Showing papers on "Scalar potential published in 2000"

Curvature Singularities: the Good, the Bad, and the Naked

Abstract: Necessary conditions are proposed for the admissibility of singular classical solutions with 3+1-dimensional Poincare invariance to five-dimensional gravity coupled to scalars. Finite temperature considerations and examples from AdS/CFT support the conjecture that the scalar potential must remain bounded above for a solution to be physical. Having imposed some restrictions on naked singularities allows us to comment on a recent proposal for solving the cosmological constant problem.

Noncommutative Solitons

Abstract: We find classically stable solitons (instantons) in odd (even) dimensional scalar noncommutative field theories whose scalar potential, $V(\ph)$, has at least two minima These solutions are bubbles of the false vacuum whose size is set by the scale of noncommutativity Our construction uses the correspondence between non-commutative fields and operators on a single particle Hilbert space In the case of noncommutative gauge theories we note that expanding around a simple solution shifts away the kinetic term and results in a purely quartic action with linearly realised gauge symmetries

Curvature Singularities: the Good, the Bad, and the Naked

Abstract: Necessary conditions are proposed for the admissibility of singular classical solutions with 3+1-dimensional Poincare invariance to five-dimensional gravity coupled to scalars. Finite temperature considerations and examples from AdS/CFT support the conjecture that the scalar potential must remain bounded above for a solution to be physical. Having imposed some restrictions on naked singularities allows us to comment on a recent proposal for solving the cosmological constant problem.

Inflation and quintessence with nonminimal coupling

Abstract: The nonminimal coupling (NMC) of the scalar field to the Ricci curvature is unavoidable in many cosmological scenarios. Inflation and quintessence models based on nonminimally coupled scalar fields are studied, with particular attention to the balance between the scalar potential and the NMC term $\ensuremath{\xi}R{\ensuremath{\varphi}}^{2}/2$ in the action. NMC makes acceleration of the universe harder to achieve for the usual potentials, but it is beneficial in obtaining cosmic acceleration with unusual potentials. The slow-roll approximation with NMC, conformal transformation techniques, and other aspects of the physics of NMC are clarified.

Self-similar cosmological solutions with a nonminimally coupled scalar field

Abstract: We present self-similar cosmological solutions for a barotropic fluid plus scalar field with Brans-Dicke-type coupling to the spacetime curvature and an arbitrary power-law potential energy. We identify all the fixed points in the autonomous phase plane, including a scaling solution where the fluid density scales with the scalar field's kinetic and potential energy. This is related by a conformal transformation to a scaling solution for a scalar field with an exponential potential minimally coupled to the spacetime curvature, but nonminimally coupled to the barotropic fluid. Radiation is automatically decoupled from the scalar field, but energy transfer between the field and nonrelativistic dark matter can lead to a change to an accelerated expansion at late times in the Einstein frame. The scalar field density can mimic a cosmological constant even for steep potentials in the strong-coupling limit.

Q Ball formation in the gravity mediated SUSY breaking scenario

Abstract: We study the formation of Q balls which are made of flat directions that appear in the supersymmetric extension of the standard model in the context of gravity-mediated supersymmetry breaking. The full nonlinear calculations for the dynamics of the complex scalar field are made. Since the scalar potential in this model is flatter than ${\ensuremath{\varphi}}^{2},$ we have found that fluctuations develop and go nonlinear to form nontopological solitons, Q balls. The size of a Q ball is determined by the most amplified mode, which is completely determined by the model parameters. On the other hand, the charge of Q balls depends linearly on the initial charge density of the Affleck-Dine (AD) field. Almost all the charges are absorbed into Q balls, and only a tiny fraction of the charges is carried by a relic AD field. It may lead to some constraints on the baryogenesis and/or parameters in the particle theory. The peculiarity of gravity mediation is the moving Q balls. This results in collisions between Q balls. It may increase the charge of the Q balls, and change its fate.

The cosmological constant problem from a brane-world perspective

Abstract: We point out several subtleties arising in brane-world scenarios of cosmological constant cancellation. We show that solutions with curvature singularities are inconsistent, unless the contribution to the effective four-dimentional cosmological constant of the physics that resolves the singularities is fine-tuned. This holds for both flat and curved branes. Irrespective of this problem, we then study an isolated class of flat solutions in models where a bulk scalar field with a vanishing potential couples to a 3-brane. We give an example where the introduction of a bulk scalar potential results in a non-zero cosmological constant. Finally we comment on the stability of classical solutions of the brane system with respect to quantum corrections.

Constrained motion control using vector potential fields

Abstract: Discusses the generation of a control signal that would instruct the actuators of a robotics manipulator to drive motion along a safe and well-behaved path to a desired target. The proposed concept of navigation control along with the tools necessary for its construction achieve this goal. The most significant tool is the artificial vector potential field which shows a better ability to steer motion than does a scalar potential field. The synthesis procedure emphasizes flexibility so that the effort needed to modify the control is commensurate with the change in the geometry of the workspace. Theoretical development along with simulation results are provided.

