9,296 research outputs found
Chern-Simons Theory with Sources and Dynamical Quantum Groups I: Canonical Analysis and Algebraic Structures
We study the quantization of Chern-Simons theory with group coupled to
dynamical sources. We first study the dynamics of Chern-Simons sources in the
Hamiltonian framework. The gauge group of this system is reduced to the Cartan
subgroup of We show that the Dirac bracket between the basic dynamical
variables can be expressed in term of dynamical matrix of rational type.
We then couple minimally these sources to Chern-Simons theory with the use of
a regularisation at the location of the sources. In this case, the gauge
symmetries of this theory split in two classes, the bulk gauge transformation
associated to the group and world lines gauge transformations associated to
the Cartan subgroup of . We give a complete hamiltonian analysis of this
system and analyze in detail the Poisson algebras of functions invariant under
the action of bulk gauge transformations. This algebra is larger than the
algebra of Dirac observables because it contains in particular functions which
are not invariant under reparametrization of the world line of the sources. We
show that the elements of this Poisson algebra have Poisson brackets expressed
in term of dynamical matrix of trigonometric type. This algebra is a
dynamical generalization of Fock-Rosly structure. We analyze the quantization
of these structures and describe different star structures on these algebras,
with a special care to the case where and
having in mind to apply these results to the
study of the quantization of massive spinning point particles coupled to
gravity with a cosmological constant in 2+1 dimensions.Comment: 32 pages and 1 eps figur
Harmonic Analysis on the quantum Lorentz group
This work begins with a review of complexification and realification of Hopf
algebras. We emphasize the notion of multiplier Hopf algebras for the
description of different classes of functions (compact supported, bounded,
unbounded) on complex quantum groups and the construction of the associated
left and right Haar measure. Using a continuation of symbols of
with complex spins, we give a new description of the unitary representations of
SL_q (2,\CC)_{\RR} and find explicit expressions for the characters of SL_q
(2,\CC)_{\RR}. The major theorem of this article is the Plancherel theorem for
the Quantum Lorentz Group.Comment: 60 pages, tared gzipped Postscript file, major revision of the
previous version, the Plancherel theorem is established in the more general
sense and we delay the study of Fusion theory to the next part of this pape
Shot-noise statistics in diffusive conductors
We study the full probability distribution of the charge transmitted through
a mesoscopic diffusive conductor during a measurement time T. We have
considered a semi-classical model, with an exclusion principle in a discretized
single-particle phase-space. In the large T limit, numerical simulations show a
universal probability distribution which agrees very well with the quantum
mechanical prediction of Lee, Levitov and Yakovets [PRB {51} 4079 (1995)] for
the charge counting statistics. Special attention is given to its third
cumulant, including an analysis of finite size effects and of some experimental
constraints for its accurate measurement.Comment: Submitted to Eur. Phys. J. B (Jan. 2002
Applicability of Boussinesq approximation in a turbulent fluid with constant properties
The equations of motion describing buoyant fluids are often simplified using
a set of approximations proposed by J. Boussinesq one century ago. To resume,
they consist in assuming constant fluid properties, incompressibility and
conservation of calories during heat transport. Assuming fulfilment of the
first requirement (constant fluid properties), we derive a set of 4 criteria
for assessing the validity of the two other requirements in turbulent
Rayleigh-B\'enard convection. The first criterion simply
results from the incompressibility condition in the thermal boundary layer
( and are the thermal expansion coefficient and the
temperature difference driving the flow). The 3 other criteria are proportional
or quadratic with the density stratification or, equivalently with the
temperature difference resulting from the adiabatic gradient across the cell
. Numerical evaluations with air, water and cryogenic helium show
that most laboratory experiments are free from such Boussinesq violation as
long as the first criterion is fulfilled. In ultra high Rayleigh numbers
() experiments in He, one of the stratification criteria, scaling
with , could be violated. This criterion garanties that
pressure fluctuations have a negligible influence both on the density variation
and on the heat transfer equation through compression/expansion cycles.
Extrapolation to higher suggests that strong violation of Boussinesq
approximation could occur in atmospheric convection.Comment: Submitted to Phys.Fluids (oct 2007
Universal Solutions of Quantum Dynamical Yang-Baxter Equations
We construct a universal trigonometric solution of the Gervais-Neveu-Felder
equation in the case of finite dimensional simple Lie algebras and finite
dimensional contragredient simple Lie superalgebras.Comment: 12 pages, LaTeX2e with packages vmargin, wasysym, amsmath, amssym
Quantum Dynamical coBoundary Equation for finite dimensional simple Lie algebras
For a finite dimensional simple Lie algebra g, the standard universal
solution R(x) in of the Quantum Dynamical Yang--Baxter
Equation can be built from the standard R--matrix and from the solution F(x) in
of the Quantum Dynamical coCycle Equation as
It has been conjectured that, in the case
where g=sl(n+1) n greater than 1 only, there could exist an element M(x) in
such that in which is
the universal cocycle associated to the Cremmer--Gervais's solution. The aim of
this article is to prove this conjecture and to study the properties of the
solutions of the Quantum Dynamical coBoundary Equation. In particular, by
introducing new basic algebraic objects which are the building blocks of the
Gauss decomposition of M(x), we construct M(x) in as an explicit
infinite product which converges in every finite dimensional representation. We
emphasize the relations between these basic objects and some Non Standard Loop
algebras and exhibit relations with the dynamical quantum Weyl group.Comment: 46 page
Vortex spectrum in superfluid turbulence: interpretation of a recent experiment
We discuss a recent experiment in which the spectrum of the vortex line
density fluctuations has been measured in superfluid turbulence. The observed
frequency dependence of the spectrum, , disagrees with classical
vorticity spectra if, following the literature, the vortex line density is
interpreted as a measure of the vorticity or enstrophy. We argue that the
disagrement is solved if the vortex line density field is decomposed into a
polarised field (which carries most of the energy) and an isotropic field
(which is responsible for the spectrum).Comment: Submitted for publication
http://crtbt.grenoble.cnrs.fr/helio/GROUP/infa.html
http://www.mas.ncl.ac.uk/~ncfb
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