On a graded q-differential algebra

Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differential algebra in the case of a reduced quantum plane which can be endowed with a structure of a graded algebra. We consider the differential d satisfying d to power N equals zero as an analog of an exterior differential and study the first order differential calculus induced by this differential.Comment: 6 pages, submitted to the Proceedings of the "International Conference on High Energy and Mathematical Physics", Morocco, Marrakech, April 200

A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds

We present an invariant of a three-dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. Our invariant is related to a finite-dimensional fermionic topological quantum field theory

Examples of derivation-based differential calculi related to noncommutative gauge theories

Some derivation-based differential calculi which have been used to construct models of noncommutative gauge theories are presented and commented. Some comparisons between them are made.Comment: 22 pages, conference given at the "International Workshop in honour of Michel Dubois-Violette, Differential Geometry, Noncommutative Geometry, Homology and Fundamental Interactions". To appear in a special issue of International Journal of Geometric Methods in Modern Physic

Electronic transport in quantum cascade structures

The transport in complex multiple quantum well heterostructures is theoretically described. The model is focused on quantum cascade detectors, which represent an exciting challenge due to the complexity of the structure containing 7 or 8 quantum wells of different widths. Electronic transport can be fully described without any adjustable parameter. Diffusion from one subband to another is calculated with a standard electron-optical phonon hamiltonian, and the electronic transport results from a parallel flow of electrons using all the possible paths through the different subbands. Finally, the resistance of such a complex device is given by a simple expression, with an excellent agreement with experimental results. This relation involves the sum of transitions rates between subbands, from one period of the device to the next one. This relation appears as an Einstein relation adapted to the case of complex multiple quantum structures.Comment: 6 pages, 5 figures, 1 tabl

Field induced anisotropic cooperativity in a magnetic colloidal glass

The translational dynamics in a repulsive colloidal glass-former is probed by time-resolved X-ray Photon Correlation Spectroscopy. In this dense dispersion of charge-stabilized and magnetic nanoparticles, the interaction potential can be tuned, from quasi-isotropic to anisotropic by applying an external magnetic field. Structural and dynamical anisotropies are reported on interparticle lengthscales associated with highly anisotropic cooperativity, almost two orders of magnitude larger in the field direction than in the perpendicular direction and in zero field

Z_3-graded exterior differential calculus and gauge theories of higher order

We present a possible generalization of the exterior differential calculus, based on the operator d such that d^3=0, but d^2\not=0. The first and second order differentials generate an associative algebra; we shall suppose that there are no binary relations between first order differentials, while the ternary products will satisfy the cyclic relations based on the representation of cyclic group Z_3 by cubic roots of unity. We shall attribute grade 1 to the first order differentials and grade 2 to the second order differentials; under the associative multiplication law the grades add up modulo 3. We show how the notion of covariant derivation can be generalized with a 1-form A, and we give the expression in local coordinates of the curvature 3-form. Finally, the introduction of notions of a scalar product and integration of the Z_3-graded exterior forms enables us to define variational principle and to derive the differential equations satisfied by the curvature 3-form. The Lagrangian obtained in this way contains the invariants of the ordinary gauge field tensor F_{ik} and its covariant derivatives D_i F_{km}.Comment: 13 pages, no figure

Local methylthiolate adsorption geometry on Au(111) from photoemission core-level shifts

The local adsorption structure of methylthiolate in the ordered Au(111)-(√3×√3)R30° phase has been investigated using core-level-shift measurements of the surface and bulk components of the Au 4f7/2 photoelectron binding energy. The amplitude ratio of the core-level-shift components associated with surface Au atoms that are, and are not, bonded to the thiolate is found to be compatible only with the previously proposed Au-adatom-monothiolate moiety in which the thiolate is bonded atop Au adatoms in hollow sites, and not on an unreconstructed surface, or in Au-adatom-dithiolate species

Observation of superspin glass state in magnetically textured ferrofluid (gamma-Fe2O3)

Magnetic properties in a magnetically textured ferrofluid made out of interacting maghemite (gamma-Fe2O3) nanoparticles suspended in glycerin have been investigated. Despite the loss of uniform distribution of anisotropy axes, a superspin glass state exists at low temperature in a concentrated, textured ferrofluid as in the case of its non-textured counterpart. The onset of superspin glass state was verified from the sample's AC susceptibility. The influence of the anisotropy axis orientation on the aging behavior in the glassy states is also discussed