Response to Cross-Petition for a Writ of Certiorari to the United States Court of Appeals for the Second Circuit

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On an exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions

We derive an exact solution to the Thomas-Fermi equation for a Bose-Einstein condensate which has dipole-dipole interactions as well as the usual s-wave contact interaction, in a harmonic trap. Remarkably, despite the non-local anisotropic nature of the dipolar interaction the solution is an inverted parabola, as in the pure s-wave case, but with a different aspect ratio. Various properties such as electrostriction and stability are discussed.Comment: 11 pages, 5 figure

Genetic mapping and identification of QTL for earliness in the globe artichoke / cultivated cardoon complex.

BACKGROUND: The Asteraceae species Cynara cardunculus (2n = 2x = 34) includes the two fully cross-compatible domesticated taxa globe artichoke (var. scolymus L.) and cultivated cardoon (var. altilis DC). As both are out-pollinators and suffer from marked inbreeding depression, linkage analysis has focussed on the use of a two way pseudo-test cross approach. RESULTS: A set of 172 microsatellite (SSR) loci derived from expressed sequence tag DNA sequence were integrated into the reference C. cardunculus genetic maps, based on segregation among the F(1) progeny of a cross between a globe artichoke and a cultivated cardoon. The resulting maps each detected 17 major linkage groups, corresponding to the species’ haploid chromosome number. A consensus map based on 66 co-dominant shared loci (64 SSRs and two SNPs) assembled 694 loci, with a mean inter-marker spacing of 2.5 cM. When the maps were used to elucidate the pattern of inheritance of head production earliness, a key commercial trait, seven regions were shown to harbour relevant quantitative trait loci (QTL). Together, these QTL accounted for up to 74% of the overall phenotypic variance. CONCLUSION: The newly developed consensus as well as the parental genetic maps can accelerate the process of tagging and eventually isolating the genes underlying earliness in both the domesticated C. cardunculus forms. The largest single effect mapped to the same linkage group in each parental maps, and explained about one half of the phenotypic variance, thus representing a good candidate for marker assisted selection

Magnetic order in double-layer manganites (La(1-z)Pr(z))1.2Sr1.8Mn2O7: intrinsic properties and role of the intergrowths

We report on an investigation of the double-layer manganite series (La(1-z)Pr(z))1.2Sr1.8Mn2O7 (0 <= z <= 1), carried out on single crystals by means of both macroscopic magnetometry and local probes of magnetism (muSR, 55Mn NMR). Muons and NMR demonstrate an antiferromagnetically ordered ground state at non-ferromagnetic compositions (z >= 0.6), while more moderate Pr substitutions (0.2 <= z <= 0.4) induce a spin reorientation transition within the ferromagnetic phase. A large magnetic susceptibility is detected at {Tc,TN} < T < 250K at all compositions. From 55Mn NMR spectroscopy, such a response is unambiguously assigned to the intergrowth of a ferromagnetic pseudocubic phase (La(1-z)Pr(z))(1-x)Sr(x)MnO3, with an overall volume fraction estimated as 0.5-0.7% from magnetometry. Evidence is provided for the coupling of the magnetic moments of these inclusions with the magnetic moments of the surrounding (La(1-z)Pr(z))1.2Sr1.8Mn2O7 phase, as in the case of finely dispersed impurities. We argue that the ubiquitous intergrowth phase may play a role in the marked first-order character of the magnetic transition and the metamagnetic properties above Tc reported for double-layer manganites.Comment: 11 pages, 9 figures. Submitted to Phys. Rev.

Faraday effect : a field theoretical point of view

We analyze the structure of the vacuum polarization tensor in the presence of a background electromagnetic field in a medium. We use various discrete symmetries and crossing symmetry to constrain the form factors obtained for the most general case. From these symmetry arguments, we show why the vacuum polarization tensor has to be even in the background field when there is no background medium. Taking then the background field to be purely magnetic, we evaluate the vacuum polarization to linear order in it. The result shows the phenomenon of Faraday rotation, i.e., the rotation of the plane of polarization of a plane polarized light passing through this background. We find that the usual expression for Faraday rotation, which is derived for a non-degenerate plasma in the non-relativistic approximation, undergoes substantial modification if the background is degenerate and/or relativistic. We give explicit expressions for Faraday rotation in completely degenerate and ultra-relativistic media.Comment: 20 pages, Latex, uses axodraw.st

Electronic measurement and control of spin transport in Silicon

The electron spin lifetime and diffusion length are transport parameters that define the scale of coherence in spintronic devices and circuits. Since these parameters are many orders of magnitude larger in semiconductors than in metals, semiconductors could be the most suitable for spintronics. Thus far, spin transport has only been measured in direct-bandgap semiconductors or in combination with magnetic semiconductors, excluding a wide range of non-magnetic semiconductors with indirect bandgaps. Most notable in this group is silicon (Si), which (in addition to its market entrenchment in electronics) has long been predicted a superior semiconductor for spintronics with enhanced lifetime and diffusion length due to low spin-orbit scattering and lattice inversion symmetry. Despite its exciting promise, a demonstration of coherent spin transport in Si has remained elusive, because most experiments focused on magnetoresistive devices; these methods fail because of universal impedance mismatch obstacles, and are obscured by Lorentz magnetoresistance and Hall effects. Here we demonstrate conduction band spin transport across 10 microns undoped Si, by using spin-dependent ballistic hot-electron filtering through ferromagnetic thin films for both spin-injection and detection. Not based on magnetoresistance, the hot electron spin-injection and detection avoids impedance mismatch issues and prevents interference from parasitic effects. The clean collector current thus shows independent magnetic and electrical control of spin precession and confirms spin coherent drift in the conduction band of silicon.Comment: Single PDF file with 4 Figure