209 research outputs found
Linear Connections on the Two Parameter Quantum Plane
We apply a recently proposed definition of a linear connection in non
commutative geometry based on the natural bimodule structure of the algebra of
differential forms to the case of the two-parameter quantum plane. We find that
there exists a non trivial family of linear connections only when the two
parameters obeys a specific relation.Comment: 7 pages, Te
Global quantum Hall phase diagram from visibility diagrams
We propose a construction of a global phase diagram for the quantum Hall
effect. This global phase diagram is based on our previous constructions of
visibility diagrams in the context of the Quantum Hall Effect. The topology of
the phase diagram we obtain is in good agreement with experimental observations
(when the spin effect can be neglected). This phase diagram does not show
floating.Comment: LaTeX2e, 9 pages, 5 eps figure
Vortex in Maxwell-Chern-Simons models coupled to external backgrounds
We consider Maxwell-Chern-Simons models involving different non-minimal
coupling terms to a non relativistic massive scalar and further coupled to an
external uniform background charge. We study how these models can be
constrained to support static radially symmetric vortex configurations
saturating the lower bound for the energy. Models involving Zeeman-type
coupling support such vortices provided the potential has a "symmetry breaking"
form and a relation between parameters holds. In models where minimal coupling
is supplemented by magnetic and electric field dependant coupling terms, non
trivial vortex configurations minimizing the energy occur only when a non
linear potential is introduced. The corresponding vortices are studied
numericallyComment: LaTeX file, 2 figure
The static potential in QED with non-minimal coupling
Here we study the effect of the non-minimal coupling j^{\mu}\eps
\partial^{\nu} A^{\alpha} on the static potential in multiflavor QED.
Both cases of four and two components fermions are studied separately at
leading order in the expansion. Although a non-local Chern-Simons term
appears, in the four components case the photon is still massless leading to a
confining logarithmic potential similar to the classical one. In the two
components case, as expected, the parity breaking fermion mass term generates a
traditional Chern-Simons term which makes the photon massive and we have a
screening potential which vanishes at large inter-charge distance. The extra
non-minimal couplings have no important influence on the static potential at
large inter-charge distances. However, interesting effects show up at finite
distances. In particular, for strong enough non-minimal coupling we may have a
new massive pole in the photon propagator while in the opposite limit there may
be no poles at all in the irreducible case. We also found that, in general, the
non-minimal couplings lead to a finite range {\bf repulsive} force between
charges of opposite signs.Comment: 19 pages and 7 figure
Visibility diagrams and experimental stripe structure in the quantum Hall effect
We analyze various properties of the visibility diagrams that can be used in
the context of modular symmetries and confront them to some recent experimental
developments in the Quantum Hall Effect. We show that a suitable physical
interpretation of the visibility diagrams which permits one to describe
successfully the observed architecture of the Quantum Hall states gives rise
naturally to a stripe structure reproducing some of the experimental features
that have been observed in the study of the quantum fluctuations of the Hall
conductance. Furthermore, we exhibit new properties of the visibility diagrams
stemming from the structure of subgroups of the full modular group.Comment: 8 pages in plain TeX, 7 figures in a single postscript fil
Galactic Spiral Structure
We describe the structure and composition of six major stellar streams in a
population of 20 574 local stars in the New Hipparcos Reduction with known
radial velocities. We find that, once fast moving stars are excluded, almost
all stars belong to one of these streams. The results of our investigation have
lead us to re-examine the hydrogen maps of the Milky Way, from which we
identify the possibility of a symmetric two-armed spiral with half the
conventionally accepted pitch angle. We describe a model of spiral arm motions
which matches the observed velocities and composition of the six major streams,
as well as the observed velocities of the Hyades and Praesepe clusters at the
extreme of the Hyades stream. We model stellar orbits as perturbed ellipses
aligned at a focus in coordinates rotating at the rate of precession of
apocentre. Stars join a spiral arm just before apocentre, follow the arm for
more than half an orbit, and leave the arm soon after pericentre. Spiral
pattern speed equals the mean rate of precession of apocentre. Spiral arms are
shown to be stable configurations of stellar orbits, up to the formation of a
bar and/or ring. Pitch angle is directly related to the distribution of orbital
eccentricities in a given spiral galaxy. We show how spiral galaxies can evolve
to form bars and rings. We show that orbits of gas clouds are stable only in
bisymmetric spirals. We conclude that spiral galaxies evolve toward grand
design two-armed spirals. We infer from the velocity distributions that the
Milky Way evolved into this form about 9 Gyrs ago.Comment: Published in Proc Roy Soc A. A high resolution version of this file
can be downloaded from http://papers.rqgravity.net/SpiralStructure.pdf. A
simplified account with animations begins at
http://rqgravity.net/SpiralStructur
3D MHD Modeling of the Gaseous Structure of the Galaxy: Synthetic Observations
We generated synthetic observations from the four-arm model presented in
Gomez & Cox (2004) for the Galactic ISM in the presence of a spiral
gravitational perturbation. We found that velocity crowding and diffusion have
a strong effect in the l-v diagram. The v-b diagram presents structures at the
expected spiral arm velocities, that can be explained by the off-the-plane
structure of the arms presented in previous papers of this series. Such
structures are observed in the Leiden/Dwingeloo HI survey. The rotation curve,
as measured from the inside of the modeled galaxy, shows similarities with the
observed one for the Milky Way Galaxy, although it has large deviations from
the smooth circular rotation corresponding to the background potential. The
magnetic field inferred from a synthetic synchrotron map shows a largely
circular structure, but with interesting deviations in the midplane due to
distortion of the field from circularity in the interarm regions.Comment: Accepted for publication in ApJ. Better quality figures in
http://www.astro.umd.edu/~gomez/publica/3d_galaxy-3.pd
Renormalization of modular invariant Coulomb gas and Sine-Gordon theories, and quantum Hall flow diagram
Using the renormalisation group (RG) we study two dimensional electromagnetic
coulomb gas and extended Sine-Gordon theories invariant under the modular group
SL(2,Z). The flow diagram is established from the scaling equations, and we
derive the critical behaviour at the various transition points of the diagram.
Following proposal for a SL(2,Z) duality between different quantum Hall fluids,
we discuss the analogy between this flow and the global quantum Hall phase
diagram.Comment: 10 pages, 1 EPS figure include
Quantum Hall Conductivity in a Landau Type Model with a Realistic Geometry
In this paper, we revisit some quantum mechanical aspects related to the
Quantum Hall Effect. We consider a Landau type model, paying a special
attention to the experimental and geometrical features of Quantum Hall
experiments. The resulting formalism is then used to compute explicitely the
Hall conductivity from a Kubo formula.Comment: LaTeX, 1 eps figur
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