18,770 research outputs found
The time evolution of marginally trapped surfaces
In previous work we have shown the existence of a dynamical horizon or
marginally trapped tube (MOTT) containing a given strictly stable marginally
outer trapped surface (MOTS). In this paper we show some results on the global
behavior of MOTTs assuming the null energy condition. In particular we show
that MOTSs persist in the sense that every Cauchy surface in the future of a
given Cauchy surface containing a MOTS also must contain a MOTS. We describe a
situation where the evolving outermost MOTS must jump during the coalescence of
two seperate MOTSs. We furthermore characterize the behavior of MOTSs in the
case that the principal eigenvalue vanishes under a genericity assumption. This
leads to a regularity result for the tube of outermost MOTSs under the
genericity assumption. This tube is then smooth up to finitely many jump times.
Finally we discuss the relation of MOTSs to singularities of a space-time.Comment: 21 pages. This revision corrects some typos and contains more
detailed proofs than the original versio
Maximum observable correlation for a bipartite quantum system
The maximum observable correlation between the two components of a bipartite
quantum system is a property of the joint density operator, and is achieved by
making particular measurements on the respective components. For pure states it
corresponds to making measurements diagonal in a corresponding Schmidt basis.
More generally, it is shown that the maximum correlation may be characterised
in terms of a `correlation basis' for the joint density operator, which defines
the corresponding (nondegenerate) optimal measurements. The maximum coincidence
rate for spin measurements on two-qubit systems is determined to be (1+s)/2,
where s is the spectral norm of the spin correlation matrix, and upper bounds
are obtained for n-valued measurements on general bipartite systems. It is
shown that the maximum coincidence rate is never greater than the computable
cross norm measure of entanglement, and a much tighter upper bound is
conjectured. Connections with optimal state discrimination and entanglement
bounds are briefly discussed.Comment: Revtex, no figure
Buoyancy and g-modes in young superfluid neutron stars
We consider the local dynamics of a realistic neutron star core, including
composition gradients, superfluidity and thermal effects. The main focus is on
the gravity g-modes, which are supported by composition stratification and
thermal gradients. We derive the equations that govern this problem in full
detail, paying particular attention to the input that needs to be provided
through the equation of state and distinguishing between normal and superfluid
regions. The analysis highlights a number of key issues that should be kept in
mind whenever equation of state data is compiled from nuclear physics for use
in neutron star calculations. We provide explicit results for a particular
stellar model and a specific nucleonic equation of state, making use of cooling
simulations to show how the local wave spectrum evolves as the star ages. Our
results show that the composition gradient is effectively dominated by the
muons whenever they are present. When the star cools below the superfluid
transition, the support for g-modes at lower densities (where there are no
muons) is entirely thermal. We confirm the recent suggestion that the g-modes
in this region may be unstable, but our results indicate that this instability
will be weak and would only be present for a brief period of the star's life.
Our analysis accounts for the presence of thermal excitations encoded in
entrainment between the entropy and the superfluid component. Finally, we
discuss the complete spectrum, including the normal sound waves and, in
superfluid regions, the second sound.Comment: 29 pages, 9 figures, submitted to MNRA
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The Parenthood “Happiness Penalty”: The Effects of Social Policies in 22 Countries
A large body of research has established that parents are less happy than nonparents. But is it always true that parents are less happy than nonparents? This research brief, by PRC faculty research associate Jennifer Glass and colleagues, shows that the “happiness penalty” is entirely explained by the presence or absence of social policies that allow parents to better combine paid work with family obligations.Population Research Cente
String Effects on Fermi--Dirac Correlation Measurements
We investigate some recent measurements of Fermi--Dirac correlations by the
LEP collaborations indicating surprisingly small source radii for the
production of baryons in -annihilation at the peak. In the
hadronization models there are besides the Fermi--Dirac correlation effect also
a strong dynamical (anti-)correlation. We demonstrate that the extraction of
the pure FD effect is highly dependent on a realistic Monte Carlo event
generator, both for separation of those dynamical correlations which are not
related to Fermi--Dirac statistics, and for corrections of the data and
background subtractions. Although the model can be tuned to well reproduce
single particle distributions, there are large model-uncertainties when it
comes to correlations between identical baryons. We therefore, unfortunately,
have to conclude that it is at present not possible to make any firm conclusion
about the source radii relevant for baryon production at LEP
Seismology of adolescent neutron stars: Accounting for thermal effects and crust elasticity
We study the oscillations of relativistic stars, incorporating key physics
associated with internal composition, thermal gradients and crust elasticity.
