Alkali oxide-tantalum, niobium and antimony oxide ionic conductors

The phase equilibrium relations of four systems were investigated in detail. These consisted of sodium and potassium antimonates with antimony oxide and tantalum and niobium oxide with rubidium oxide as far as the ratio 4Rb2O:llB2O5 (B=Nb, Ta). The ternary system NaSbO3-Sb2O4-NaF was investigated extensively to determine the actual composition of the body centered cubic sodium antimonate. Various other binary and ternary oxide systems involving alkali oxides were examined in lesser detail. The phases synthesized were screened by ion exchange methods to determine mobility of the mobility of the alkali ion within the niobium, tantalum or antimony oxide (fluoride) structural framework. Five structure types warranted further investigation; these structure types are (1) hexagonal tungsten bronze (HTB), (2) pyrochlore, (3) the hybrid HTB-pyrochlore hexagonal ordered phases, (4) body centered cubic antimonates and (5) 2K2O:3Nb2O5. Although all of these phases exhibit good ion exchange properties only the pyrochlore was prepared with Na(+) ions as an equilibrium phase and as a low porosity ceramic. Sb(+3) in the channel interferes with ionic conductivity in this case, although relatively good ionic conductivity was found for the metastable Na(+) ion exchanged analogs of RbTa2O5F and KTaWO6 pyrochlore phases

Diffractive Higgs Production by AdS Pomeron Fusion

The double diffractive Higgs production at central rapidity is formulated in terms of the fusion of two AdS gravitons/Pomerons first introduced by Brower, Polchinski, Strassler and Tan in elastic scattering. Here we propose a simple self-consistent holographic framework capable of providing phenomenologically compelling estimates of diffractive cross sections at the LHC. As in the traditional weak coupling approach, we anticipate that several phenomenological parameters must be tested and calibrated through factorization for a self-consistent description of other diffractive process such as total cross sections, deep inelastic scattering and heavy quark production in the central region.Comment: 53 pages, 8 figure

Lagrangian planetary equations in Schwarzschild space--time

We have developed a method to study the effects of a perturbation to the motion of a test point--like object in a Schwarzschild spacetime. Such a method is the extension of the Lagrangian planetary equations of classical celestial mechanics into the framework of the full theory of general relativity. The method provides a natural approach to account for relativistic effects in the unperturbed problem in an exact way.Comment: 7 pages; revtex; accepted for publication in Class. Quantum Gra

Effective Field Theories

Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low ultraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term which is quadratic in the fields, and physical predictions can be read straight from the effective Lagrangean. Methods will be discussed how to compute an effective low energy action from a given fundamental action, either analytically or numerically, or by a combination of both methods. Basically,the idea is to integrate out the high frequency components of fields. This requires the choice of a "blockspin",i.e. the specification of a low frequency field as a function of the fundamental fields. These blockspins will be the fields of the effective field theory. The blockspin need not be a field of the same type as one of the fundamental fields, and it may be composite. Special features of blockspins in nonabelian gauge theories will be discussed in some detail. In analytical work and in multigrid updating schemes one needs interpolation kernels \A from coarse to fine grid in addition to the averaging kernels $C$ which determines the blockspin. A neural net strategy for finding optimal kernels is presented. Numerical methods are applicable to obtain actions of effective theories on lattices of finite volume. The constraint effective potential) is of particular interest. In a Higgs model it yields the free energy, considered as a function of a gauge covariant magnetization. Its shape determines the phase structure of the theory. Its loop expansion with and without gauge fields can be used to determine finite size corrections to numerical data.Comment: 45 pages, 9 figs., preprint DESY 92-070 (figs. 3-9 added in ps format

Deep Inelastic Scattering in Conformal QCD

We consider the Regge limit of a CFT correlation function of two vector and two scalar operators, as appropriate to study small-x deep inelastic scattering in N=4 SYM or in QCD assuming approximate conformal symmetry. After clarifying the nature of the Regge limit for a CFT correlator, we use its conformal partial wave expansion to obtain an impact parameter representation encoding the exchange of a spin j Reggeon for any value of the coupling constant. The CFT impact parameter space is the three-dimensional hyperbolic space H3, which is the impact parameter space for high energy scattering in the dual AdS space. We determine the small-x structure functions associated to the exchange of a Reggeon. We discuss unitarization from the point of view of scattering in AdS and comment on the validity of the eikonal approximation. We then focus on the weak coupling limit of the theory where the amplitude is dominated by the exchange of the BFKL pomeron. Conformal invariance fixes the form of the vector impact factor and its decomposition in transverse spin 0 and spin 2 components. Our formalism reproduces exactly the general results predict by the Regge theory, both for a scalar target and for gamma*-gamma* scattering. We compute current impact factors for the specific examples of N=4 SYM and QCD, obtaining very simple results. In the case of the R-current of N=4 SYM, we show that the transverse spin 2 component vanishes. We conjecture that the impact factors of all chiral primary operators of N=4 SYM only have components with 0 transverse spin.Comment: 44+16 pages, 7 figures. Some correction

