Spin-catalyzed hopping conductivity in disordered strongly interacting quantum wires

In one-dimensional electronic systems with strong repulsive interactions, charge excitations propagate much faster than spin excitations. Such systems therefore have an intermediate temperature range [termed the "spin-incoherent Luttinger liquid'" (SILL) regime] where charge excitations are "cold" (i.e., have low entropy) whereas spin excitations are "hot." We explore the effects of charge-sector disorder in the SILL regime in the absence of external sources of equilibration. We argue that the disorder localizes all charge-sector excitations; however, spin excitations are protected against full localization, and act as a heat bath facilitating charge and energy transport on asymptotically long timescales. The charge, spin, and energy conductivities are widely separated from one another. The dominant carriers of energy are neither charge nor spin excitations, but neutral "phonon" modes, which undergo an unconventional form of hopping transport that we discuss. We comment on the applicability of these ideas to experiments and numerical simulations.Comment: 14 pages, 6 figure

An analogue of the Narasimhan-Seshadri theorem and some applications

We prove an analogue in higher dimensions of the classical Narasimhan-Seshadri theorem for strongly stable vector bundles of degree 0 on a smooth projective variety $X$ with a fixed ample line bundle $\Theta$. As applications, over fields of characteristic zero, we give a new proof of the main theorem in a recent paper of Balaji and Koll\'ar and derive an effective version of this theorem; over uncountable fields of positive characteristics, if $G$ is a simple and simply connected algebraic group and the characteristic of the field is bigger than the Coxeter index of $G$, we prove the existence of strongly stable principal $G$ bundles on smooth projective surfaces whose holonomy group is the whole of $G$.Comment: 42 pages. Theorem 3 of this version is new. Typos have been corrected. To appear in Journal of Topolog

Metalevel programming in robotics: Some issues

Computing in robotics has two important requirements: efficiency and flexibility. Algorithms for robot actions are implemented usually in procedural languages such as VAL and AL. But, since their excessive bindings create inflexible structures of computation, it is proposed that Logic Programming is a more suitable language for robot programming due to its non-determinism, declarative nature, and provision for metalevel programming. Logic Programming, however, results in inefficient computations. As a solution to this problem, researchers discuss a framework in which controls can be described to improve efficiency. They have divided controls into: (1) in-code and (2) metalevel and discussed them with reference to selection of rules and dataflow. Researchers illustrated the merit of Logic Programming by modelling the motion of a robot from one point to another avoiding obstacles

Monodromy group for a strongly semistable principal bundle over a curve, II

Let $X$ be a geometrically irreducible smooth projective curve defined over a field $k$. Assume that $X$ has a $k$-rational point; fix a $k$-rational point $x\in X$. From these data we construct an affine group scheme ${\mathcal G}_X$ defined over the field $k$ as well as a principal ${\mathcal G}_X$-bundle $E_{{\mathcal G}_X}$ over the curve $X$. The group scheme ${\mathcal G}_X$ is given by a ${\mathbb Q}$--graded neutral Tannakian category built out of all strongly semistable vector bundles over $X$. The principal bundle $E_{{\mathcal G}_X}$ is tautological. Let $G$ be a linear algebraic group, defined over $k$, that does not admit any nontrivial character which is trivial on the connected component, containing the identity element, of the reduced center of $G$. Let $E_G$ be a strongly semistable principal $G$-bundle over $X$. We associate to $E_G$ a group scheme $M$ defined over $k$, which we call the monodromy group scheme of $E_G$, and a principal $M$-bundle $E_M$ over $X$, which we call the monodromy bundle of $E_G$. The group scheme $M$ is canonically a quotient of ${\mathcal G}_X$, and $E_M$ is the extension of structure group of $E_{{\mathcal G}_X}$. The group scheme $M$ is also canonically embedded in the fiber ${\rm Ad}(E_G)_{x}$ over $x$ of the adjoint bundle.Comment: This final version includes strengthening of the result by referee's comments. K-Theory (to appear

On the geometry of regular maps from a quasi-projective surface to a curve

By exploring the consequences of the triviality of the monodromy group for a class of surfaces of which the mixed Hodge structure is pure, we extend results of Miyanishi and Sugie, Dimca, Zaidenberg and Kaliman.Comment: 19 pages. Some corrections and more references. European Journal of Mathematics, to appea