9,575 research outputs found
Non-renormalization of two and three Point Correlators of N=4 SYM in N=1 Superspace
Certain two and three point functions of gauge invariant primary operators of
SYM are computed in superspace keeping all the
-components. This allows one to read off many component descendent
correlators. Our results show the only possible corrections to the
free field correlators are contact terms. Therefore they vanish for operators
at separate points, verifying the known non-renormalization theorems. This also
implies the results are consistent with supersymmetry even though
the Lagrangian we use has only manifest supersymmetry. We repeat
some of the calculations using supersymmetric Landau gauge and obtain, as
expected, the same results as those of supersymmetric Feynman gauge.Comment: 10 pages, 20 eps figures, references adde
Breathers in inhomogeneous nonlinear lattices: an analysis via centre manifold reduction
We consider an infinite chain of particles linearly coupled to their nearest
neighbours and subject to an anharmonic local potential. The chain is assumed
weakly inhomogeneous. We look for small amplitude discrete breathers. The
problem is reformulated as a nonautonomous recurrence in a space of
time-periodic functions, where the dynamics is considered along the discrete
spatial coordinate. We show that small amplitude oscillations are determined by
finite-dimensional nonautonomous mappings, whose dimension depends on the
solutions frequency. We consider the case of two-dimensional reduced mappings,
which occurs for frequencies close to the edges of the phonon band. For an
homogeneous chain, the reduced map is autonomous and reversible, and
bifurcations of reversible homoclinics or heteroclinic solutions are found for
appropriate parameter values. These orbits correspond respectively to discrete
breathers, or dark breathers superposed on a spatially extended standing wave.
Breather existence is shown in some cases for any value of the coupling
constant, which generalizes an existence result obtained by MacKay and Aubry at
small coupling. For an inhomogeneous chain the study of the nonautonomous
reduced map is in general far more involved. For the principal part of the
reduced recurrence, using the assumption of weak inhomogeneity, we show that
homoclinics to 0 exist when the image of the unstable manifold under a linear
transformation intersects the stable manifold. This provides a geometrical
understanding of tangent bifurcations of discrete breathers. The case of a mass
impurity is studied in detail, and our geometrical analysis is successfully
compared with direct numerical simulations
Bright and dark breathers in Fermi-Pasta-Ulam lattices
In this paper we study the existence and linear stability of bright and dark
breathers in one-dimensional FPU lattices. On the one hand, we test the range
of validity of a recent breathers existence proof [G. James, {\em C. R. Acad.
Sci. Paris}, 332, Ser. 1, pp. 581 (2001)] using numerical computations.
Approximate analytical expressions for small amplitude bright and dark
breathers are found to fit very well exact numerical solutions even far from
the top of the phonon band. On the other hand, we study numerically large
amplitude breathers non predicted in the above cited reference. In particular,
for a class of asymmetric FPU potentials we find an energy threshold for the
existence of exact discrete breathers, which is a relatively unexplored
phenomenon in one-dimensional lattices. Bright and dark breathers superposed on
a uniformly stressed static configuration are also investigated.Comment: 11 pages, 16 figure
Equilibrium Phases of Tilted Dipolar Lattice Bosons
The recent advances in creating nearly degenerate quantum dipolar gases in
optical lattices are opening the doors for the exploration of equilibrium
physics of quantum systems with anisotropic and long-range dipolar
interactions. In this paper we study the zero- and finite-temperature phase
diagrams of a system of hard-core dipolar bosons at half-filling, trapped in a
two-dimensional optical lattice. The dipoles are aligned parallel to one
another and tilted out of the optical lattice plane by means of an external
electric field. At zero-temperature, the system is a superfluid at all tilt
angles provided that the strength of dipolar interaction is below a
critical value . Upon increasing the interaction strength while
keeping fixed, the superfluid phase is destabilized in favor of a
checkerboard or a stripe solid depending on the tilt angle. We explore the
nature of the phase transition between the two solid phases and find evidence
of a micro-emulsion phase, following the Spivak-Kivelson scenario, separating
these two solid phases. Additionally, we study the stability of these quantum
phases against thermal fluctuations and find that the stripe solid is the most
robust, making it the best candidate for experimental observation.Comment: 7 pages, 6 figure
Breathers in FPU systems, near and far from the phonon band
There exists a recent mathematical proof on the existence of small amplitude
breathers in FPU systems near the phonon band, which includes a prediction of
their amplitude and width. In this work we obtain numerically these breathers,
and calculate the range of validity of the predictions, which extends
relatively far from the phonon band. There exist also large amplitude breathers
with the same frequency, with the consequence that there is an energy gap for
breather creation in these systems.Comment: 3 pages, 2 figures, proceeding of the conference on Localization and
to and Energy Transfer in Nonlinear Systems, June 17-21, 2002, San Lorenzo de
El Escorial, Madrid, Spain. To be published by World Scientifi
Nilpotent invariants in N=4 SYM
It is shown that there are no nilpotent invariants in N=4 analytic superspace
for points. It is argued that there is (at least) one such invariant
for n=5 points which is not invariant under U(1)_Y. The consequences of these
results are that the n=2 and 3 point correlation functions of the N=4
gauge-invariant operators which correspond to KK multiplets in AdS supergravity
are given exactly by their tree level expressions, the 4 point correlation
functions of such operators are invariant under U(1)_Y and correlation
functions with points have non-trivial dependence on the Yang-Mills
coupling constant.Comment: 9 page
Thermodynamics of quantum degenerate gases in optical lattices
The entropy-temperature curves are calculated for non-interacting Bose and
Fermi gases in a 3D optical lattice. These curves facilitate understanding of
how adiabatic changes in the lattice depth affect the temperature, and we
demonstrate regimes where the atomic sample can be significantly heated or
cooled by the loading process. We assess the effects of interactions on a Bose
gas in a deep optical lattice, and show that interactions ultimately limit the
extent of cooling that can occur during lattice loading.Comment: 6 pages, 4 figures. Submitted to proceedings of Laser Physics 2006
Worksho
The Axion and the Goldstone Higgs
We consider the renormalizable -model, in which the
Higgs particle has a pseudo-Nambu-Goldstone boson character, and explore what
the minimal field extension required to implement the Peccei-Quinn symmetry
(PQ) is, within the partial compositeness scenario. It turns out that the
minimal model does not require the enlargement of the exotic fermionic sector,
but only the addition of a singlet scalar: it is sufficient that the exotic
fermions involved in partial compositeness and the singlet scalar become
charged under Peccei-Quinn transformations. We explore the phenomenological
predictions for photonic signals in axion searches for all models discussed.
Because of the constraints imposed on the exotic fermion sector by the Standard
Model fermion masses, the expected range of allowed axion-photon couplings
turns out to be generically narrowed with respect to that of standard invisible
axion models, impacting the experimental quest.Comment: 31 pages, 2 Figures. Description improved, results unchange
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