Showing papers on "Scalar potential published in 2001"

Scalar hair on the black hole in asymptotically anti--de Sitter spacetime

Abstract: We examine the no-hair conjecture in asymptotically anti--de Sitter (AdS) spacetime. First, we consider a real scalar field as the matter field and assume static spherically symmetric spacetime. Analysis of the asymptotics shows that the scalar field must approach the extremum of its potential. Using this fact, it is proved that there is no regular black hole solution when the scalar field is massless or has a 'convex' potential. Surprisingly, while the scalar field has a growing mode around the local minimum of the potential, there is no growing mode around the local maximum. This implies that the local maximum is a kind of 'attractor' of the asymptotic scalar field. We give two examples of the new black hole solutions with a nontrivial scalar field configuration numerically in the symmetric or asymmetric double well potential models. We study the stability of these solutions by using the linear perturbation method in order to examine whether or not the scalar hair is physical. In the symmetric double well potential model, we find that the potential function of the perturbation equation is positive semidefinite in some wide parameter range and that the new solution is stable. This implies that the black hole no-hair more » conjecture is violated in asymptotically AdS spacetime. « less

Scaling solutions and reconstruction of scalar field potentials

Abstract: Starting from the hypothesis of scaling solutions, the general exact form of the scalar field potential is found In the case of two fluids, it turns out to be a negative power of hyperbolic sine In the case of three fluids the analytic form is not found, but is obtained by quadratures

On fermion masses, gradient flows and potential in supersymmetric theories.

Abstract: In any low energy effective supergravity theory general formulae exist which allow one to discuss fermion masses, the scalar potential and breaking of symmetries in a model independent set up. A particular role in this discussion is played by Killing vectors and Killing prepotentials. We outline these relations in general and specify then in the context of N = 1 and N = 2 supergravities in four dimensions. Useful relations of gauged quaternionic geometry underlying hypermultiplets dynamics are discussed.

On different approaches to calculating lightning electric fields

Abstract: Three different approaches to the computation of lightning electric fields are compared. These approaches are the traditional dipole (Lorentz condition) technique and two versions of the monopole (continuity equation) technique. The latter two techniques are based on two different formulations of the continuity equation, one used by Thottappillil et al. [1997] and the other by Thomson [1999], the difference between the formulations being related to different treatments of retardation effects. The three approaches involve the same expression for the vector potential but different expressions for the scalar potential. It is analytically shown that the three different expressions for the scalar potential are equivalent and satisfy the Lorentz condition. Further, the three approaches yield the same total fields and the same Poynting vectors. However, expressions in the three approaches for the individual electric field components in the time domain, traditionally identified by their distance dependence as electrostatic, induction, and radiation terms, are different, suggesting that explicit distance dependence is not an adequate identifier. It is shown that the so identified individual field components in the electric field equation in terms of charge density derived by Thottappillil et al. [1997] are equivalent to the corresponding field components in the traditional equation for electric field in terms of current based on the dipole technique. However, the individual field components in the electric field equation based on Thomson's [1999] approach are not equivalent to their counterparts in the traditional dipole technique equation. Further, in Thottappillil et al.'s [1997] technique and in the traditional dipole technique, the gradient of scalar potential contributes to all three electric field components, while in Thomson's [1999] technique it contributes only to the electrostatic and induction components. Calculations of electric fields at different distances from the lightning channel show that the differences between the corresponding field components identified by their distance dependence in different techniques are considerable at close ranges but become negligible at far ranges.

