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Publication How Physicists Get Started Thinking About New Phenomena(2024-07-26) Nelson, Philip C.Main ideas of dimensional reasoning are outlined starting with high-school physics and arriving at Planck's universal units.Publication Physics 5516: Electromagnetic Phenomena (Fall 2023)(2023-11-14) Nelson, Philip CThese course notes are made publicly available in the hope that they will be useful. All reports of errata will be gratefully received. I will also be glad to hear from anyone who reads them, whether or not you find errors: pcn@upenn.edu.Publication Warped Resolved La,b,c Cones(2008-06-03) Cvetič, Mirjam; Vázquez-Poritz, J. F.We construct supergravity solutions describing a stack of D3-branes localized at a point on a blown-up cycle of a resolved La,b,c cone. The geometry flows from AdS5 × La,b,c to AdS5 × S5 × Zk. The corresponding quiver gauge theory undergoes a renormalization group flow between two superconformal fixed points, which leads to semi-infinite chains of flows between the various La;b;c fixed points. The general system is described by a triplet of Heun equations, which can each be solved by an expansion with a three-term recursion relation, though there are closed-form solutions for certain cases. This enables us to read off the operators that acquire nonzero vacuum expectation values as the quiver gauge theory flows away from a fixed point.Publication Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator(2008-03-06) Fu, Liang; Kane, Charles LWe study the proximity effect between an s-wave superconductor and the surface states of a strong topological insulator. The resulting two-dimensional state resembles a spinless px + ipy superconductor, but does not break time reversal symmetry. This state supports Majorana bound states at vortices. We show that linear junctions between superconductors mediated by the topological insulator form a nonchiral one-dimensional wire for Majorana fermions, and that circuits formed from these junctions provide a method for creating, manipulating, and fusing Majorana bound states.Publication Anomalous Elasticity in Nematic and Smectic Elastomer Tubule Phases(2008-09-03) Stenull, OlafWe study anomalous elasticity in the tubule phases of nematic and smectic elastomer membranes, which are flat in one direction and crumpled in another. These phases share the same macroscopic symmetry properties including spontaneously broken in-plane isotropy and hence belong to the same universality class. Below an upper critical value Dc=3 of the membranes’ intrinsic dimension D, thermal fluctuations renormalize the elasticity with respect to elastic displacements along the tubule axis so that elastic moduli for compression along the tubule axis and for bending the tubule axis become length-scale dependent. This anomalous elasticity belongs to the same universality class as that of d-dimensional conventional smectic liquid crystals with D taking on the role of d. For physical tubule phases, D=2, this anomaly is of power-law type and thus might by easier to detect experimentally than the logarithmic anomaly in conventional smectics.Publication Casimir Effect for Massless Fermions in One Dimension: A Force-Operator Approach(2008-12-30) Zhabinskaya, Dina; Kinder, Jesse M.; Mele, Eugene JWe calculate the Casimir interaction between two short-range scatterers embedded in a background of one-dimensional massless Dirac fermions using a force-operator approach. We obtain the force between two finite-width square barriers and take the limit of zero width and infinite potential strength to study the Casimir force mediated by the fermions. For the case of identical scatterers, we recover the conventional attractive one-dimensional Casimir force. For the general problem with inequivalent scatterers, we find that the magnitude and sign of this force depend on the relative spinor polarizations of the two scattering potentials, which can be tuned to give an attractive, a repulsive, or a compensated null Casimir interaction.Publication Analytic Model for the Bispectrum of Galaxies in Redshift Space(2008-07-18) Smith, Robert E.; Sheth, Ravi K.; Scoccimarro, RománWe develop an analytic theory for the redshift space bispectrum of dark matter, haloes, and galaxies. This is done within the context of the halo model of structure formation, as this allows for the self consistent inclusion of linear and nonlinear redshift-space distortions and also for the nonlinearity of the halo bias. The model is applicable over a wide range of scales: on the largest scales the predictions reduce to those of the standard perturbation theory (PT); on smaller scales they are determined primarily by the nonlinear virial velocities of galaxies within haloes, and this gives rise to the U-shaped anisotropy in the reduced bispectrum—a finger print of the Finger-Of-God distortions. We then confront the predictions with measurements of the redshift-space bispectrum of dark matter from an ensemble of numerical simulations. On very large scales, k = 0.05h Mpc-1, we find reasonably good agreement between our halo model, PT and the data, to within the errors. On smaller scales, k = 0.1h Mpc-1, the measured bispectra differ from the PT at the level of ∼10%–20%, especially for colinear triangle configurations. The halo model predictions improve over PT, but are accurate to no better than 10%. On smaller scales k = 0.5–1.0h Mpc-1, our model provides a significant improvement over PT, which breaks down. This implies that studies which use the lowest order PT to extract galaxy bias information are not robust on scales k ≳ 0.1h Mpc-1. The analytic and simulation results also indicate that there is no observable scale for which the configuration dependence of the reduced bispectrum is constant—hierarchical models for the higher-order correlation functions in redshift space are unlikely to be useful. It is hoped that our model will facilitate extraction of information from large-scale structure surveys of the Universe, because different galaxy populations are naturally included into our description.Publication D-Instanton Generated Dirac Neutrino Masses(2008-09-18) Cvetič, Mirjam; Langacker, PaulWe present a stringy mechanism to generate Dirac neutrino masses by D-instantons in an experimentally relevant mass scale without fine-tuning. Within type IIA string theory with intersecting D6-branes, we spell out specific conditions for the emergence of such couplings and provide a class of supersymmetric local SU(5) grand unified models, based on the Z2 × Z'2 orientifold compactification, where perturbatively absent Dirac neutrino masses can be generated by D2-brane instantons in the experimentally observed mass regime, while Majorana masses remain absent, thus providing an intriguing mechanism for the origin of small neutrino masses due to nonperturbative stringy effects.Publication Detecting Topological Features of Chaotic Fluid Flow(2008-12-31) Ouellette, Nicholas T; Gollub, Jerry P.Publication Electron Beam Nanosculpting of Suspended Graphene Sheets(2008-09-16) Fischbein, Michael D.; Drndić, MarijaWe demonstrate high-resolution modification of suspended multilayer graphene sheets by controlled exposure to the focused electron beam of a transmission electron microscope. We show that this technique can be used to realize, on time scales of a few seconds, a variety of features, including nanometer-scale pores, slits, and gaps that are stable and do not evolve over time. Despite the extreme thinness of the suspended graphene sheets, extensive removal of material to produce the desired feature geometries is found not to introduce long-range distortion of the suspended sheet structure.