10,586 research outputs found
Parametrization of the Driven Betatron Oscillation
An AC dipole is a magnet which produces a sinusoidally oscillating dipole
field and excites coherent transverse beam motion in a synchrotron. By
observing this coherent motion, the optical parameters can be directly measured
at the beam position monitor locations. The driven oscillation induced by an AC
dipole will generate a phase space ellipse which differs from that of the free
oscillation. If not properly accounted for, this difference can lead to a
misinterpretation of the actual optical parameters, for instance, of 6% or more
in the cases of the Tevatron, RHIC, or LHC. The effect of an AC dipole on the
linear optics parameters is identical to that of a thin lens quadrupole. By
introducing a new amplitude function to describe this new phase space ellipse,
the motion produced by an AC dipole becomes easier to interpret. Beam position
data taken under the influence of an AC dipole, with this new interpretation in
mind, can lead to more precise measurements of the normal Courant-Snyder
parameters. This new parameterization of the driven motion is presented and is
used to interpret data taken in the FNAL Tevatron using an AC dipole.Comment: 8 pages, 8 figures, and 1 tabl
Hawking radiation of a vector field and gravitational anomalies
Recently, the relation between Hawking radiation and gravitational anomalies
has been used to estimate the flux of Hawking radiation for a large class of
black objects. In this paper, we extend the formalism, originally proposed by
Robinson and Wilczek, to the Hawking radiation of vector particles (photons).
It is explicitly shown, with Hamiltonian formalism, that the theory of an
electromagnetic field on d-dimensional spherical black holes reduces to one of
an infinite number of massive complex scalar fields on 2-dimensional spacetime,
for which the usual anomaly-cancellation method is available. It is found that
the total energy emitted from the horizon for the electromagnetic field is just
(d-2) times as that for a scalar field. The results support the picture that
Hawking radiation can be regarded as an anomaly eliminator on horizons.
Possible extensions and applications of the analysis are discussed.Comment: 14 pages, 1 figur
Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems
The long-time behavior of the survival probability for unstable multilevel
systems that follows the power-decay law is studied based on the N-level
Friedrichs model, and is shown to depend on the initial population in unstable
states. A special initial state maximizing the asymptote of the survival
probability at long times is found and examined by considering the spontaneous
emission process for the hydrogen atom interacting with the electromagnetic
field.Comment: 5 pages, 1 table. Accepted for publication in Phys. Rev.
Zero energy resonance and the logarithmically slow decay of unstable multilevel systems
The long time behavior of the reduced time evolution operator for unstable
multilevel systems is studied based on the N-level Friedrichs model in the
presence of a zero energy resonance.The latter means the divergence of the
resolvent at zero energy. Resorting to the technique developed by Jensen and
Kato [Duke Math. J. 46, 583 (1979)], the zero energy resonance of this model is
characterized by the zero energy eigenstate that does not belong to the Hilbert
space. It is then shown that for some kinds of the rational form factors the
logarithmically slow decay of the reduced time evolution operator can be
realized.Comment: 31 pages, no figure
Long-Lived Double-Barred Galaxies: Critical Mass and Length Scales
A substantial fraction of disk galaxies is double-barred. We analyze the
dynamical stability of such nested bar systems by means of Liapunov
exponents,by fixing a generic model and varying the inner (secondary) bar mass.
We show that there exists a critical mass below which the secondary bar cannot
sustain its own orbital structure, and above which it progressively destroys
the outer (primary) bar-supporting orbits. In this critical state, a large
fraction of the trajectories (regular and chaotic) are aligned with either bar,
suggesting the plausibility of long-lived dynamical states when
secondary-to-primary bar mass ratio is of the order of a few percent.