The Dynamics of a Meandering River

We present a statistical model of a meandering river on an alluvial plane which is motivated by the physical non-linear dynamics of the river channel migration and by describing heterogeneity of the terrain by noise. We study the dynamics analytically and numerically. The motion of the river channel is unstable and we show that by inclusion of the formation of ox-bow lakes, the system may be stabilised. We then calculate the steady state and show that it is in agreement with simulations and measurements of field data.Comment: Revtex, 12 pages, 2 postscript figure

On The Pomeron at Large 't Hooft Coupling

We begin the process of unitarizing the Pomeron at large 't Hooft coupling. We do so first in the conformal regime, which applies to good accuracy to a number of real and toy problems in QCD. We rewrite the conformal Pomeron in the $J$-plane and transverse position space, and then work out the eikonal approximation to multiple Pomeron exchange. This is done in the context of a more general treatment of the complex $J$-plane and the geometric consequences of conformal invariance. The methods required are direct generalizations of our previous work on single Pomeron exchange and on multiple graviton exchange in AdS space, and should form a starting point for other investigations. We consider unitarity and saturation in the conformal regime, noting elastic and absorptive effects, and exploring where different processes dominate. Our methods extend to confining theories and we briefly consider the Pomeron kernel in this context. Though there is important model dependence that requires detailed consideration, the eikonal approximation indicates that the Froissart bound is generically both satisfied and saturated.Comment: 63 pages, 7 figures; published version: references updated and several typos correcte

Odderon in baryon-baryon scattering from the AdS/CFT correspondence

Based on the AdS/CFT correspondence, we present a holographic description of various C-odd exchanges in high energy baryon-baryon and baryon-antibaryon scattering, and calculate their respective contributions to the difference in the total cross sections. We predict that, due to the warp factor of AdS_5, the total cross section in pp collisions is larger than in p\bar{p} collisions at asymptotically high energies.Comment: 23 pages, v2: minor changes, to be published in JHE

Eikonal Methods in AdS/CFT: BFKL Pomeron at Weak Coupling

We consider correlators of N=4 super Yang Mills of the form A ~ < O_1 O_2 O*_1 O*_2 >, where the operators O_1 and O_2 are scalar primaries. In particular, we analyze this correlator in the planar limit and in a Lorentzian regime corresponding to high energy interactions in AdS. The planar amplitude is dominated by a Regge pole whose nature varies as a function of the 't Hooft coupling g^2. At large g, the pole corresponds to graviton exchange in AdS, whereas at weak g, the pole is that of the hard perturbative BFKL pomeron. We concentrate on the weak coupling regime and analyze pomeron exchange directly in position space. The analysis relies heavily on the conformal symmetry of the transverse space E^2 and of its holographic dual hyperbolic space H_3, describing with an unified language, both the weak and strong 't Hooft coupling regimes. In particular, the form of the impact factors is highly constrained in position space by conformal invariance. Finally, the analysis suggests a possible AdS eikonal resummation of multi-pomeron exchanges implementing AdS unitarity, which differs from the usual 4-dimensional eikonal exponentiation. Relations to violations of 4-dimensional unitarity at high energy and to the onset of nonlinear effects and gluon saturation become immediate questions for future research.Comment: 42 pages, 13 figure

Survival probability of large rapidity gaps in QCD and N=4 SYM motivated model

In this paper we present a self consistent theoretical approach for the calculation of the Survival Probability for central dijet production . These calculations are performed in a model of high energy soft interactions based on two ingredients:(i) the results of N=4 SYM, which at the moment is the only theory that is able to deal with a large coupling constant; and (ii) the required matching with high energy QCD. Assuming, in accordance with these prerequisites, that soft Pomeron intercept is rather large and the slope of the Pomeron trajectory is equal to zero, we derive analytical formulae that sum both enhanced and semi-enhanced diagrams for elastic and diffractive amplitudes. Using parameters obtained from a fit to the available experimental data, we calculate the Survival Probability for central dijet production at energies accessible at the LHC. The results presented here which include the contribution of semi-enhanced and net diagrams, are considerably larger than our previous estimates.Comment: 11 pages, 10 pictures in .eps file