38,610 research outputs found
Residue currents associated with weakly holomorphic functions
We construct Coleff-Herrera products and Bochner-Martinelli type residue
currents associated with a tuple of weakly holomorphic functions, and show
that these currents satisfy basic properties from the (strongly) holomorphic
case, as the transformation law, the Poincar\'e-Lelong formula and the
equivalence of the Coleff-Herrera product and the Bochner-Martinelli type
residue current associated with when defines a complete intersection.Comment: 28 pages. Updated with some corrections from the revision process. In
particular, corrected and clarified some things in Section 5 and 6 regarding
products of weakly holomorphic functions and currents, and the definition of
the Bochner-Martinelli type current
Event-by-event fluctuations of the charged particle ratio from non-equilibrium transport theory
The event by event fluctuations of the ratio of positively to negatively
charged hadrons are predicted within the UrQMD model. Corrections for finite
acceptance and finite net charge are derived. These corrections are relevant to
compare experimental data and transport model results to previous predictions.
The calculated fluctuations at RHIC and SPS energies are shown to be compatible
with a hadron gas. Thus, deviating by a factor of 3 from the predictions for a
thermalized quark-gluon plasma.Comment: This paper clarifies the previous predictions of Jeon and Koch
(hep-ph/0003168) and addresses issues raised in hep-ph/0006023. 2 Figures,
10pp, uses RevTe
Superfluid instability of r-modes in "differentially rotating" neutron stars
Superfluid hydrodynamics affects the spin-evolution of mature neutron stars,
and may be key to explaining timing irregularities such as pulsar glitches.
However, most models for this phenomenon exclude the global instability
required to trigger the event. In this paper we discuss a mechanism that may
fill this gap. We establish that small scale inertial r-modes become unstable
in a superfluid neutron star that exhibits a rotational lag, expected to build
up due to vortex pinning as the star spins down. Somewhat counterintuitively,
this instability arises due to the (under normal circumstances dissipative)
vortex-mediated mutual friction. We explore the nature of the superfluid
instability for a simple incompressible model, allowing for entrainment
coupling between the two fluid components. Our results recover a previously
discussed dynamical instability in systems where the two components are
strongly coupled. In addition, we demonstrate for the first time that the
system is secularly unstable (with a growth time that scales with the mutual
friction) throughout much of parameter space. Interestingly, large scale
r-modes are also affected by this new aspect of the instability. We analyse the
damping effect of shear viscosity, which should be particularly efficient at
small scales, arguing that it will not be sufficient to completely suppress the
instability in astrophysical systems.Comment: RevTex, 11 figure
Weighted integral formulas on manifolds
We present a method of finding weighted Koppelman formulas for -forms
on -dimensional complex manifolds which admit a vector bundle of rank
over , such that the diagonal of has a defining
section. We apply the method to \Pn and find weighted Koppelman formulas for
-forms with values in a line bundle over \Pn. As an application, we
look at the cohomology groups of -forms over \Pn with values in
various line bundles, and find explicit solutions to the \dbar-equation in
some of the trivial groups. We also look at cohomology groups of -forms
over \Pn \times \Pm with values in various line bundles. Finally, we apply
our method to developing weighted Koppelman formulas on Stein manifolds.Comment: 25 page
Non-adiabatic holonomic quantum computation
We develop a non-adiabatic generalization of holonomic quantum computation in
which high-speed universal quantum gates can be realized by using non-Abelian
geometric phases. We show how a set of non-adiabatic holonomic one- and
two-qubit gates can be implemented by utilizing optical transitions in a
generic three-level configuration. Our scheme opens up for universal
holonomic quantum computation on qubits characterized by short coherence times.Comment: Some changes, journal reference adde
Advective collisions
Small particles advected in a fluid can collide (and therefore aggregate) due
to the stretching or shearing of fluid elements. This effect is usually
discussed in terms of a theory due to Saffman and Turner [J. Fluid Mech., 1,
16-30, (1956)]. We show that in complex or random flows the Saffman-Turner
theory for the collision rate describes only an initial transient (which we
evaluate exactly). We obtain precise expressions for the steady-state collision
rate for flows with small Kubo number, including the influence of fractal
clustering on the collision rate for compressible flows. For incompressible
turbulent flows, where the Kubo number is of order unity, the Saffman-Turner
theory is an upper bound.Comment: 4 pages, 1 figur
R-mode oscillations and rocket effect in rotating superfluid neutron stars. I. Formalism
We derive the hydrodynamical equations of r-mode oscillations in neutron
stars in presence of a novel damping mechanism related to particle number
changing processes. The change in the number densities of the various species
leads to new dissipative terms in the equations which are responsible of the
{\it rocket effect}. We employ a two-fluid model, with one fluid consisting of
the charged components, while the second fluid consists of superfluid neutrons.
We consider two different kind of r-mode oscillations, one associated with
comoving displacements, and the second one associated with countermoving, out
of phase, displacements.Comment: 10 page
Gravitational-wave astronomy: the high-frequency window
This contribution is divided in two parts. The first part provides a
text-book level introduction to gravitational radiation. The key concepts
required for a discussion of gravitational-wave physics are introduced. In
particular, the quadrupole formula is applied to the anticipated
``bread-and-butter'' source for detectors like LIGO, GEO600, EGO and TAMA300:
inspiralling compact binaries. The second part provides a brief review of high
frequency gravitational waves. In the frequency range above (say) 100Hz,
gravitational collapse, rotational instabilities and oscillations of the
remnant compact objects are potentially important sources of gravitational
waves. Significant and unique information concerning the various stages of
collapse, the evolution of protoneutron stars and the details of the
supranuclear equation of state of such objects can be drawn from careful study
of the gravitational-wave signal. As the amount of exciting physics one may be
able to study via the detections of gravitational waves from these sources is
truly inspiring, there is strong motivation for the development of future
generations of ground based detectors sensitive in the range from hundreds of
Hz to several kHz.Comment: 21 pages, 5 figures, Lectures presented at the 2nd Aegean Summer
School on the Early Universe, Syros, Greece, September 200
Pulsar spin-down: the glitch-dominated rotation of PSR J0537-6910
The young, fast-spinning, X-ray pulsar J0537-6910 displays an extreme glitch
activity, with large spin-ups interrupting its decelerating rotation every ~100
days. We present nearly 13 years of timing data from this pulsar, obtained with
the {\it Rossi X-ray Timing Explorer}. We discovered 22 new glitches and
performed a consistent analysis of all 45 glitches detected in the complete
data span. Our results corroborate the previously reported strong correlation
between glitch spin-up size and the time to the next glitch, a relation that
has not been observed so far in any other pulsar. The spin evolution is
dominated by the glitches, which occur at a rate ~3.5 per year, and the
post-glitch recoveries, which prevail the entire inter-glitch intervals. This
distinctive behaviour provides invaluable insights into the physics of
glitches. The observations can be explained with a multi-component model which
accounts for the dynamics of the neutron superfluid present in the crust and
core of neutron stars. We place limits on the moment of inertia of the
component responsible for the spin-up and, ignoring differential rotation, the
velocity difference it can sustain with the crust. Contrary to its rapid
decrease between glitches, the spin-down rate increased over the 13 years, and
we find the long-term braking index , the only negative
braking index seen in a young pulsar. We briefly discuss the plausible
interpretations of this result, which is in stark contrast to the predictions
of standard models of pulsar spin-down.Comment: Minor changes to match the MNRAS accepted versio
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