420 research outputs found
Correction of non-linearity effects in detectors for electron spectroscopy
Using photoemission intensities and a detection system employed by many
groups in the electron spectroscopy community as an example, we have
quantitatively characterized and corrected detector non-linearity effects over
the full dynamic range of the system. Non-linearity effects are found to be
important whenever measuring relative peak intensities accurately is important,
even in the low-countrate regime. This includes, for example, performing
quantitative analyses for surface contaminants or sample bulk stoichiometries,
where the peak intensities involved can differ by one or two orders of
magnitude, and thus could occupy a significant portion of the detector dynamic
range. Two successful procedures for correcting non-linearity effects are
presented. The first one yields directly the detector efficiency by measuring a
flat-background reference intensity as a function of incident x-ray flux, while
the second one determines the detector response from a least-squares analysis
of broad-scan survey spectra at different incident x-ray fluxes. Although we
have used one spectrometer and detection system as an example, these
methodologies should be useful for many other cases.Comment: 13 pages, 12 figure
A Note on Hartle-Hawking Vacua
The purpose of this note is to establish the basic properties--- regularity
at the horizon, time independence, and thermality--- of the generalized
Hartle-Hawking vacua defined in static spacetimes with bifurcate Killing
horizon admitting a regular Euclidean section. These states, for free or
interacting fields, are defined by a path integral on half the Euclidean
section. The emphasis is on generality and the arguments are simple but formal.Comment: 5 pages, LaTe
Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
We consider a general, classical theory of gravity with arbitrary matter
fields in dimensions, arising from a diffeomorphism invariant Lagrangian,
\bL. We first show that \bL always can be written in a ``manifestly
covariant" form. We then show that the symplectic potential current
-form, , and the symplectic current -form, \om, for the
theory always can be globally defined in a covariant manner. Associated with
any infinitesimal diffeomorphism is a Noether current -form, \bJ, and
corresponding Noether charge -form, \bQ. We derive a general
``decomposition formula" for \bQ. Using this formula for the Noether charge,
we prove that the first law of black hole mechanics holds for arbitrary
perturbations of a stationary black hole. (For higher derivative theories,
previous arguments had established this law only for stationary perturbations.)
Finally, we propose a local, geometrical prescription for the entropy,
, of a dynamical black hole. This prescription agrees with the Noether
charge formula for stationary black holes and their perturbations, and is
independent of all ambiguities associated with the choices of \bL, , and
\bQ. However, the issue of whether this dynamical entropy in general obeys a
``second law" of black hole mechanics remains open. In an appendix, we apply
some of our results to theories with a nondynamical metric and also briefly
develop the theory of stress-energy pseudotensors.Comment: 30 pages, LaTe
On the Particle Definition in the presence of Black Holes
A canonical particle definition via the diagonalisation of the Hamiltonian
for a quantum field theory in specific curved space-times is presented. Within
the provided approach radial ingoing or outgoing Minkowski particles do not
exist. An application of this formalism to the Rindler metric recovers the
well-known Unruh effect. For the situation of a black hole the Hamiltonian
splits up into two independent parts accounting for the interior and the
exterior domain, respectively. It turns out that a reasonable particle
definition may be accomplished for the outside region only. The Hamiltonian of
the field inside the black hole is unbounded from above and below and hence
possesses no ground state. The corresponding equation of motion displays a
linear global instability. Possible consequences of this instability are
discussed and its relations to the sonic analogues of black holes are
addressed. PACS-numbers: 04.70.Dy, 04.62.+v, 10.10.Ef, 03.65.Db.Comment: 44 pages, LaTeX, no figures, accepted for publication in Phys. Rev.
How to estimate kinship.
The concept of kinship permeates many domains of fundamental and applied biology ranging from social evolution to conservation science to quantitative and human genetics. Until recently, pedigrees were the gold standard to infer kinship, but the advent of next-generation sequencing and the availability of dense genetic markers in many species make it a good time to (re)evaluate the usefulness of genetic markers in this context. Using three published data sets where both pedigrees and markers are available, we evaluate two common and a new genetic estimator of kinship. We show discrepancies between pedigree values and marker estimates of kinship and explore via simulations the possible reasons for these. We find these discrepancies are attributable to two main sources: pedigree errors and heterogeneity in the origin of founders. We also show that our new marker-based kinship estimator has very good statistical properties and behaviour and is particularly well suited for situations where the source population is of small size, as will often be the case in conservation biology, and where high levels of kinship are expected, as is typical in social evolution studies
The "physical process" version of the first law and the generalized second law for charged and rotating black holes
We investigate both the ``physical process'' version of the first law and the
second law of black hole thermodynamics for charged and rotating black holes.
