21,400 research outputs found
Large N_c in chiral perturbation theory
The construction of the effective Lagrangian relevant for the mesonic sector
of QCD in the large N_c limit meets with a few rather subtle problems. We
thoroughly examine these and show that, if the variables of the effective
theory are chosen suitably, the known large N_c counting rules of QCD can
unambiguously be translated into corresponding counting rules for the effective
coupling constants. As an application, we demonstrate that the Kaplan-Manohar
transformation is in conflict with these rules and is suppressed to all orders
in 1/N_c. The anomalous dimension of the axial singlet current generates an
additional complication: The corresponding external field undergoes
nonmultiplicative renormalization. As a consequence, the Wess-Zumino-Witten
term, which accounts for the U(3)_R x U(3)_L anomalies in the framework of the
effective theory, contains pieces that depend on the running scale of QCD. The
effect only shows up at nonleading order in 1/N_c, but requires specific
unnatural parity contributions in the effective Lagrangian that restore
renormalization group invariance.Comment: 56 page
Driven collective instabilities in magneto-optical traps: a fluid-dynamical approach
We present a theoretical model to describe an instability mechanism in
ultra-cold gases, where long-range interactions are taken into account.
Focusing on the nonlinear coupling between the collective (plasma-like) and the
center-of-mass modes, we show that the resulting dynamics is governed by a
parametric equation of the generalized Mathieu type and compute the
corresponding stability chart. We apply our model to typical ranges of
magneto-optical traps (MOT) parameters and find a good agreement with previous
experimental observations.Comment: 4 pages, 3 figures. Some minor changes in the published version
Inflationary paradigm after Planck 2013
Models of cosmic inflation posit an early phase of accelerated expansion of
the universe, driven by the dynamics of one or more scalar fields in curved
spacetime. Though detailed assumptions about fields and couplings vary across
models, inflation makes specific, quantitative predictions for several
observable quantities, such as the flatness parameter ()
and the spectral tilt of primordial curvature perturbations (), among others---predictions that match the latest
observations from the {\it Planck} satellite to very good precision. In the
light of data from {\it Planck} as well as recent theoretical developments in
the study of eternal inflation and the multiverse, we address recent criticisms
of inflation by Ijjas, Steinhardt, and Loeb. We argue that their conclusions
rest on several problematic assumptions, and we conclude that cosmic inflation
is on a stronger footing than ever before.Comment: 11 pages, no figures; added references, and brief additions to
Footnote 1, Section VI, and the Acknowledgment
A Kohn-Sham system at zero temperature
An one-dimensional Kohn-Sham system for spin particles is considered which
effectively describes semiconductor {nano}structures and which is investigated
at zero temperature. We prove the existence of solutions and derive a priori
estimates. For this purpose we find estimates for eigenvalues of the
Schr\"odinger operator with effective Kohn-Sham potential and obtain
-bounds of the associated particle density operator. Afterwards,
compactness and continuity results allow to apply Schauder's fixed point
theorem. In case of vanishing exchange-correlation potential uniqueness is
shown by monotonicity arguments. Finally, we investigate the behavior of the
system if the temperature approaches zero.Comment: 27 page
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