Our aim is to develop a formalism which is able to account for the
state-of-the-art understanding of the complex physics associated with these
systems. As a first step, we build models using a modern equation of state
including composition gradients and density discontinuities associated with
internal phase-transitions (like the crust-core transition and the point where
muons first appear in the core). In order to understand the nature of the
oscillation spectrum, we carry out cooling simulations to provide realistic
snapshots of the temperature distribution in the interior as the star evolves
through adolescence. The associated thermal pressure is incorporated in the
perturbation analysis, and we discuss the presence of -modes arising as a
result of thermal effects. We also consider interface modes due to
phase-transitions and the gradual formation of the star's crust and the
emergence of a set of shear modes.Comment: 27 pages, 14 figure
Implications of an r-mode in XTE J1751-305: Mass, radius and spin evolution
Recently Strohmayer and Mahmoodifar presented evidence for a coherent
oscillation in the X-ray light curve of the accreting millisecond pulsar XTE
J1751-305, using data taken by RXTE during the 2002 outburst of this source.
They noted that a possible explanation includes the excitation of a non-radial
oscillation mode of the neutron star, either in the form of a g-mode or an
r-mode. The r-mode interpretation has connections with proposed spin-evolution
scenarios for systems such as XTE J1751-305. Here we examine in detail this
interesting possible interpretation. Using the ratio of the observed
oscillation frequency to the star's spin frequency, we derive an approximate
neutron star mass-radius relation which yields reasonable values for the mass
over the range of expected stellar radius (as constrained by observations of
radius-expansion burst sources). However, we argue that the large mode
amplitude suggested by the Strohmayer and Mahmoodifar analysis would inevitably
lead to a large spin-down of the star, inconsistent with its observed spin
evolution, regardless of whether the r-mode itself is in a stable or unstable
regime. We therefore conclude that the r-mode interpretation of the observed
oscillation is not consistent with our current understanding of neutron star
dynamics and must be considered unlikely. Finally we note that, subject to the
availability of a sufficiently accurate timing model, a direct
gravitational-wave search may be able to confirm or reject an r-mode
interpretation unambiguously, should such an event, with a similar inferred
mode amplitude, recur during the Advanced detector era.Comment: 8 pages, 3 figures; submitted to MNRA
Finding the Kraus decomposition from a master equation and vice versa
For any master equation which is local in time, whether Markovian,
non-Markovian, of Lindblad form or not, a general procedure is reviewed for
constructing the corresponding linear map from the initial state to the state
at time t, including its Kraus-type representations. Formally, this is
equivalent to solving the master equation. For an N-dimensional Hilbert space
it requires (i) solving a first order N^2 x N^2 matrix time evolution (to
obtain the completely positive map), and (ii) diagonalising a related N^2 x N^2
matrix (to obtain a Kraus-type representation). Conversely, for a given
time-dependent linear map, a necessary and sufficient condition is given for
the existence of a corresponding master equation, where the (not necessarily
unique) form of this equation is explicitly determined. It is shown that a
`best possible' master equation may always be defined, for approximating the
evolution in the case that no exact master equation exists. Examples involving
qubits are given.Comment: 16 pages, no figures. Appeared in special issue for conference
QEP-16, Manchester 4-7 Sep 200
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