundary layer flows may transition to turbulence via rapid amplification of the high-frequency secondary instabilities of finite-amplitude stationary crossflow vortices. The amplification characteristics of these secondary instabilities are investigated for crossflow vortices generated by an azimuthally periodic array of roughness elements over a 7° half-angle circular cone in a Mach 6 free stream. The analysis is based on both quasiparallel stability theory in the form of a partial-differential-equation-based eigenvalue analysis and plane marching parabolized stability equations that account for the effects of the nonparallel basic state on the growth of secondary disturbances. Depending on the local amplitude of the stationary crossflow mode, the most unstable high-frequency disturbances either originate from the second (i.e., Mack) mode instabilities of the unperturbed boundary layer or correspond to genuine secondary instabilities that reduce to stable disturbances at sufficiently small amplitudes of the stationary crossflow vortex. The predicted frequencies of the dominant secondary disturbances of either type are similar to those measured during wind tunnel experiments at Purdue University and the Technical University of Braunschweig, Germany. Including transverse surface curvature within the quasiparallel predictions does not alter the topology of the unstable modes; however, the resulting changes in both mode shape and disturbance growth rate are rather significant and curvature can be either stabilizing or destabilizing depending on the disturbance frequency and mode type. Nonparallel effects are shown to be strongly destabilizing for secondary instabilities originating from

Optical response in Weyl semimetal in model with gapped Dirac phase

Science.gov (United States)

Mukherjee, S. P.; Carbotte, J. P.

2017-10-01

We study the optical properties of Weyl semimetal (WSM) in a model which features, in addition to the usual term describing isolated Dirac cones proportional to the Fermi velocity v F, a gap term m and a Zeeman spin-splitting term b with broken time reversal symmetry. Transport is treated within Kubo formalism and particular attention is payed to the modifications that result from a finite m and b. We consider how these modifications change when a finite residual scattering rate \

Modified Darboux transformations with foreign auxiliary equations

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2011-01-01

We construct a new type of first-order Darboux transformations for the stationary Schroedinger equation. In contrast to the conventional case, our Darboux transformations support arbitrary (foreign) auxiliary equations. We show that among other applications, our formalism can be used to systematically construct Darboux transformations for Schroedinger equations with energy-dependent potentials, including a recent result (Lin et al., 2007) as a special case. -- Highlights: → We generalize the Darboux transformation for the Schroedinger equation. → By admitting arbitrary auxiliary functions, we provide a new tool for generating solutions. → As a special case we recover a recent result on energy-dependent potentials. → We extend the latter result to very general energy-dependence.

Existence of solution for a general fractional advection-dispersion equation

Science.gov (United States)

Torres Ledesma, César E.

2018-05-01

In this work, we consider the existence of solution to the following fractional advection-dispersion equation -d/dt ( p {_{-∞}}It^{β }(u'(t)) + q {t}I_{∞}^{β }(u'(t))) + b(t)u = f(t, u(t)),t\\in R where β \\in (0,1) , _{-∞}It^{β } and tI_{∞}^{β } denote left and right Liouville-Weyl fractional integrals of order β respectively, 0continuous functions. Due to the general assumption on the constant p and q, the problem (0.1) does not have a variational structure. Despite that, here we study it performing variational methods, combining with an iterative technique, and give an existence criteria of solution for the problem (0.1) under suitable assumptions.

Numerical Modeling of the Thomson Ring in Stationary Levitation Using FEM-Electrical Network and Newton-Raphson

Directory of Open Access Journals (Sweden)

Guzmán Juan

2015-07-01

Full Text Available There are a lot of applications of the Thomson ring: levitation of superconductor materials, power interrupters (used as actuator and elimination of electric arcs. Therefore, it is important the numerical modeling of Thomson ring. The aim of this work is to model the stationary levitation of the Thomson ring. This Thomson ring consists of a copper coil with ferromagnetic core and an aluminum ring threaded in the core. The coil is fed by a cosine voltage to ensure that the aluminum ring is in a stationary levitated position. In this situation, the state of the electromagnetic field is stable and can be used the phasor equations of the electromagnetic field. These equations are discretized using the Galerkin method in the Lagrange base space (finite element method, FEM. These equations are solved using the COMSOL software. A methodology is also described (which uses the Newton-Raphson method that obtains the separation between coil and aluminum ring. The numerical solutions of this separation are compared with experimental data. The conclusion is that the magnetic coupling of the aluminum ring on the coil can be neglected if the source voltage is high.

