Phi-four solitary waves in a parabolic potentia: existence, stability, and collisional dynamics

We explore a φ4 model with an added external parabolic potential term. This term dramatically alters the spectral properties of the system. We identify single and multiple kink solutions and examine their stability features; importantly, all of the stationary structures turn out to be unstable. We complement these with a dynamical study of the evolution of a single kink in the trap, as well as of the scattering of kink and anti-kink solutions of the model. We observe that some of the key characteristics of kink-antikink collisions, such as the critical velocity and the multi-bounce windows, are sensitively dependent on the trap strength parameter, as well as the initial displacement of the kink and antikink.Accepted manuscrip

Prepyramid-to-pyramid transition of SiGe islands on Si(001)

The morphology of the first three-dimensional islands appearing during strained growth of SiGe alloys on Si(001) was investigated by scanning tunneling microscopy. High resolution images of individual islands and a statistical analysis of island shapes were used to reconstruct the evolution of the island shape as a function of size. As they grow, islands undergo a transition from completely unfacetted rough mounds (prepyramids) to partially {105} facetted islands and then they gradually evolve to {105} facetted pyramids. The results are in good agreement with the predictions of a recently proposed theoretical model

On Witten's Instability and Winding Tachyons

We investigate, from a spacetime perspective, some aspects of Horowitz's recent conjecture that black strings may catalyze the decay of Kaluza-Klein spacetimes into a bubble of nothing. We identify classical configurations that interpolate between flat space and the bubble, and discuss the energetics of the transition. We investigate the effects of winding tachyons on the size and shape of the barrier and find no evidence at large compactification radius that tachyons enhance the tunneling rate. For the interesting radii, of order the string scale, the question is difficult to answer due to the failure of the $\alpha^\prime$ expansion.Comment: 15 pages, 2 figures, Late

Twin Paradox and the logical foundation of relativity theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization SpecRel of special relativity from the literature. SpecRel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in SpecRel. As it turns out, this is practically equivalent to asking whether SpecRel is strong enough to "handle" (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to SpecRel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of SpecRel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that the Twin Paradox becomes provable in AccRel, but it is not provable without IND.Comment: 24 pages, 6 figure

The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes

This work considers the way that quantum loop effects modify the propagation of light in curved space. The calculation of the refractive index for scalar QED is reviewed and then extended for the first time to QED with spinor particles in the loop. It is shown how, in both cases, the low frequency phase velocity can be greater than c, as found originally by Drummond and Hathrell, but causality is respected in the sense that retarded Green functions vanish outside the lightcone. A "phenomenology" of the refractive index is then presented for black holes, FRW universes and gravitational waves. In some cases, some of the polarization states propagate with a refractive index having a negative imaginary part indicating a potential breakdown of the optical theorem in curved space and possible instabilities.Comment: 62 pages, 14 figures, some signs corrected in formulae and graph

Lodged in the throat: Internal infinities and AdS/CFT

In the context of AdS3/CFT2, we address spacetimes with a certain sort of internal infinity as typified by the extreme BTZ black hole. The internal infinity is a null circle lying at the end of the black hole's infinite throat. We argue that such spacetimes may be described by a product CFT of the form CFT-L * CFT-R, where CFT-R is associated with the asymptotically AdS boundary while CFT-L is associated with the null circle. Our particular calculations analyze the CFT dual of the extreme BTZ black hole in a linear toy model of AdS3/CFT2. Since the BTZ black hole is a quotient of AdS3, the dual CFT state is a corresponding quotient of the CFT vacuum state. This state turns out to live in the aforementioned product CFT. We discuss this result in the context of general issues of AdS/CFT duality and entanglement entropy.Comment: 11 pages, 2 figures; v2 - some typos corrected, minor revision

Superconducting p-branes and Extremal Black Holes

In Einstein-Maxwell theory, magnetic flux lines are `expelled' from a black hole as extremality is approached, in the sense that the component of the field strength normal to the horizon goes to zero. Thus, extremal black holes are found to exhibit the sort of `Meissner effect' which is characteristic of superconducting media. We review some of the evidence for this effect, and do present new evidence for it using recently found black hole solutions in string theory and Kaluza-Klein theory. We also present some new solutions, which arise naturally in string theory, which are non-superconducting extremal black holes. We present a nice geometrical interpretation of these effects derived by looking carefully at the higher dimensional configurations from which the lower dimensional black hole solutions are obtained. We show that other extremal solitonic objects in string theory (such as p-branes) can also display superconducting properties. In particular, we argue that the relativistic London equation will hold on the worldvolume of `light' superconducting p-branes (which are embedded in flat space), and that minimally coupled zero modes will propagate in the adS factor of the near-horizon geometries of `heavy', or gravitating, superconducting p-branes.Comment: 22 pages, 2 figure

Implications of the HERA Events for the R-Parity Breaking SUSY Signals at Tevatron

The favoured R-parity violating SUSY scenarios for the anomalous HERA events correspond to top and charm squark production via the $\lambda'_{131}$ and $\lambda'_{121}$ couplings. In both cases the corresponding electronic branching fractions of the squarks are expected to be $\ll 1$. Consequently the canonical leptoquark signature is incapable of probing these scenarios at the Tevatron collider over most of the MSSM parameter space. We suggest alternative signatures for probing them at Tevatron, which seem to be viable over the entire range of MSSM parameters.Comment: 20 pages Latex file with 4 ps files containing 4 figure

Neutrino masses in R-parity violating supersymmetric models

We study neutrino masses and mixing in R-parity violating supersymmetric models with generic soft supersymmetry breaking terms. Neutrinos acquire masses from various sources: Tree level neutrino--neutralino mixing and loop effects proportional to bilinear and/or trilinear R-parity violating parameters. Each of these contributions is controlled by different parameters and have different suppression or enhancement factors which we identified. Within an Abelian horizontal symmetry framework these factors are related and specific predictions can be made. We found that the main contributions to the neutrino masses are from the tree level and the bilinear loops and that the observed neutrino data can be accommodated once mild fine-tuning is allowed.Comment: 18 pages; minor typos corrected. To be published in Physical Review

An overview of Polaroid sun eyewear: Function, application and market

Patients are constantly looking for the newest technologies that will assist them in accomplishing the activities that they desire more comfortably and efficiently, in both their personal and professional lives. It is our responsibility as primary care practitioners to be current with the latest advancement in ophthalmic therapies, and effectively pass this knowledge on to our patients. This paper will encompass the properties of specialty protective sun eyewear, emphasizing polarized sunglasses, and how they can be incorporated into a private practice as a viable profit center. The intent is to provide the practitioner with a general overview of the basic properties of light and the history of polarized sunglasses and the functional benefits that they may offer consumers. This review will help to enable a practitioner to feel confident and more comfortable in prescribing and recommending these specialty performance lenses to their patients