Oscillatons revisited

Abstract: In this paper, we study some interesting properties of a spherically symmetric oscillating soliton star made of a real time-dependent scalar field which is called an oscillaton The known final configuration of an oscillaton consists of a stationary stage in which the scalar field and the metric coefficients oscillate in time if the scalar potential is quadratic The differential equations that arise in the simplest approximation, that of coherent scalar oscillations, are presented for a quadratic scalar potential This allows us to take a closer look at the interesting properties of these oscillating objects The leading terms of the solutions considering a quartic and a cosh scalar potentials are worked in the so called stationary limit procedure This procedure reveals the form in which oscillatons and boson stars may be related and useful information about oscillatons is obtained from the known results of boson stars Oscillatons could compete with boson stars as interesting astrophysical objects, since they would be predicted by scalar field dark matter models

Domain walls with localized gravity and domain-wall/quantum field theory correspondence

Abstract: We review general domain-wall solutions supported by a delta-function source, together with a single pure exponential scalar potential in supergravity. These scalar potentials arise from a sphere reduction in M theory or string theory. There are several examples of flat (BPS) domain walls that lead to a localization of gravity on the brane, and for these we obtain the form of the corrections to Newtonian gravity. These solutions are lifted back on certain internal spheres to D=11 and D=10 as M-branes and D-branes. We find that the domain walls that can trap gravity yield M-branes or Dp-branes that have a natural decoupling limit, i.e., p{<=}5, with the delta-function source providing an ultraviolet cutoff in a dual quantum field theory. This suggests that the localization of gravity can generally be realized within a domain-wall/QFT correspondence, with the delta-function domain-wall source providing a cutoff from the space-time boundary for these domain-wall solutions. We also discuss the form of the one-loop corrections to the graviton propagator from the boundary QFT that would reproduce the corrections to the Newtonian gravity on the domain wall.

Time‐domain electric‐field integral equation with central finite difference

Abstract: In this paper, we present a new formulation using the time-domain electric-field integral equation (TD–EFIE) to obtain a transient scattering response from arbitrarily shaped conducting bodies The time derivative of the magnetic vector potential is approximated with a central finite difference, and the scalar potential is time averaged by dividing it into two terms This approach with an implicit method using central-difference results in accurate and stable transient scattering responses from conducting objects Detailed mathematical steps are included, and several numerical results are presented © 2001 John Wiley & Sons, Inc Microwave Opt Technol Lett 31: 429–435, 2001

UV/IR mixing for noncommutative complex scalar field theory interacting with gauge fields

Abstract: We consider noncommutative analogs of scalar electrodynamics and N = 2 D = 4 SUSY Yang-Mills theory. We show that one-loop renormalizability of noncommutative scalar electrodynamics requires the scalar potential to be an anticommutator squared. This form of the scalar potential differs from the one expected from the point of view of noncommutative gauge theories with extended SUSY containing a square of commutator. We show that fermion contributions restore the commutator in the scalar potential. This provides one-loop renormalizability of noncommutative N = 2 SUSY gauge theory. We demonstrate a presence of non-integrable IR singularities in noncommutative scalar electrodynamics for general coupling constants. We find that for a special ratio of coupling constants these IR singularities vanish. Also we show that IR poles are absent in noncommutative N = 2 SUSY gauge theory.

Generalized slow-roll conditions and the possibility of intermediate scale inflation in scalar-tensor theory

Abstract: Generalized slow-roll conditions and parameters are obtained for a general form of scalar-tensor theory (with no external sources), having arbitrary functions describing a non-minimal gravitational coupling F(), a Kahler-like kinetic function k(), and a scalar potential V(). These results are then used to analyse a simple toy model example of chaotic inflation with a single scalar field and a standard Higgs potential and a simple gravitational coupling function. In this type of model inflation can occur with inflaton field values at an intermediate scale of roughly 1011 GeV when the particle physics symmetry-breaking scale is approximately 1 TeV, provided that the theory is realized within the Jordan frame. If the theory is realized in the Einstein frame, however, the intermediate scale inflation does not occur.