Variational analysis of topological stationary barotropic MHD in the case of single-valued magnetic surfaces

International Nuclear Information System (INIS)

Yahalom, A

2014-01-01

Variational principles for magnetohydrodynamics have been introduced by previous authors both in Lagrangian and Eulerian form. Yahalom and Lynden-Bell (2008) have previously introduced simpler Eulerian variational principles from which all the relevant equations of barotropic magnetohydrodynamics can be derived. These variational principles were given in terms of six independent functions for non-stationary barotropic flows with given topologies and three independent functions for stationary barotropic flows. This is less then the seven variables which appear in the standard equations of barotropic magnetohydrodynamics which are the magnetic field B-vector the velocity field v-vector and the density ρ. Later, Yahalom (2010) introduced a simpler variational principle in terms of four functions for non-stationary barotropic magnetohydrodynamics. It was shown that the above variational principles are also relevant for flows of non-trivial topologies and in fact using those variational variables one arrives at additional topological conservation laws in terms of cuts of variables which have close resemblance to the Aharonov- Bohm phase (Yahalom (2013)). In previous examples (Yahalom and Lynden-Bell (2008); Yahalom (2013)) the magnetic field lines with non-trivial topology were at the intersection of two surface one of which was always multivalued; in this paper an example is introduced in which the magnetic helicity is not zero yet both surfaces are single-valued

New Non-Stationary Gradient Model of Heat-Mass-Electric Charge Transfer in Thin Porous Media

Directory of Open Access Journals (Sweden)

V. Rogankov

2017-10-01

Full Text Available The well-known complicated system of non-equilibrium balance equations for a continuous fluid (f medium needs the new non-Gibbsian model of f-phase to be applicable for description of the heterogeneous porous media (PMs. It should be supplemented by the respective coupled thermal and caloric equations of state (EOS developed specially for PMs to become adequate and solvable for the irreversible transport f-processes. The set of standard assumptions adopted by the linear (or quasi-linear non-equilibrium thermodynamics are based on the empirical gradient-caused correlations between flows and forces. It leads, in particular, to the oversimplified stationary solutions for PMs. The most questionable but typical modeling suppositions of the stationary gradient (SG theory are: 1 the assumption of incompressibility accepted, as a rule, for f-flows; 2 the ignorance of distinctions between the hydrophilic and hydrophobic influence of a porous matrix on the properties; 3 the omission of effects arising due to the concomitant phase intra-porous transitions between the neighboring f-fragments with the sharp differences in densities; 4 the use of exclusively Gibbsian (i.e. homogeneous and everywhere differentiable description of any f-phase in PM; 5 the very restrictive reduction of the mechanical velocity field to its specific potential form in the balance equation of f-motion as well as of the heat velocity field in the balance equation of internal energy; 6 the neglect of the new specific peculiarities arising due to the study of any non-equilibrium PM in the meso- and nano-scales of a finite-size macroscopic (N,V-system of discrete particles. This work is an attempt to develop the alternative non-stationary gradient (NSG model of real irreversible processes in PM. Another aim is to apply it without the above restrictions 1-6 to the description of f-flows through the obviously non-Gibbsian thin porous medium (TPM. We will suppose that it is composed by two

STEADY STATE AND PSEUDO-TRANSIENT ELECTRIC POTENTIAL USING THE POISSONBOLTZMANN EQUATION

Directory of Open Access Journals (Sweden)

L. C. dos Santos

2015-03-01

Full Text Available A method for analysis of the electric potential profile in saline solutions was developed for systems with one or two infinite flat plates. A modified Poisson-Boltzmann equation, taking into account nonelectrostatic interactions between ions and surfaces, was used. To solve the stated problem in the steady-state approach the finite-difference method was used. For the formulated pseudo-transient problem, we solved the set of ordinary differential equations generated from the algebraic equations of the stationary case. A case study was also carried out in relation to temperature, solution concentration, surface charge and salt-type. The results were validated by the stationary problem solution, which had also been used to verify the ionic specificity for different salts. The pseudo-transient approach allowed a better understanding of the dynamic behavior of the ion-concentration profile and other properties due to the surface charge variation.

Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle.

