2,143 research outputs found
Lab-based limits on the Carroll-Field-Jackiw Lorentz-violating electrodynamics
The CPT-odd and Lorentz-violating Carroll-Field-Jackiw modification of
electrodynamics is discussed and we study its effects on the energy spectrum of
hydrogen, as well as in the generation of a momentum-dependent electric dipole
moment for charged leptons. We also briefly comment on the possibility of the
detection of Lorentz violation in measurements of vacuum birefringence in
resonant cavities. The bounds found are based on local laboratory experimental
limits and are not competitive with the ones coming from astrophysical
considerations.Comment: Reviewed version in two columns (8 pages, 1 figure): small
corrections. Matches the version accepted for publication (Phys. Rev. D
Morin singularities and global geometry in a class of ordinary differential operators
We consider the operator acting on periodic real
valued functions. Generically, critical points of are infinite dimensional
Morin-like singularities and we provide operational characterizations of the
singularities of different orders. A global Lyapunov-Schmidt decomposition of
converts into adapted coordinates, \Fbd(\tilde v, \overline u) =
(\tilde v, \overline v), where is a function of average zero and
both and are numbers. Thus, global geometric
aspects of reduce to the study of a family of one-dimensional maps: we use
this approach to obtain normal forms for several nonlinearities . For
example, we characterize autonomous nonlinearities giving rise to global folds
and, in general, we show that is a global fold if all critical points are
folds. Also, , or, more generally, the Cafagna-Donati
nonlinearity, yield global cusps; for interpreted as a map between
appropriate Hilbert spaces, the requested changes of variable to bring to
normal form can be taken to be diffeomorphisms. A key ingredient in the
argument is the contractibility of both the critical set and the set of
non-folds for a generic autonomous nonlinearity. We also obtain a numerical
example of a polynomial of degree 4 for which contains butterflies
(Morin singularities of order 4)---% it then follows that has six
solutions for some .Comment: This is a corrected version of the paper published in 1997. 34 pages,
4 figure
Lancret helices
Helical configurations of inhomogeneous symmetric rods with non-constant
bending and twisting stiffness are studied within the framework of the
Kirchhoff rod model. From the static Kirchhoff equations, we obtain a set of
differential equations for the curvature and torsion of the centerline of the
rod and the Lancret's theorem is used to find helical solutions. We obtain a
free standing helical solution for an inhomogeneous rod whose curvature and
torsion depend on the form of variation of the bending coefficient along the
rod. These results are obtained for inhomogeneous rods without intrinsic
curvature, and for a particular case of intrinsic curvature.Comment: 31 pages, 3 figure
Helical filaments with varying cross section radius
The tridimensional configuration and the twist density of helical rods with
varying cross section radius are studied within the framework of the Kirchhoff
rod model. It is shown that the twist density increases when the cross section
radius decreases. Some tridimensional configurations of helix-like rods are
displayed showing the effects of the nonhomogeneity considered here. Since the
helix-like solutions of the nonhomogeneous rods do not present constant
curvature and torsion a set of differential equations for these quantities is
presented. We discuss the results and possible consequences.Comment: 10 pages and 5 figure
Circular and helical equilibrium solutions of inhomogeneous rods
Real filaments are not perfectly homogeneous. Most of them have various
materials composition and shapes making their stiffnesses not constant along
the arclength. We investigate the existence of circular and helical equilibrium
solutions of an intrinsically straight rod with varying bending and twisting
stiffnesses, within the framework of the Kirchhoff model. The planar ring
equilibrium solution only exists for a rod with a given form of variation of
the bending stiffness. We show that the well known circular helix is not an
equilibrium solution of the static Kirchhoff equations for a rod with non
constant bending stiffness. Our results may provide an explanation for the
variation of the curvature seen in small closed DNAs immersed in a solution
containing Zn^{2+}, and in the DNA wrapped around a nucleosome.Comment: 27 pages, 2 figure
Is it possible to grow amorphous normal nanosprings ?
Nanosprings have been object of intense investigations in recent years. They
can be classified as normal or binormal depending on the geometry of their
cross-section. Normal amorphous nanosprings have not been observed
experimentally up to now, and only recently the synthesis of a crystalline ZnO
normal nanohelix has been reported. We discuss the shape of the catalyst in
terms of the cross-sectional shape of the nanospring, and show that, within the
vapor-liquid-solid model, the growth of amorphous normal nanospring is not
energetically favoured.Comment: 12 pages, 6 figure
The Schrodinger picture and the zero-point radiation
Dalibard, Dupont-Roc and Cohen-Tannoudji (J. Physique 43 (1982) 1617; 45
(1984) 637) used the Heisenberg picture to show that the atomic transitions,
and the stability of the ground state, can only be explained by introducing
radiation reaction and vacuum fluctuation forces. Here we consider the simple
case of nonrelativistic charged harmonic oscillator, in one dimension, to
investigate how to take into account the radiation reaction and vacuum
fluctuation forces within the Schrodinger picture. We consider classical vacuum
fields and large mass oscillator.Comment: 7 pages. To be published in "Quanta, Relativity and Electromagnetism:
The Search for Unity in Physics", Proceedings of a Symposium in Honor of
Jean-Pierre Vigier (Paris, September, 2003). Kluwer Academic Publisher
Mechanical properties of amorphous nanosprings
Helical amorphous nanosprings have attracted particular interest due to their
special mechanical properties. In this work we present a simple model, within
the framework of the Kirchhoff rod model, for investigating the structural
properties of nanosprings having asymmetric cross section. We have derived
expressions that can be used to obtain the Young's modulus and Poisson's ratio
of the nanospring material composite. We also address the importance of the
presence of a catalyst in the growth process of amorphous nanosprings in terms
of the stability of helical rods.Comment: 14 pages, 4 figure
A novel test of Lorentz violation in the photon sector with an LC circuit
In the presence of an external magnetic field, the Carroll-Field-Jackiw term
introduces a displacement current proportional to the Lorentz-violating
background that induces a time-dependent magnetic field. Axion-like particles
or hidden photons could generate an analogous signal, potentially detectable
with the set-up suggested by Sikivie, Tanner and Sullivan - a sensitive
magnetometer coupled to a superconducting LC circuit. We show that a similar
set-up, but with an externally driven pick-up loop whose area varies
harmonically at Hz, can be used to probe the spatial components of the
Lorentz-violating background to the level of GeV. This is
eight orders of magnitude more sensitive than previous laboratory-based limits.Comment: 6 pages, 1 figure, matches published versio
Lorentz violation in simple QED processes
We determine the effect of a CPT-even and Lorentz violating non-minimal
coupling on the differential cross sections for some of the most important
tree-level processes in QED, namely, Compton and Bhabha scatterings, as well as
electron-positron annihilation. Experimental limits constraining the allowed
deviation of the differential cross sections relative to pure QED allow us to
place upper bounds on the Lorentz violating parameters. A constraint based on
the decay rate of para-positronium is also obtained.Comment: Final version, includind suggestions of the referee. Published in PR
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