Qualitatively similar results are obtained by varying the size of the secondary
bar, within certain limits, while keeping its mass constant. In both cases, an
important role appears to be played by chaotic trajectories which are trapped
around (especially) the primary bar for long periods of time.Comment: 7 pages, 1 figure, to be published in Astrophysical Journal Letters
(Vol. 595, 9/20/03 issue). Replaced by revised figure and corrected typo
Instabilities and stickiness in a 3D rotating galactic potential
We study the dynamics in the neighborhood of simple and double unstable
periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic
type. In order to visualize the four dimensional spaces of section we use the
method of color and rotation. We investigate the structure of the invariant
manifolds that we found in the neighborhood of simple and double unstable
periodic orbits in the 4D spaces of section. We consider orbits in the
neighborhood of the families x1v2, belonging to the x1 tree, and the z-axis
(the rotational axis of our system). Close to the transition points from
stability to simple instability, in the neighborhood of the bifurcated simple
unstable x1v2 periodic orbits we encounter the phenomenon of stickiness as the
asymptotic curves of the unstable manifold surround regions of the phase space
occupied by rotational tori existing in the region. For larger energies, away
from the bifurcating point, the consequents of the chaotic orbits form clouds
of points with mixing of color in their 4D representations. In the case of
double instability, close to x1v2 orbits, we find clouds of points in the four
dimensional spaces of section. However, in some cases of double unstable
periodic orbits belonging to the z-axis family we can visualize the associated
unstable eigensurface. Chaotic orbits close to the periodic orbit remain sticky
to this surface for long times (of the order of a Hubble time or more). Among
the orbits we studied we found those close to the double unstable orbits of the
x1v2 family having the largest diffusion speed.Comment: 29pages, 25 figures, accepted for publication in the International
Journal of Bifurcation and Chao
Constraining global properties of the Draco dwarf spheroidal galaxy
By fitting a flexible stellar anisotropy model to the observed surface
brightness and line-of-sight velocity dispersion profiles of Draco we derive a
sequence of cosmologically plausible two-component (stars + dark matter) models
for this galaxy. The models are consistent with all the available observations
and can have either cuspy Navarro-Frenk-White or flat-cored dark matter density
profiles. The dark matter halos either formed relatively recently (at z~2...7)
and are massive (up to ~5x10^9 M_Sun), or formed before the end of the
reionization of the universe (z~7...11) and are less massive (down to ~7x10^7
M_Sun). Our results thus support either of the two popular solutions of the
"missing satellites" problem of Lambda cold dark matter cosmology - that dwarf
spheroidals are either very massive, or very old. We carry out high-resolution
simulations of the tidal evolution of our two-component Draco models in the
potential of the Milky Way. The results of our simulations suggest that the
observable properties of Draco have not been appreciably affected by the
Galactic tides after 10 Gyr of evolution. We rule out Draco being a "tidal
dwarf" - a tidally disrupted dwarf galaxy. Almost radial Draco orbits (with the
pericentric distance <15 kpc) are also ruled out by our analysis. The case of a
harmonic dark matter core can be consistent with observations only for a very
limited choice of Draco orbits (with the apocentric-to-pericentric distances
ratio of <2.5).Comment: 18 pages, 14 figures; accepted by Ap
Disordered Carbon nanotube alloys in the Effect Medium Super Cell Approximation
We investigate a disordered single-walled carbon nanotube (SWCNT) in an
effective medium super cell approximation (EMSCA).
First type of disorder that we consider is the presence of vacancies.
Our results show that the vacancies induce some bound states on their
neighbor host sites, leading to the creation of a band around the Fermi energy
in the SWCNT average density of states.Second type of disorder considered is a
substitutional alloy due to it's applications in
hetrojunctions. We found that for a fixed boron (nitrogen) concentration, by
increasing the nitrogen (boron) concentration the averaged semiconducting gap,
, decreases and at a critical concentration it disappears. A consequence
of our results for nano electronic devices is that by changing the
boron(nitrogen) concentration, one can make a semiconductor SWCNT with a
pre-determined energy gap.Comment: 4 page
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