11,323 research outputs found
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
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
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
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
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