D-wave-like nodal superconductivity in the organic conductor (TMTSF)2ClO4

We suggest theoretical explanation of the high upper critical magnetic field, perpendicular to conducting chains, Hc2, experimentally observed in the superconductor (TMTSF)2ClO4, in terms of singlet superconducting pairing. In particular, we compare the results of d-wave-like nodal, d-wave-like node-less, and s-wave scenarios of superconductivity. We show that, in d-wave-like nodal scenario, superconductivity can naturally exceed both the orbital upper critical magnetic field and Clogston-Shandrasekhar paramagnetic limit as well as reach experimental value, Hc2 = 6T, in contrast to d-wave-like node-less and s-wave scenarios. In our opinion, the obtained results are strongly in favor of d-wave-like nodal superconductivity in (TMTSF)2ClO4, whereas, in a sister compound, (TMTSF)2PF6, we expect either the existence of triplet order parameter or the coexistence of triplet and singlet order parameters.Comment: Talk at the ECRYS-2011 international conferenc

pi N --> Multi-pi N Scattering in the 1/N_c Expansion

We extend the 1/N_c expansion meson-baryon scattering formalism to cases in which the final state contains more than two particles. We first show that the leading-order large N_c processes proceed through resonant intermediate states (e.g., rho N or pi Delta). We then tabulate linear amplitude expressions for relevant processes and find that the pole structure of baryon resonances can be uniquely identified by their (non)appearance in eta N or mixed partial-wave pi Delta final states. We also show that quantitative predictions of pi N to pi Delta branching ratios predicted at leading order alone do not agree with measurements, but the inclusion of 1/N_c corrections is ample to explain the discrepancies.Comment: 23 pages, 3 eps figures, ReVTeX4, added reference and discussion, identical to PRD versio

Unification Theory of Angular Magnetoresistance Oscillations in Quasi-One-Dimensional Conductors

We present a unification theory of angular magnetoresistance oscillations, experimentally observed in quasi-one-dimensional organic conductors, by solving the Boltzmann kinetic equation in the extended Brillouin zone. We find that, at commensurate directions of a magnetic field, resistivity exhibits strong minima. In two limiting cases, our general solution reduces to the results, previously obtained for the Lebed Magic Angles and Lee-Naughton-Lebed oscillations. We demonstrate that our theoretical results are in good qualitative and quantitative agreement with the existing measurements of resistivity in (TMTSF)$_2$ClO$_4$ conductor.Comment: 6 pages, 2 figure

Homologies of Algebraic Structures via Braidings and Quantum Shuffles

In this paper we construct "structural" pre-braidings characterizing different algebraic structures: a rack, an associative algebra, a Leibniz algebra and their representations. Some of these pre-braidings seem original. On the other hand, we propose a general homology theory for pre-braided vector spaces and braided modules, based on the quantum co-shuffle comultiplication. Applied to the structural pre-braidings above, it gives a generalization and a unification of many known homology theories. All the constructions are categorified, resulting in particular in their super- and co-versions. Loday's hyper-boundaries, as well as certain homology operations are efficiently treated using the "shuffle" tools

Applications of self-distributivity to Yang-Baxter operators and their cohomology

Self-distributive (SD) structures form an important class of solutions to the Yang--Baxter equation, which underlie spectacular knot-theoretic applications of self-distributivity. It is less known that one go the other way round, and construct an SD structure out of any left non-degenerate (LND) set-theoretic YBE solution. This structure captures important properties of the solution: invertibility, involutivity, biquandle-ness, the associated braid group actions. Surprisingly, the tools used to study these associated SD structures also apply to the cohomology of LND solutions, which generalizes SD cohomology. Namely, they yield an explicit isomorphism between two cohomology theories for these solutions, which until recently were studied independently. The whole story leaves numerous open questions. One of them is the relation between the cohomologies of a YBE solution and its associated SD structure. These and related questions are covered in the present survey

Cohomology of finite monogenic self-distributive structures

A shelf is a set with a binary operation~\op satisfying a \op (b \op c) = (a \op b) \op (a \op c). Racks are shelves with invertible translations b \mapsto a \op b; many of their aspects, including cohomological, are better understood than those of general shelves. Finite monogenic shelves (FMS), of which Laver tables and cyclic racks are the most famous examples, form a remarkably rich family of structures and play an important role in set theory. We compute the cohomology of FMS with arbitrary coefficients. On the way we develop general tools for studying the cohomology of shelves. Moreover, inside any finite shelf we identify a sub-rack which inherits its major characteristics, including the cohomology. For FMS, these sub-racks are all cyclic

Cohomology of idempotent braidings, with applications to factorizable monoids

We develop new methods for computing the Hochschild (co)homology of monoids which can be presented as the structure monoids of idempotent set-theoretic solutions to the Yang--Baxter equation. These include free and symmetric monoids; factorizable monoids, for which we find a generalization of the K{\"u}nneth formula for direct products; and plactic monoids. Our key result is an identification of the (co)homologies in question with those of the underlying YBE solutions, via the explicit quantum symmetrizer map. This partially answers questions of Farinati--Garc{\'i}a-Galofre and Dilian Yang. We also obtain new structural results on the (co)homology of general YBE solutions