Picard-Fuchs Equations and Whitham Hierarchy in N=2 Supersymmetric SU(r+1) Yang-Mills Theory

In general, Whitham dynamics involves infinitely many parameters called Whitham times, but in the context of N=2 supersymmetric Yang-Mills theory it can be regarded as a finite system by restricting the number of Whitham times appropriately. For example, in the case of SU(r+1) gauge theory without hypermultiplets, there are r Whitham times and they play an essential role in the theory. In this situation, the generating meromorphic 1-form of the Whitham hierarchy on Seiberg-Witten curve is represented by a finite linear combination of meromorphic 1-forms associated with these Whitham times, but it turns out that there are various differential relations among these differentials. Since these relations can be written only in terms of the Seiberg-Witten 1-form, their consistency conditions are found to give the Picard-Fuchs equations for the Seiberg-Witten periods.Comment: to be published in J. Math. Phys, revtex, 14 page

Superconductivity in S-substituted FeTe

We have successfully synthesized a new superconducting phase of FeTe1-xSx with a PbO-type structure. It has the simplest crystal structure in iron-based superconductors. Superconducting transition temperature is about 10 K at x = 0.2. The upper critical field Hc2 was estimated to be ~70 T. The coherent length was calculated to be ~2.2 nm. Because FeTe1-xSx is composed of nontoxic elements, this material is a candidate for applications and will activate more and more research on iron-based superconductor.Comment: 13 pages, 10 figure

Prebiotic Organic Microstructures

Micro- and sub-micrometer spheres, tubules and fiber-filament soft structures have been synthesized in our experiments conducted with 3 MeV proton irradiations of a mixture of simple inorganic constituents, CO, N2 and H2O. We analysed the irradiation products, with scanning electron microscopy (SEM) and atomic force microscopy (AFM). These laboratory organic structures produced wide variety of proteinous and non-proteinous amino acids after HCl hydrolysis. The enantiomer analysis for D-, L- alanine confirmed that the amino acids were abiotically synthesized during the laboratory experiment. Considering hydrothermal activity, the presence of CO2 and H2, of a ferromagnesian silicate mineral environment, of an Earth magnetic field which was much less intense during Archean times than nowadays and consequently of a proton excitation source which was much more abundant, we propose that our laboratory organic microstructures might be synthesized during Archean times. We show similarities in morphology and in formation with some terrestrial Archean microstructures and we suggest that some of the observed Archean carbon spherical and filamentous microstructures might be composed of abiogenic organic molecules. We further propose a search for such prebiotic organic signatures on Mars. This article has been posted on Nature precedings on 21 July 2010 [1]. Extinct radionuclides as source of excitation have been replaced by cosmic radiations which were much more intense 3.5 Ga ago because of a much less intense Earth magnetic field. The new version of the article has been presented at the ORIGINS conference in Montpellier in july 2011 [2] and has since been published in Origins of Life and Evolution of Biospheres 42 (4) 307-316, 2012. 
DOI: 10.1007/s11084-012-9290-5 

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Spin Gap of Two-Dimensional Antiferromagnet Representing CaV4_4O9_9

We examined a two-dimensional Heisenberg model with two kinds of exchange energies, $J_e$ and $J_c$. This model describes localized spins at vanadium ions in a layer of CaV$_4$O$_9$, for which a spin gap is found by a recent experiment. Comparing the high temperature expansion of the magnetic susceptibility to experimental data, we determined the exchange energies as $J_e \simeq$ 610 K and $J_c \simeq$ 150 K. By the numerical diagonalization we estimated the spin gap as $\Delta \sim 0.2J_e \simeq$ 120 K, which consists with the experimental value 107 K. Frustration by finite $J_c$ enhances the spin gap.Comment: 12 pages of LaTex, 4 figures availavule upon reques