Noncommutative algebras related with Schubert calculus on Coxeter groups

For any finite Coxeter system (W,S) we construct a certain noncommutative algebra, the so-called bracket algebra, together with a family of commuting elements, the so-called Dunkl elements. The Dunkl elements conjecturally generate an algebra which is canonically isomorphic to the coinvariant algebra of the Coxeter group W. We prove this conjecture for classical Coxeter groups and I₂(m). We define a “quantization” and a multiparameter deformation of our construction and show that for Lie groups of classical type and G₂, the algebra generated by Dunkl’s elements in the quantized bracket algebra is canonically isomorphic to the small quantum cohomology ring of the corresponding flag variety, as described by B. Kim. For crystallographic Coxeter systems we define the so-called quantum Bruhat representation of the corresponding bracket algebra. We study in more detail the structure of the relations in B_n-, D_n- and G₂-bracket algebras, and as an application, discover a Pieri-type formula in the B_n-bracket algebra. As a corollary, we obtain a Pieri-type formula for multiplication of an arbitrary B_n-Schubert class by some special ones. Our Pieri-type formula is a generalization of Pieri’s formulas obtained by A. Lascoux and M.-P. Schützenberger for flag varieties of type A. We also introduce a super-version of the bracket algebra together with a family of pairwise anticommutative elements, the so-called flat connections with constant coefficients, which describes “a noncommutative differential geometry on a finite Coxeter group” in the sense of S. Majid.     

Mechanism of hopping transport in disordered mott insulators

By using a combination of detailed experimental studies and simple theoretical arguments, we identify a novel mechanism characterizing the hopping transport in the Mott insulating phase of Ca2-xSrxRuO4 near the metal-insulator transition. The hopping exponent alpha shows a systematic evolution from a value of alpha=1/2 deeper in the insulator to the conventional Mott value alpha=1/3 closer to the transition. This behavior, which we argue to be a universal feature of disordered Mott systems close to the metal-insulator transition, is shown to reflect the gradual emergence of disorder-induced localized electronic states populating the Mott-Hubbard gap.     

Gap structure of the spin-triplet superconductor Sr2RuO4 determined from the field-orientation dependence of the specific heat

We report the field-orientation dependent specific heat of the spin-triplet superconductor Sr2RuO4 under the magnetic field aligned parallel to the RuO2 planes with high accuracy. Below about 0.3 K, striking fourfold oscillations of the density of states reflecting the superconducting gap structure have been resolved for the first time. We also obtained strong evidence of multiband superconductivity and concluded that the superconducting gap in the active band, responsible for the superconducting instability, is modulated with a minimum along the [100] direction.     

Fermi surface, surface states, and surface reconstruction in Sr2RuO4

The electronic structure of Sr2RuO4 is investigated by high angular resolution ARPES at several incident photon energies. We address the controversial issues of the Fermi surface (FS) topology and the van Hove singularity at the M point, showing that a surface state and the replica of the primary FS due to sqrt[2]xsqrt[2] surface reconstruction are responsible for previous conflicting interpretations. The FS thus determined by ARPES is consistent with the de Haas-van Alphen results, and it provides additional information on the detailed shape of the alpha, beta, and gamma sheets.     

Tactile impression and friction of water on human skin

Water has a unique touch as well as characteristic physical properties. However, nobody knows the real identity of its touch. Here, we show that water creates a stick-slip feel when a small amount is rubbed using fingertip on an artificial skin that mimics the structure of human skin. The results of frictional analyses predict that this stick-slip feel is caused by a drastic change in frictional resistance. The present result is valuable for biologists and robot engineers as well as cognitive scientists and tribologists, because it is a new example of stick-slip phenomena on biological surfaces. The tactile texture of this most familiar material could also be applied to consumer products or virtual reality systems.     

Ion-size effects on the structure and superconductivity of La-214 compounds at 1/8 doping

A structural transition to a low-temperature tetragonal (TLT) phase occurs below T_d2≈60 K in La_2−xBa_xCuO₄ only around x=0.125, accompanied by sharp suppression of superconductivity. In this study we investigated the effects of partial substitution of smaller divalent cations for Ba²⁺ ions (Ba²⁺ > Sr²⁺ > Ca²⁺) on these anomalous low-temperature properties. The suppression of superconductivity is strongly affected by the appearance of the TLT phase for this carrier concentration. We also show that the variations of T_d2 and T_c are quantitatively scaled by the averaged size of cations at the La site. This dependence can be interpreted as chemical effects acting effectively as applied pressure. We discuss how our observation is related to recent reports which claim that the TLT structure itself does not necessarily destroy the superconductivity.     

Influence of halogen substituents on the catalytic oxidation of 2,4,6-halogenated phenols by Fe(III)-tetrakis(p-hydroxyphenyl) porphyrins and potassium monopersulfate

The influence of halogen substituents on the catalytic oxidation of 2,4,6-trihalogenated phenols (TrXPs) by iron(III)-porphyrin/KHSO? catalytic systems was investigated. Iron(III)-5,10,15,20-tetrakis(p-hydroxyphenyl)porphyrin (FeTHP) and its supported variants were employed, where the supported catalysts were synthesized by introducing FeTHP into hydroquinone-derived humic acids via formaldehyde poly-condensation. F (TrFP), Cl (TrCP), Br (TrBP) and I (TrIP) were examined as halogen substituents for TrXPs. Although the supported catalysts significantly enhanced the degradation and dehalogenation of TrFP and TrCP, the oxidation of TrBP and TrIP was not enhanced, compared to the FeTHP catalytic system. These results indicate that the degree of oxidation of TrXPs is strongly dependent on the types of halogen substituent. The order of dehalogenation levels for halogen substituents in TrXPs was F > Cl > Br > I, consistent with their order of electronegativity. The electronegativity of a halogen substituent affects the nucleophilicity of the carbon to which it is attached. The levels of oxidation products in the reaction mixtures were analyzed by GC/MS after extraction with n-hexane. The most abundant dimer product from TrFP via 2,6-difluoroquinone is consistent with a scenario where TrXP, with a more electronegative halogen substituent, is readily oxidized, while less electronegative halogen substituents are oxidized less readily by iron(III)-porphyrin/KHSO? catalytic systems.