We begin by deriving general formulas for the first order variation in ADM mass
and angular momentum for linear perturbations off a stationary, electrovac
background in terms of the perturbed non-electromagnetic stress-energy, , and the perturbed charge current density, . Using these
formulas, we prove the "physical process version" of the first law for charged,
stationary black holes. We then investigate the generalized second law of
thermodynamics (GSL) for charged, stationary black holes for processes in which
a box containing charged matter is lowered toward the black hole and then
released (at which point the box and its contents fall into the black hole
and/or thermalize with the ``thermal atmosphere'' surrounding the black hole).
Assuming that the thermal atmosphere admits a local, thermodynamic description
with respect to observers following orbits of the horizon Killing field, and
assuming that the combined black hole/thermal atmosphere system is in a state
of maximum entropy at fixed mass, angular momentum, and charge, we show that
the total generalized entropy cannot decrease during the lowering process or in
the ``release process''. Consequently, the GSL always holds in such processes.
No entropy bounds on matter are assumed to hold in any of our arguments.Comment: 35 pages; 1 eps figur
On the massive wave equation on slowly rotating Kerr-AdS spacetimes
The massive wave equation is
studied on a fixed Kerr-anti de Sitter background
. We first prove that in the Schwarzschild case
(a=0), remains uniformly bounded on the black hole exterior provided
that , i.e. the Breitenlohner-Freedman bound holds. Our proof
is based on vectorfield multipliers and commutators: The usual energy current
arising from the timelike Killing vector field (which fails to be
non-negative pointwise) is shown to be non-negative with the help of a Hardy
inequality after integration over a spacelike slice. In addition to , we
construct a vectorfield whose energy identity captures the redshift producing
good estimates close to the horizon. The argument is finally generalized to
slowly rotating Kerr-AdS backgrounds. This is achieved by replacing the Killing
vectorfield with for an
appropriate , which is also Killing and--in contrast to the
asymptotically flat case--everywhere causal on the black hole exterior. The
separability properties of the wave equation on Kerr-AdS are not used. As a
consequence, the theorem also applies to spacetimes sufficiently close to the
Kerr-AdS spacetime, as long as they admit a causal Killing field which is
null on the horizon.Comment: 1 figure; typos corrected, references added, introduction revised; to
appear in CM
Applications of a New Proposal for Solving the "Problem of Time" to Some Simple Quantum Cosmological Models
We apply a recent proposal for defining states and observables in quantum
gravity to simple models. First, we consider a Klein-Gordon particle in an ex-
ternal potential in Minkowski space and compare our proposal to the theory ob-
tained by deparametrizing with respect to a time slicing prior to quantiza-
tion. We show explicitly that the dynamics of the deparametrization approach
depends on the time slicing. Our proposal yields a dynamics independent of the
choice of time slicing at intermediate times but after the potential is turned
off, the dynamics does not return to the free particle dynamics. Next we apply
our proposal to the closed Robertson-Walker quantum cosmology with a massless
scalar field with the size of the universe as our time variable, so the only
dynamical variable is the scalar field. We show that the resulting theory has
the semi-classical behavior up to the classical turning point from expansion to
contraction, i.e., given a classical solution which expands for much longer
than the Planck time, there is a quantum state whose dynamical evolution
closely approximates this classical solution during the expansion. However,
when the "time" gets larger than the classical maximum, the scalar field be-
comes "frozen" at its value at the maximum expansion. We also obtain similar
results in the Taub model. In an Appendix we derive the form of the Wheeler-
DeWitt equation for the Bianchi models by performing a proper quantum reduc-
tion of the momentum constraints; this equation differs from the usual one ob-
tained by solving the momentum constraints classically, prior to quantization.Comment: 30 pages, LaTeX 3 figures (postscript file or hard copy) available
upon request, BUTP-94/1
The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
Quantum fields propagating on a curved spacetime are investigated in terms of
microlocal analysis. We discuss a condition on the wave front set for the
corresponding n-point distributions, called ``microlocal spectrum condition''
(SC). On Minkowski space, this condition is satisfied as a consequence of
the usual spectrum condition. Based on Radzikowski's determination of the wave
front set of the two-point function of a free scalar field, satisfying the
Hadamard condition in the Kay and Wald sense, we construct in the second part
of this paper all Wick polynomials including the energy-momentum tensor for
this field as operator valued distributions on the manifold and prove that they
satisfy our microlocal spectrum condition.Comment: 21 pages, AMS-LaTeX, 2 figures appended as Postscript file
How much energy do closed timelike curves in 2+1 spacetimes need?
By noticing that, in open 2+1 gravity, polarized surfaces cannot converge in
the presence of timelike total energy momentum (except for a rotation of 2 pi),
we give a simple argument which shows that, quite generally, closed timelike
curves cannot exist in the presence of such energy condition.Comment: 3 pages, with no figures. Accepted in PRD as Rapid Communicatio
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