Brane worlds with bolts

Abstract: We construct a family of (p+3)-dimensional brane worlds in which the brane has one compact extra dimension, the bulk has two extra dimensions, and the bulk closes regularly at codimension two submanifolds known as bolts. The (p+1)-dimensional low energy spacetime M_{low} may be any Einstein space with an arbitrary cosmological constant, the value of the bulk cosmological constant is arbitrary, and the only fields are the metric and a bulk Maxwell field. The brane can be chosen to have positive tension, and the closure of the bulk provides a singularity-free boundary condition for solutions that contain black holes or gravitational waves in M_{low}. The spacetimes admit a nonlinear gravitational wave whose properties suggest that the Newtonian gravitational potential on a flat M_{low} will behave essentially as the static potential of a massless minimally coupled scalar field with Neumann boundary conditions. When M_{low} is (p+1)-dimensional Minkowski with p\ge3 and the bulk cosmological constant vanishes, this static scalar potential is shown to have the long distance behaviour characteristic of p spatial dimensions.

Application of a new MPIE formulation to the analysis of a dielectric resonator embedded in a multilayered medium coupled to a microstrip circuit

Abstract: A new mixed-potential integral-equation (MPIE) formulation is developed for the analysis of electromagnetic problems due to conducting or dielectric objects of arbitrary shape embedded in a planarly stratified medium. In the new MPIE formulation, the dyadic kernel of the vector potential is kept in the simple form originally developed by Sommerfeld. The scalar potential, which is related to the vector potential via the Lorenz gauge, is then represented by a double dot product of a dyadic kernel with a dyadic charge density. An extra line integral term, which is well behaved and nonsingular, will appear when the object penetrates an interface. The numerical implementation of the double dot product is found to be trivial if one takes advantage of the well-established basis functions in which the unknown current density is expressed. The new MPIE formulation is employed in conjunction with the triangular patch model to treat the problem of a dielectric resonator (DR) excited by microstrip circuit. A matched-load simulation procedure has been used to extract the network S-parameters of a DR microstrip circuit. The diameters of the Q circles have been measured to determine the coupling coefficients and the Q factors of the DR excited by a microstrip circuit. The validity of the new MPIE formulation and the numerical procedure have been verified by comparing the obtained S-parameters, with available measurement data.

Static charge coupling of intrinsic Josephson junctions

Abstract: A microscopic theory for the coupling of intrinsic Josephson oscillations due to charge fluctuations on the quasi-two-dimensional superconducting layers is presented. Thereby in close analogy to the normal state the effect of the scalar potential on the transport current is taken into account consistently. The dispersion of collective modes is derived and an estimate of the coupling constant is given. It is shown that the correct treatment of the quasiparticle current is essential in order to get the correct position of Shapiro steps. In this case the influence of the coupling on dc properties like the I – V curve is negligible.

Violation of the gauge equivalence

Abstract: F V Gubarev et al (``On the significance of the vector potential squared'', Phys Rev Lett 86, 2220) have argued that the vector potential itself may have physical meaning, in defiance of the gauge equivalence principle Earlier R I Khrapko proposed a gauge noninvariant electrodynamics spin tensor (``Spin density of electromagnetic waves'') The standard electrodynamics spin tensor is zero Here we point out that the Biot-Savarat formula uniquely results in a preferred, "true" vector potential field which is generated from a given magnetic field A similar integral formula uniquely permits to find a "true" scalar potential field generated from a given electric field even in the case of a nonpotential electric field A conception of differential forms is used We say that an exterior derivative of a form is the boundary of this form and the integration of a form by the Biot-Savarat-type formula results in a new form named the generation Generating from a generation yields zero The boundary of a boundary is zero A boundary is closed A generation is sterile A conjugation is considered The conjugation converts closed forms to sterile forms and back It permits to construct chains of forms The conjunction differs from the Hodge star operation: the conjugation does not imply the dualization A circularly polarized wave is considered in view of the electrodynamics spin tensor problem A new anthropic principle is presented

The Covariant Stark Effect

Abstract: This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schrodinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the nonrelativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire an imaginary part which is linear in the applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformations on the invariant evolution parameter.

Pauli operator and Aharonov Casher theorem for measure valued magnetic fields

Abstract: We define the two dimensional Pauli operator and identify its core for magnetic fields that are regular Borel measures. The magnetic field is generated by a scalar potential hence we bypass the usual $\bA\in L^2_{loc}$ condition on the vector potential which does not allow to consider such singular fields. We extend the Aharonov-Casher theorem for magnetic fields that are measures with finite total variation and we present a counterexample in case of infinite total variation. One of the key technical tools is a weighted $L^2$ estimate on a singular integral operator.