Science.gov (United States)

Shalymov, Dmitry S; Fradkov, Alexander L

2016-01-01

We propose dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle. The equations are derived on the basis of the speed-gradient principle originated in the control theory. The maximum of the Rényi entropy principle is analysed for discrete and continuous cases, and both a discrete random variable and probability density function (PDF) are used. We consider mass conservation and energy conservation constraints and demonstrate the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases. The coincidence of the limit distribution of the proposed equations with the Rényi distribution is examined.

Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients

Energy Technology Data Exchange (ETDEWEB)

Zielinski, Lech [Universite Paris 7 (D. Diderot), Institut de Mathematiques de Paris-Jussieu UMR9994 (France)

1999-09-15

The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hoermander''s type for the spectral function of pseudo differential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients.

Planck scale physics of the single-particle Schrödinger equation ...

Indian Academy of Sciences (India)

... t ) is the wave function and is the mass of the particle. This leads to a nonlinear equation, the 'Newton–Schrödinger' equation, which has been found to possess stationary self-bound solutions, whose energy can be determined using an asymptotic method. We find that such a particle strongly violates the superposition ...

A different approach to obtain Mayer’s extension to stationary single particle Wigner distribution

International Nuclear Information System (INIS)

Bose, Anirban; Janaki, M. S.

2012-01-01

It is shown that the stationary collisionless single-particle Wigner equation in one dimension containing quantum corrections at the lowest order is satisfied by a distribution function that is similar in form to the Maxwellian distribution with an effective mass and a generalized potential. The distribution is used to study quantum corrections to electron hole solutions.

Molecular theory of chromatography for blocklike solutes in anisotropic stationary phases and its application

International Nuclear Information System (INIS)

Yan, Chao; Martire, D.E.

1992-01-01

DiMarzio's lattice model is successfully applied to describe the equilibrium partitioning of blocklike molecules between an isotropic mobile phase and an anisotropic stationary phase in various types of fluid chromatography to obtain a retention equation. A linear relationship between the logarithm of the solute distribution coefficient and minimum area is predicted. 44 refs., 8 figs., 2 tabs

Stochastic substitute for coupled rate equations in the modeling of highly ionized transient plasmas

International Nuclear Information System (INIS)

Eliezer, S.; Falquina, R.; Minguez, E.

1994-01-01

Plasmas produced by intense laser pulses incident on solid targets often do not satisfy the conditions for local thermodynamic equilibrium, and so cannot be modeled by transport equations relying on equations of state. A proper description involves an excessively large number of coupled rate equations connecting many quantum states of numerous species having different degrees of ionization. Here we pursue a recent suggestion to model the plasma by a few dominant states perturbed by a stochastic driving force. The driving force is taken to be a Poisson impulse process, giving a Langevin equation which is equivalent to a Fokker-Planck equation for the probability density governing the distribution of electron density. An approximate solution to the Langevin equation permits calculation of the characteristic relaxation rate. An exact stationary solution to the Fokker-Planck equation is given as a function of the strength of the stochastic driving force. This stationary solution is used, along with a Laplace transform, to convert the Fokker-Planck equation to one of Schroedinger type. We consider using the classical Hamiltonian formalism and the WKB method to obtain the time-dependent solution

Central-Upwind Schemes for Two-Layer Shallow Water Equations

KAUST Repository

Kurganov, Alexander; Petrova, Guergana

2009-01-01

We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions

Adjamagbo Determinant and Serre conjecture for linear groups over Weyl algebras

OpenAIRE

Adjamagbo, Kossivi

2008-01-01

Thanks to the theory of determinants over an Ore domain, also called Adjamagbo determinant by the Russian school of non commutative algebra, we extend to any Weyl algebra over a field of characteristic zero Suslin theorem solving what Suslin himself called the $K_1$-analogue of the well-known Serre Conjecture and asserting that for any integer $n$ greater than 2, any $n$ by $n$ matrix with coefficients in any algebra of polynomials over a field and with determinant one is the product of eleme...

Weyl-van-der-Waerden formalism for helicity amplitudes of massive particles

CERN Document Server

Dittmaier, Stefan

1999-01-01

The Weyl-van-der-Waerden spinor technique for calculating helicity amplitudes of massive and massless particles is presented in a form that is particularly well suited to a direct implementation in computer algebra. Moreover, we explain how to exploit discrete symmetries and how to avoid unphysical poles in amplitudes in practice. The efficiency of the formalism is demonstrated by giving explicit compact results for the helicity amplitudes of the processes gamma gamma -> f fbar, f fbar -> gamma gamma gamma, mu^- mu^+ -> f fbar gamma.

