Fermions in the background of the sphaleron barrier

We demonstrate the level crossing phenomenon for fermions in the background field of the sphaleron barrier, by numerically determining the fermion eigenvalues along the minimal energy path from one vacuum to another. We assume that the fermions of a doublet are degenerate in mass, allowing for spherically symmetric ans\"atze for all of the fields, when the mixing angle dependence is neglected.Comment: 9 pages, latex, 4 figures appended as postscript files after \end{document}. THU-93/0

Reconstructing depositional rates and their effect on paleoenvironmental proxies : the case of the Lau Carbon Isotope Excursion in Gotland, Sweden

Variations in depositional rates affect the temporal depositional resolutions of proxies used for paleoenvironmental reconstructions; for example, condensation can make reconstructed environmental changes appear very abrupt. This is commonly addressed by transforming proxy data using age models, but this approach is limited to situations where numerical ages are available or can be reliably inferred by correlation. Here we propose a new solution, in which relative age models are constructed based on proxies for depositional rates. As a case study, we use the onset of the late Silurian Lau Carbon Isotope Excursion (LCIE) in Gotland, Sweden. The studied succession is a gradual record of shallowing upward in a tropical, neritic carbonate platform. As proxies for depositional rates we tested thorium concentration, carbonate content, and the concentration of pelagic palynomorphs. These three proxies were used to create relative age models using the previously published DAIME model. We applied these models to transform the delta C-13(carb) values as well as concentrations of selected redox-sensitive elements. The three relative age models yielded qualitatively similar results. In our case study, variations in depositional rates resulted in peaks of redox proxies appearing up to 76% higher when taken at face value, compared to when accounting for these rates. In the most extreme cases, our corrections resulted in a reversal in the stratigraphic trend of elemental concentrations. This approach can be applied and developed across depositional setting and types of paleoenvironmental proxies. It provides a flexible tool for developing quantitative models to improve our understanding of the stratigraphic record

A sphaleron for the non-Abelian anomaly

A self-consistent Ansatz for a new sphaleron of SU(3) Yang-Mills-Higgs theory is presented. With a single triplet of Weyl fermions added, there exists, most likely, one pair of fermion zero modes, which is known to give rise to the non-Abelian (Bardeen) anomaly as a Berry phase. The corresponding SU(3) gauge field configuration could take part in the nonperturbative dynamics of Quantum Chromodynamics.Comment: LaTeX with elsart.cls, 26 pages, v4: published versio

Algebraic Attacks on the Crypto-1 Stream Cipher in MiFare Classic and Oyster Cards

MiFare Crypto 1 is a lightweight stream cipher used in London\u27s Oyster card, Netherland\u27s OV-Chipcard, US Boston\u27s CharlieCard, and in numerous wireless access control and ticketing systems worldwide. Recently, researchers have been able to recover this algorithm by reverse engineering. We have examined MiFare from the point of view of the so called algebraic attacks . We can recover the full 48-bit key of MiFare algorithm in 200 seconds on a PC, given 1 known IV (from one single encryption). The security of this cipher is therefore close to zero. This is particularly shocking, given the fact that, according to the Dutch press, 1 billion of MiFare Classic chips are used worldwide, including in many governmental security systems

Neutrino Zero Modes on Electroweak Strings

Zero modes of massive standard model fermions have been found on electroweak Z-strings. A zero mode solution for a massless left-handed neutrino is also known, but was thought to be non-normalizable. Here we show that although this mode is not discretely normalizable, it is delta-function normalizable and the correct interpretation of this solution is within the framework of the continuum spectrum. We also analyze an extension of the standard model including right-handed neutrinos in which neutrinos have Dirac masses, arising from a Yukawa coupling to the usual SU(2) Higgs doublet, and right-handed Majorana masses. The Majorana mass terms are taken to be spatially homogeneous and are presumed to arise from the vacuum expectation value of some field acquired in a phase transition well above the electroweak phase transition. The resulting zero energy equations have a discrete zero mode.Comment: 5 pages, 1 figures, version to appear in Phys. Rev.

Wear of human teeth: a tribological perspective

The four main types of wear in teeth are attrition (enamel-on-enamel contact), abrasion (wear due to abrasive particles in food or toothpaste), abfraction (cracking in enamel and subsequent material loss), and erosion (chemical decomposition of the tooth). They occur as a result of a number of mechanisms including thegosis (sliding of teeth into their lateral position), bruxism (tooth grinding), mastication (chewing), toothbrushing, tooth flexure, and chemical effects. In this paper the current understanding of wear of enamel and dentine in teeth is reviewed in terms of these mechanisms and the major influencing factors are examined. In vitro tooth wear simulation and in vivo wear measurement and ranking are also discussed

Level Crossing Along Sphaleron Barriers

In the electroweak sector of the standard model topologically inequivalent vacua are separated by finite energy barriers, whose height is given by the sphale\-ron. For large values of the Higgs mass there exist several sphaleron solutions and the barriers are no longer symmetric. We construct paths of classical configurations from one vacuum to a neighbouring one and solve the fermion equations in the background field configurations along such paths, choosing the fermions of a doublet degenerate in mass. As in the case of light Higgs masses we observe the level crossing phenomenon also for large Higgs masses.Comment: 17 pages, latex, 10 figures in uuencoded postscript files. THU-94/0

The Sphaleron Barrier in the Presence of Fermions

We calculate the minimal energy path over the sphaleron barrier in the pre\-sen\-ce of fermions, assuming that the fermions of a doublet are degenerate in mass. This allows for spherically symmetric ans\"atze for the fields, when the mixing angle dependence is neglected. While light fermions have little influence on the barrier, the presence of heavy fermions ($M_F \sim$ TeV) strongly deforms the barrier, giving rise to additional sphalerons for very heavy fermions ($M_F \sim$ 10 TeV). Heavy fermions form non-topological solitons in the vacuum sector.Comment: 19 pages, latex, 18 figures in 3 seperate uuencoded postscript files THU-93/1

Nondegenerate Fermions in the Background of the Sphaleron Barrier

We consider level crossing in the background of the sphaleron barrier for nondegenerate fermions. The mass splitting within the fermion doublets allows only for an axially symmetric ansatz for the fermion fields. In the background of the sphaleron we solve the partial differential equations for the fermion functions. We find little angular dependence for our choice of ansatz. We therefore propose a good approximate ansatz with radial functions only. We generalize this approximate ansatz with radial functions only to fermions in the background of the sphaleron barrier and argue, that it is a good approximation there, too.Comment: LATEX, 20 pages, 11 figure

Sphalerons, spectral flow, and anomalies

The topology of configuration space may be responsible in part for the existence of sphalerons. Here, sphalerons are defined to be static but unstable finite-energy solutions of the classical field equations. Another manifestation of the nontrivial topology of configuration space is the phenomenon of spectral flow for the eigenvalues of the Dirac Hamiltonian. The spectral flow, in turn, is related to the possible existence of anomalies. In this review, the interconnection of these topics is illustrated for three particular sphalerons of SU(2) Yang-Mills-Higgs theory.Comment: 35 pages with revtex4; invited paper for the August special issue of JMP on "Integrability, topological solitons and beyond