Cosmology and the Korteweg-de Vries Equation

The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has played a fundamental role in diverse branches of mathematical and theoretical physics. In the present paper, we consider its significance to cosmology. It is found that the KdV equation arises in a number of important scenarios, including inflationary cosmology, the cyclic universe, loop quantum cosmology and braneworld models. Analogies can be drawn between cosmic dynamics and the propagation of the solitonic wave solution to the equation, whereby quantities such as the speed and amplitude profile of the wave can be identified with cosmological parameters such as the spectral index of the density perturbation spectrum and the energy density of the universe. The unique mathematical properties of the Schwarzian derivative operator are important to the analysis. A connection with dark solitons in Bose-Einstein condensates is briefly discussed.Comment: 7 pages; References adde

Lithium and carbon isotopic fractionations between the alteration assemblages of Nakhla and Lafayette

Nakhla and Lafayette delta 7Li values for samples and extracts (4.1-14.2�) are consistent with brine evaporation. Relatively 13C-poor siderite in Lafayette suggests more than one carbon source was sampled

Possible world-wide middle miocene iridium anomaly and its relationship to periodicity of impacts and extinctions

In a study of one million years of Middle Miocene sediment deposition in ODP Hole 689B in the Weddell Sea near Antarctica, a single iridium (Ir) anomaly of 44 (+ or - 10) x 10 to the 12th gram Ir per gram rock (ppt) was observed in core 6H, section 3, 50 to 60 cm, after background contributions associated with manganese precipitates and clay are subtracted. The ODP Hole 689B is 10,000 km away from another site, DSDP Hole 588B in the Tasman Sea north of New Zealand, where a single Ir anomaly of 144 + or - 7 ppt over a background of 11 ppt was found in an earlier study of 3 million years of deposition. From chemical measurements the latter deposition was thought to be impact-related. Ir measurements were made, following neutron activation, with the Iridium Coincidence Spectrometer. The age vs depth calibration curves given in the DSDP and ODP preliminary reports indicate the ages of the Iranomalies are identical, 11.7 million years, but the absolute and relative uncertainties in the curves are not known. Based on the newest age data the age estimate is 10 million years. As the Ir was deposited at the two sites at about the same time and they are one quarter of the way around the world from each other it seems likely that the deposition was world-wide. The impact of a large asteroid or comet could produce the wide distribution, and this data is supportive of the impact relationship deduced for Deep Sea Drilling Project (DSDP) 588B from the chemical evidence. If the surface densities of Ir at the two sites are representative of the world-wide average, the diameter of a Cl type asteroid containing the necessary Ir would be 3 + or - 1 km, which is large enough to cause world-wide darkness and hence extinctions although the latter point is disputed

Construction of Non-Perturbative, Unitary Particle-Antiparticle Amplitudes for Finite Particle Number Scattering Formalisms

Starting from a unitary, Lorentz invariant two-particle scattering amplitude , we show how to use an identification and replacement process to construct a unique, unitary particle-antiparticle amplitude. This process differs from conventional on-shell Mandelstam s,t,u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel non-perturbative, cluster decomposable, relativistic scattering equations of the Faddeev-type integral equations recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle-antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the non-relativistic Coulomb problem, including the forward scattering singularity, the essential singularity in the phase, and the Bohr bound-state spectrum

Vortex Origin of Tricritical Point in Ginzburg-Landau Theory

Motivated by recent experimental progress in the critical regime of high-$T_c$ superconductors we show how the tricritical point in a superconductor can be derived from the Ginzburg-Landau theory as a consequence of vortex fluctuations. Our derivation explains why usual renormalization group arguments always produce a first-order transition, in contrast to experimental evidence and Monte Carlo simulations.Comment: 4 pages,1 figur

The Blob Algebra and the Periodic Temperley-Lieb Algebra

We determine the structure of two variations on the Temperley-Lieb algebra, both used for dealing with special kinds of boundary conditions in statistical mechanics models. The first is a new algebra, the `blob' algebra (the reason for the name will become obvious shortly!). We determine both the generic and all the exceptional structures for this two parameter algebra. The second is the periodic Temperley-Lieb algebra. The generic structure and part of the exceptional structure of this algebra have already been studied. Here we complete the analysis, using results from the study of the blob algebra.Comment: 12 page

On Preparing Entangled Pairs of Polarization Qubits in the Frequency Non-Degenerate Regime

The problems associated with practical implementation of the scheme proposed for preparation of arbitrary states of polarization ququarts based on biphotons are discussed. The influence of frequency dispersion effects are considered, and the necessity of group velocities dispersion compensation in the frequency non-degenerate case even for continuous pumping is demonstrated. A method for this compensation is proposed and implemented experimentally. Physical restrictions on the quality of prepared two-photon states are revealed.Comment: 9 pages, 6 figure

Phase transition curves for mesoscopic superconducting samples

We compute the phase transition curves for mesoscopic superconductors. Special emphasis is given to the limiting shape of the curve when the magnetic flux is large. We derive an asymptotic formula for the ground state of the Schr\"odinger equation in the presence of large applied flux. The expansion is shown to be sensitive to the smoothness of the domain. The theoretical results are compared to recent experiments.Comment: 8 pages, 1 figur

Influence of the confinement geometry on surface superconductivity

The nucleation field for surface superconductivity, $H_{c3}$, depends on the geometrical shape of the mesoscopic superconducting sample and is substantially enhanced with decreasing sample size. As an example we studied circular, square, triangular and wedge shaped disks. For the wedge the nucleation field diverges as $H_{c3}/H_{c2}=\sqrt{3}/\alpha$ with decreasing angle ($\alpha$) of the wedge, where $H_{c2}$ is the bulk upper critical field.Comment: 4 pages, 3 figures. Accepted for publication in Phys. Rev.