Charging of nanoparticles in stationary plasma in a gas aggregation cluster source

Science.gov (United States)

Blažek, J.; Kousal, J.; Biederman, H.; Kylián, O.; Hanuš, J.; Slavínská, D.

2015-10-01

Clusters that grow into nanoparticles near the magnetron target of the gas aggregation cluster source (GAS) may acquire electric charge by collecting electrons and ions or through other mechanisms like secondary- or photo-electron emissions. The region of the GAS close to magnetron may be considered as stationary plasma. The steady state charge distribution on nanoparticles can be determined by means of three possible models—fluid model, kinetic model and model employing Monte Carlo simulations—of cluster charging. In the paper the mathematical and numerical aspects of these models are analyzed in detail and close links between them are clarified. Among others it is shown that Monte Carlo simulation may be considered as a particular numerical technique of solving kinetic equations. Similarly the equations of the fluid model result, after some approximation, from averaged kinetic equations. A new algorithm solving an in principle unlimited set of kinetic equations is suggested. Its efficiency is verified on physical models based on experimental input data.

Matrix product representation of the stationary state of the open zero range process

Science.gov (United States)

Bertin, Eric; Vanicat, Matthieu

2018-06-01

Many one-dimensional lattice particle models with open boundaries, like the paradigmatic asymmetric simple exclusion process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not explicitly depend on the lattice site. In contrast, the stationary state of the open 1D zero-range process (ZRP) takes an inhomogeneous factorized form, with site-dependent probability weights. We show that in spite of the absence of correlations, the stationary state of the open ZRP can also be represented in a matrix product form, where the matrices are site-independent, non-commuting and determined from algebraic relations resulting from the master equation. We recover the known distribution of the open ZRP in two different ways: first, using an explicit representation of the matrices and boundary vectors; second, from the sole knowledge of the algebraic relations satisfied by these matrices and vectors. Finally, an interpretation of the relation between the matrix product form and the inhomogeneous factorized form is proposed within the framework of hidden Markov chains.

The algebra of Weyl symmetrised polynomials and its quantum extension

International Nuclear Information System (INIS)

Gelfand, I.M.; Fairlie, D.B.

1991-01-01

The Algebra of Weyl symmetrised polynomials in powers of Hamiltonian operators P and Q which satisfy canonical commutation relations is constructed. This algebra is shown to encompass all recent infinite dimensional algebras acting on two-dimensional phase space. In particular the Moyal bracket algebra and the Poisson bracket algebra, of which the Moyal is the unique one parameter deformation are shown to be different aspects of this infinite algebra. We propose the introduction of a second deformation, by the replacement of the Heisenberg algebra for P, Q with a q-deformed commutator, and construct algebras of q-symmetrised Polynomials. (orig.)

Weyl's search for a difference between 'physical' and 'mathematical' automorphisms

Science.gov (United States)

Scholz, Erhard

2018-02-01

During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s (ETH, Hs 91a:31) he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in the context of the later development of gauge theories.

On analytical solution of the Navier-Stokes equations

International Nuclear Information System (INIS)

Scheffel, J.

2001-04-01

An analytical method for solving the dissipative, nonlinear and non-stationary Navier-Stokes equations is presented. Velocity and pressure is expanded in power series of cartesian coordinates and time. The method is applied to 2-D incompressible gravitational flow in a bounded, rectangular domain

Analytical solution of the PNP equations at AC applied voltage

International Nuclear Information System (INIS)

Golovnev, Anatoly; Trimper, Steffen

2012-01-01

A symmetric binary polymer electrolyte subjected to an AC voltage is considered. The analytical solution of the Poisson–Nernst–Planck equations (PNP) is found and analyzed for small applied voltages. Three distinct time regimes offering different behavior can be discriminated. The experimentally realized stationary behavior is discussed in detail. An expression for the external current is derived. Based on the theoretical result a simple method is suggested of measuring the ion mobility and their concentration separately. -- Highlights: ► Analytical solution of Poisson–Nernst–Planck equations. ► Binary polymer electrolyte subjected to an external AC voltage. ► Three well separated time scales exhibiting different behavior. ► The experimentally realized stationary behavior is discussed in detail. ► A method is proposed measuring the mobility and the concentration separately.

