2,040 research outputs found
Monodromy group for a strongly semistable principal bundle over a curve, II
Let be a geometrically irreducible smooth projective curve defined over a
field . Assume that has a -rational point; fix a -rational point
. From these data we construct an affine group scheme
defined over the field as well as a principal -bundle
over the curve . The group scheme is
given by a --graded neutral Tannakian category built out of all
strongly semistable vector bundles over . The principal bundle is tautological. Let be a linear algebraic group, defined over ,
that does not admit any nontrivial character which is trivial on the connected
component, containing the identity element, of the reduced center of . Let
be a strongly semistable principal -bundle over . We associate to
a group scheme defined over , which we call the monodromy group
scheme of , and a principal -bundle over , which we call the
monodromy bundle of . The group scheme is canonically a quotient of
, and is the extension of structure group of
. The group scheme is also canonically embedded in the
fiber over of the adjoint bundle.Comment: This final version includes strengthening of the result by referee's
comments. K-Theory (to appear
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 with a fixed ample line bundle . 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 is a simple and simply connected algebraic group and the characteristic
of the field is bigger than the Coxeter index of , we prove the existence of
strongly stable principal bundles on smooth projective surfaces whose
holonomy group is the whole of .Comment: 42 pages. Theorem 3 of this version is new. Typos have been
corrected. To appear in Journal of Topolog
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
Tensor product theorem for Hitchin pairs -An algebraic approach
We give an algebraic approach to the study of Hitchin pairs and prove the
tensor product theorem for Higgs semistable Hitchin pairs over smooth
projective curves defined over algebraically closed fields of
characteristic and characteristic , with satisfying some natural
bounds. We also prove the corresponding theorem for polystable bundles.Comment: To appear in Annales de l'Institut Fourier, Volume 61 (2011
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
Disorder-driven destruction of a non-Fermi liquid semimetal via renormalization group
We investigate the interplay of Coulomb interactions and
short-range-correlated disorder in three dimensional systems where absent
disorder the non-interacting band structure hosts a quadratic band crossing.
Though the clean Coulomb problem is believed to host a 'non-Fermi liquid'
phase, disorder and Coulomb interactions have the same scaling dimension in a
renormalization group (RG) sense, and thus should be treated on an equal
footing. We therefore implement a controlled -expansion and apply it
at leading order to derive RG flow equations valid when disorder and
interactions are both weak. We find that the non-Fermi liquid fixed point is
unstable to disorder, and demonstrate that the problem inevitably flows to
strong coupling, outside the regime of applicability of the perturbative RG. An
examination of the flow to strong coupling suggests that disorder is
asymptotically more important than interactions, so that the low energy
behavior of the system can be described by a non-interacting sigma model in the
appropriate symmetry class (which depends on whether exact particle-hole
symmetry is imposed on the problem). We close with a discussion of general
principles unveiled by our analysis that dictate the interplay of disorder and
Coulomb interactions in gapless semiconductors, and of connections to many-body
localized systems with long-range interactions.Comment: 15 pages, 4 figure
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