Density perturbations arising from multiple field slow-roll inflation

Abstract: In this paper we analyze scalar gravitational perturbations on a Robertson-Walker background in the presence of multiple scalar fields that take values on a (geometrically non-trivial) field manifold during slow-roll inflation. For this purpose modified and generalized slow-roll functions are introduced and their properties examined. These functions make it possible to estimate to what extent the gravitational potential decouples from the scalar field perturbations. The correlation function of the gravitational potential is calculated in an arbitrary state. We argue that using the vacuum state seems a reasonable assumption for those perturbations that can be observed in the CMBR. Various aspects are illustrated by examples with multiple scalar fields that take values on flat and curved manifolds.

Essential self-adjointness for semi-bounded magnetic Schr\"odinger operators on non-compact manifolds

Abstract: We prove essential self-adjointness for semi-bounded below magnetic Schrodinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. Some singularities of the scalar potential are allowed. This is an extension of the Povzner--Wienholtz--Simader theorem. The proof uses the scheme of Wienholtz but requires a refined invariant integration by parts technique, as well as a use of a family of cut-off functions which are constructed by a non-trivial smoothing procedure due to Karcher.

Efficient real-space approach to time-dependent density functional theory for the dielectric response of nonmetallic crystals

Abstract: Time-dependent density functional theory has been used to calculate the static and frequency-dependent dielectric function e(ω) of nonmetallic crystals. We show that a real-space description becomes feasible for crystals by using a combination of a lattice-periodic (microscopic) scalar potential with a uniform (macroscopic) electric field as perturbation in a periodic structure calculation. The induced density and microscopic potential can be obtained self-consistently for fixed macroscopic field by using linear response theory in which Coulomb interactions and exchange-correlation effects are included. We use an iterative scheme, in which density and potential are updated in every cycle. The explicit evaluation of Kohn–Sham response kernels is avoided and their singular behavior as function of the frequency is treated analytically. Coulomb integrals are evaluated efficiently using auxiliary fitfunctions and we apply a screening technique for the lattice sums. The dielectric function can then be obtained from the induced current. We obtained e(ω) for C, Si, and GaAs within the adiabatic local density approximation in good agreement with experiment. In particular in the low-frequency range no adjustment of the local density approximation (LDA) band gap seems to be necessary.

Reconstruction and assessment of the least-squares and slope discrepancy components of the phase.

Abstract: The concept of slope discrepancy developed in the mid-1980’s to assess measurement noise in a wave-front sensor system is shown to have additional contributions that are due to fitting error and branch points. This understanding is facilitated by the development of a new formulation that employs Fourier techniques to decompose the measured gradient field (i.e., wave-front sensor measurements) into two components, one that is expressed as the gradient of a scalar potential and the other that is expressed as the curl of a vector potential. A key feature of the theory presented here is the fact that both components of the phase (one corresponding to each component of the gradient field) are easily reconstructable from the measured gradients. In addition, the scalar and vector potentials are both easily expressible in terms of the measured gradient field. The work concludes with a wave optics simulation example that illustrates the ease with which both components of the phase can be obtained. The results obtained illustrate that branch point effects are not significant until the Rytov number is greater than 0.2. In addition, the branch point contribution to the phase not only is reconstructed from the gradient data but is used to illustrate the significant performance improvement that results when this contribution is included in the correction applied by an adaptive optics system.

Exact Multi-Vortex Solutions in Noncommutative Abelian-Higgs Theory

Abstract: We consider the noncommutative Abelian-Higgs theory and construct new types of exact multi-vortex solutions that solve the static equations of motion. They in general do not follow from the BPS equations; only for some specific values of parameters, they satisfy the BPS equations saturating the Bogomol'nyi bound. We further consider the Abelian-Higgs theory with more complicated scalar potential allowing unstable minima and construct exact solutions of noncommutative false vacuum bubble with integer magnetic flux. The classical stability of the solutions is discussed.

Finite action in 5D gauged supergravity and the dilatonic conformal anomaly for dual quantum field theory

Abstract: Gauged supergravity (SG) with single scalar (dilaton) and arbitrary scalar potential is considered. Such dilatonic gravity describes special RG flows in extended SG where scalars lie in one-dimensional submanifold of total space. The surface counterterm and finite action for such gauged SG in three-, four- and five-dimensional asymptotically AdS space are derived. Using finite action and consistent gravitational stress tensor (local surface counterterm prescription) the regularized expressions for free energy, entropy and mass of d4 dilatonic AdS black hole are found. The same calculation is done within standard reference background subtraction. The dilaton-dependent conformal anomaly from d3 and d5 gauged SGs is calculated using AdS/CFT correspondence. Such anomaly should correspond to two- and four-dimensional dual quantum field theory which is classically (not exactly) conformally invariant, respectively. The candidate c-functions from d3 and d5 SGs are suggested. These c-functions which have fixed points in asymptoticaly AdS region are expressed in terms of dilatonic potential and they are positively defined and monotonic for number of potentials.