On the Solution of the Rational Matrix Equation

Directory of Open Access Journals (Sweden)

Faßbender Heike

2007-01-01

Full Text Available We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation , where is symmetric positive definite and is nonsingular. Such equations arise for instance in the analysis of stationary Gaussian reciprocal processes over a finite interval. Its unique largest positive definite solution coincides with the unique positive definite solution of a related discrete-time algebraic Riccati equation (DARE. We discuss how to use the butterfly algorithm to solve the DARE. This approach is compared to several fixed-point and doubling-type iterative methods suggested in the literature.

On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction

Czech Academy of Sciences Publication Activity Database

Ortaggio, Marcello; Pravda, Vojtěch; Pravdová, Alena

Roč. 35, č. 7 ( 2018 ), č. článku 075004. ISSN 0264-9381 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : higher-dimensional gravity * WANDs * Weyl tensor Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 3.119, year: 2016 http://iopscience.iop.org/article/10.1088/1361-6382/aaae25

Weyl and ghost number anomalies in the Polyakov's light-cone gauge

International Nuclear Information System (INIS)

Suzuki, H.

1991-01-01

In this paper the conformal (Weyl) anomaly of the ghost-anti-ghost system in the 2-dimensional quantum gravity is calculated. A background covariant formalism allows us to treat the Polyakov's light-cone gauge in a systematic way. The anomaly gives a contribution to the central charge, -28, which agrees with the result of Kniznik, Polyakov, and Zamolodchikov. The ghost number anomaly is also calculated, and the metric corrections to the naive ghost number current are given. It is suggested that a general scalar density in the light-cone gauge carries a screening ghost number

An introduction to geometric theory of fully nonlinear parabolic equations

International Nuclear Information System (INIS)

Lunardi, A.

1991-01-01

We study a class of nonlinear evolution equations in general Banach space being an abstract version of fully nonlinear parabolic equations. In addition to results of existence, uniqueness and continuous dependence on the data, we give some qualitative results about stability of the stationary solutions, existence and stability of the periodic orbits. We apply such results to some parabolic problems arising from combustion theory. (author). 24 refs

Quantum electrodynamics in the light-front Weyl gauge

International Nuclear Information System (INIS)

Przeszowski, J.; Naus, H.W.; Kalloniatis, A.C.

1996-01-01

We examine (3+1)-dimensional QED quantized in the open-quote open-quote front form close-quote close-quote with finite open-quote open-quote volume close-quote close-quote regularization, namely, in discretized light-cone quantization. Instead of the light-cone or Coulomb gauges, we impose the light-front Weyl gauge A - =0. The Dirac method is used to arrive at the quantum commutation relations for the independent variables. We apply open-quote open-quote quantum-mechanical gauge fixing close-quote close-quote to implement Gauss close-quote law, and derive the physical Hamiltonian in terms of unconstrained variables. As in the instant form, this Hamiltonian is invariant under global residual gauge transformations, namely, displacements. On the light cone the symmetry manifests itself quite differently. copyright 1996 The American Physical Society

Stationary states and rotational properties of spin-orbit-coupled Bose-Einstein condensates held under a toroidal trap

Science.gov (United States)

He, Zhang-Ming; Zhang, Xiao-Fei; Kato, Masaya; Han, Wei; Saito, Hiroki

2018-06-01

We consider a pseudospin-1/2 Bose-Einstein condensate with Rashba spin-orbit coupling in a two-dimensional toroidal trap. By solving the damped Gross-Pitaevskii equations for this system, we show that the system exhibits a rich variety of stationary states, such as vehicle wheel and flower-petal stripe patterns. These stationary states are stable against perturbation with thermal energy and can survive for a long time. In the presence of rotation, our results show that the rotating systems have exotic vortex configurations. These phenomenon originates from the interplay among spin-orbit coupling, trap geometry, and rotation.

On quantization of free fields in stationary space-times

International Nuclear Information System (INIS)

Moreno, C.

1977-01-01

In Section 1 the structure of the infinite-dimensional Hamiltonian system described by the Klein-Gordon equation (free real scalar field) in stationary space-times with closed space sections, is analysed, an existence and uniqueness theorem is given for the Lichnerowicz distribution kernel G 1 together with its proper Fourier expansion, and the Hilbert spaces of frequency-part solutions defined by means of G 1 are constructed. In Section 2 an analysis, a theorem and a construction similar to the above are formulated for the free real field spin 1, mass m>0, in one kind of static space-times. (Auth.)

Basic quantum mechanics for three Dirac equations in a curved spacetime

International Nuclear Information System (INIS)

Arminjon, Mayeul

2010-01-01

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