16,659 research outputs found
N-complexes as functors, amplitude cohomology and fusion rules
We consider N-complexes as functors over an appropriate linear category in
order to show first that the Krull-Schmidt Theorem holds, then to prove that
amplitude cohomology only vanishes on injective functors providing a well
defined functor on the stable category. For left truncated N-complexes, we show
that amplitude cohomology discriminates the isomorphism class up to a
projective functor summand. Moreover amplitude cohomology of positive
N-complexes is proved to be isomorphic to an Ext functor of an indecomposable
N-complex inside the abelian functor category. Finally we show that for the
monoidal structure of N-complexes a Clebsch-Gordan formula holds, in other
words the fusion rules for N-complexes can be determined.Comment: Final versio
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
The Origin of Chiral Anomaly and the Noncommutative Geometry
We describe the scalar and spinor fields on noncommutative sphere starting
from canonical realizations of the enveloping algebra . The gauge extension of a free spinor model, the Schwinger model on
a noncommutative sphere, is defined and the model is quantized. The
noncommutative version of the model contains only a finite number of dynamical
modes and is non-perturbatively UV-regular. An exact expresion for the chiral
anomaly is found. In the commutative limit the standard formula is recovered.Comment: 30 page
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
BRS Cohomology of the Supertranslations in D=4
Supersymmetry transformations are a kind of square root of spacetime
translations. The corresponding Lie superalgebra always contains the
supertranslation operator . We find that the
cohomology of this operator depends on a spin-orbit coupling in an SU(2) group
and has a quite complicated structure. This spin-orbit type coupling will turn
out to be basic in the cohomology of supersymmetric field theories in general.Comment: 14 pages, CTP-TAMU-13/9
Abundance of local actions for the vacuum Einstein equations
We exhibit large classes of local actions for the vacuum Einstein equations.
In presence of fermions, or more generally of matter which couple to the
connection, these actions lead to inequivalent equations revealing an arbitrary
number of parameters. Even in the pure gravitational sector, any corresponding
quantum theory would depend on these parameters.Comment: 10 pages. Final version to appear in Letters in Mathematical Physic
Magnetic monopoles in noncommutative quantum mechanics 2
In this paper we extend the analysis of magnetic monopoles in quantum
mechanics in three dimensional rotationally invariant noncommutative space
. We construct the model step-by-step and observe that
physical objects known from previous studies appear in a very natural way.
Nonassociativity became a topic of great interest lately, often in a connection
with magnetic monopoles. We show that this model does not possess this
property.Comment: 13 pages, no figure
Evidence Propagation and Consensus Formation in Noisy Environments
We study the effectiveness of consensus formation in multi-agent systems
where there is both belief updating based on direct evidence and also belief
combination between agents. In particular, we consider the scenario in which a
population of agents collaborate on the best-of-n problem where the aim is to
reach a consensus about which is the best (alternatively, true) state from
amongst a set of states, each with a different quality value (or level of
evidence). Agents' beliefs are represented within Dempster-Shafer theory by
mass functions and we investigate the macro-level properties of four well-known
belief combination operators for this multi-agent consensus formation problem:
Dempster's rule, Yager's rule, Dubois & Prade's operator and the averaging
operator. The convergence properties of the operators are considered and
simulation experiments are conducted for different evidence rates and noise
levels. Results show that a combination of updating on direct evidence and
belief combination between agents results in better consensus to the best state
than does evidence updating alone. We also find that in this framework the
operators are robust to noise. Broadly, Yager's rule is shown to be the better
operator under various parameter values, i.e. convergence to the best state,
robustness to noise, and scalability.Comment: 13th international conference on Scalable Uncertainty Managemen
Hydrodynamic lift of vesicles under shear flow in microgravity
The dynamics of a vesicle suspension in a shear flow between parallel plates
has been investigated under microgravity conditions, where vesicles are only
submitted to hydrodynamic effects such as lift forces due to the presence of
walls and drag forces. The temporal evolution of the spatial distribution of
the vesicles has been recorded thanks to digital holographic microscopy, during
parabolic flights and under normal gravity conditions. The collected data
demonstrates that vesicles are pushed away from the walls with a lift velocity
proportional to where is the shear rate,
the vesicle radius and its distance from the wall. This scaling as well
as the dependence of the lift velocity upon vesicle aspect ratio are consistent
with theoretical predictions by Olla [J. Phys. II France {\bf 7}, 1533--1540
(1997)].Comment: 6 pages, 8 figure
- …