A4 model for the quark mass matrices

Abstract: We propose a model for the quark masses and mixings based on an A4 family symmetry. Three scalar SU(2) doublets form a triplet of A4. The three left-handed-quark SU(2) doublets are also united in a triplet of A4. The right-handed quarks are singlets of A4. The A4-symmetric scalar potential leads to a vacuum in which two of the three scalar SU(2) doublets have expectation values with equal moduli. Our model makes an excellent fit of the observed |Vub/Vcb|. CP symmetry is respected in the charged gauge interactions of the quarks.

Variational characterization for eigenvalues of Dirac operators

Abstract: In this paper we give two different variational characterizations for the eigenvalues of H+V where H denotes the free Dirac operator and V is a scalar potential The first one is a min-max involving a Rayleigh quotient The second one consists in minimizing an appropriate nonlinear functional Both methods can be applied to potentials which have singularities as strong as the Coulomb potential

A method of moments solution for electromagnetic scattering by inhomogeneous dielectric bodies of revolution

Abstract: A method of calculating the electromagnetic scattering from and internal field distribution of inhomogeneous dielectric bodies of revolution (BOR) is presented. The method uses a typical mode-by-mode solution scheme. The electric flux density is chosen as the unknown quantity, which, together with the special construction of basis and testing functions, enables considerable reduction of the number of unknowns. A key element in this technique is expressing of the azimuthal field components of basis functions in terms of transverse components. A Galerkin testing procedure is used, with special attention put on the efficiency of calculating scalar potential term. Results of calculation for a few classes of dielectric bodies are given and compared with calculations done by other authors.

Generalized compactification and assisted dynamics of multi-scalar-field cosmologies

Abstract: Cosmological models arising from a generalized compactification of Einstein gravity are derived. It is shown that a redefinition of the moduli fields reduces the system to a set of massless fields and a single field with a single exponential potential, independent of the background spacetime. This solution is the unique late--time attractor for an arbitrary spacetime dimensionality. We find that if the number of dimensions is greater than or equal to seven, the scalar fields dominate a relativistic fluid and therefore constitute a potential `moduli' problem.

Edge finite element analysis of transient skin effect problems

Abstract: Formulation of transient skin effect problems in terms of potentials are presented. In case of a prescribed voltage, a magnetic vector potential and an electric scalar potential and, if the current is given, a current vector potential and a magnetic scalar potential are used. The boundary value problems are numerically solved by means of edge finite element techniques. The analysis of a complicated high power bus bar arrangement is presented as a numerical example.

Stability of Global Monopoles Revisited

Abstract: We analyze the stability of global O(3) monopoles in the infinite cutoff (or scalar mass) limit. We obtain the perturbation equations and prove that the spherically symmetric solution is classically stable (or neutrally stable) to axially symmetric, square integrable, or power-law decay perturbations. Moreover, we show that, in spite of the existence of a conserved topological charge, the energy barrier between the monopole and the vacuum is finite even in the limit where the cutoff is taken to infinity. This feature is specific of global monopoles and independent of the details of the scalar potential.

Three-Dimensional SCFTs, Supersymmetric Domain Wall and Renormalization Group Flow

Abstract: By analyzing SU(3)xU(1) invariant stationary point, studied earlier by Nicolai and Warner, of gauged N=8 supergravity, we find that the deformation of S^7 gives rise to nontrivial renormalization group flow in a three-dimensional boundary super conformal field theory from N=8, SO(8) invariant UV fixed point to N=2, SU(3)xU(1) invariant IR fixed point. By explicitly constructing 28-beins u, v fields, that are an element of fundamental 56-dimensional representation of E_7, in terms of scalar and pseudo-scalar fields of gauged N=8 supergravity, we get A_1, A_2 tensors. Then we identify one of the eigenvalues of A_1 tensor with ``superpotential'' of de Wit-Nicolai scalar potential and discuss four-dimensional supergravity description of renormalization group flow, i.e. the BPS domain wall solutions which are equivalent to vanishing of variation of spin 1/2, 3/2 fields in the supersymmetry preserving bosonic background of gauged N=8 supergravity. A numerical analysis of the steepest descent equations interpolating two critical points is given.

UV/IR Mixing for Noncommutative Complex Scalar Field Theory, II (Interaction 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.

Localized Gravity and Higher Curvature Terms

Abstract: We consider localization of gravity in smooth domain wall solutions of gravity coupled to a scalar field with a generic potential in the presence of the Gauss-Bonnet term. We discuss conditions on the scalar potential such that domain wall solutions are non-singular. We point out that the presence of the Gauss-Bonnet term does not allow flat solutions with localized gravity that violate the weak energy condition. We also point out that in the presence of the Gauss-Bonnet term infinite tension flat domain walls violate positivity. In fact, for flat solutions unitarity requires that on the solution the scalar potential be bounded below.