The Covariant Stark Effect

Abstract: This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schrodinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the non-relativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire an imaginary part which is lnear in the applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformations on the invariant evolution parameter.

F(4) supergravity and 5D superconformal field theories

Abstract: We report on the construction of D = 6 N = 2 supergravity based on the F(4) exceptional supergroup, coupled to an arbitrary number of vector multiplets The main results are the construction of the scalar potential, both in the massless and the massive case, and the explicit correspondence between the supermultiplets and the conformal field theory operators at the boundary of the six-dimensional AdS space

Charged perfect fluid and scalar field coupled to gravity

Abstract: Charged perfect fluid with vanishing Lorentz force and massless scalar field is studied for the case of stationary cylindrically symmetric spacetime. The scalar field can depend both on radial and longitudinal coordinates. Solutions are found and classified according to scalar field gradient and magnetic field relationship. Their physical and geometrical properties are examined and discussion of particular cases, directly generalizing Godel-type spacetimes, is presented.

Interaction effects in non-Hermitian models of vortex physics

Abstract: Vortex lines in superconductors in an external magnetic field slightly tilted from randomly distributed parallel columnar defects can be modeled by a system of interacting bosons in a non-Hermitian vector potential and a random scalar potential We develop a theory of the strongly disordered non-Hermitian boson Hubbard model using the Hartree-Bogoliubov approximation and apply it to calculate the complex energy spectra, the vortex tilt angle, and the tilt modulus of $(1+1)$-dimensional directed flux line systems We construct the phase diagram associated with the flux-liquid to Bose-glass transition and find that, close to the phase boundary, the tilted flux-liquid phase is characterized by a band of localized excitations, with two mobility edges in its low-energy spectrum

Calculation of electric fields in a multiple cylindrical volume conductor induced by magnetic coils

Abstract: A method is presented for calculating the electric field, that is induced in a cylindrical volume conductor by an alternating electrical current through a magnetic coil of arbitrary shape and position. The volume conductor is modeled as a set of concentric, infinitely long, homogeneous cylinders embedded in an outer space that extends to infinity. An analytic expression of the primary electric field induced by the magnetic coil, assuming quasi-static conditions, is combined with the analytic solution of the induced electric scalar potential due to the inhomogeneities of the volume conductor at the cylindrical interfaces. The latter is obtained by the method of separation of variables based on expansion with modified Bessel functions. Numerical results are presented for the case of two cylinders representing a nerve bundle with perineurium. An active cable model of a myelinated nerve fiber is included, and the effect of the nerve fiber's undulation is shown.

Theoretical development of laboratory techniques for magnetic measurement of large objects

Abstract: Equations that relate magnetic gradiometric measurements over a closed surface to the prolate spheroidal multipole moments of an object can be used to remove the uniform inducing field of a magnetic calibration facility's coil system, along with the Earth's background field, from the signature of a large test object without requiring it to be moved. This paper presents an example that shows how the equations can be used to determine the optimum number, orientation, and position of gradiometers for accurate extrapolation of the object's field signatures. In addition, it gives generalized boundary conditions that guarantee unique extrapolations of magnetic field, up to an additive constant, from a closed measurement surface instrumented only with gradiometers.

Propagation of Wave Packets and its Applications

Abstract: The purpose of this talk is to study propagation of microlocal singularities of solutions to the Schrodinger equations with magnetic vector or electric scalar potential. The Hamiltonian may grow quadratically at infinity. We will present a new powerful approach based on a microlocal conservation law in terms of the Wigner transformation of the solutions. Our method enables us to give precise information on the evolution of the wave packets of solutions in the sense of A. Cordoba and C. Fefferman. As a result, we can show reconstruction of microlocal singularities and creation of singularities from oscillatory initial data as well as smoothing effects of solutions.