3,529 research outputs found
Two-dimensional Site-Bond Percolation as an Example of Self-Averaging System
The Harris-Aharony criterion for a statistical model predicts, that if a
specific heat exponent , then this model does not exhibit
self-averaging. In two-dimensional percolation model the index .
It means that, in accordance with the Harris-Aharony criterion, the model can
exhibit self-averaging properties. We study numerically the relative variances
and for the probability of a site belongin to the
"infinite" (maximum) cluster and the mean finite cluster size . It was
shown, that two-dimensional site-bound percolation on the square lattice, where
the bonds play the role of impurity and the sites play the role of the
statistical ensemble, over which the averaging is performed, exhibits
self-averaging properties.Comment: 15 pages, 5 figure
Upper limits on gravitational-wave signals based on loudest events
Searches for gravitational-wave bursts have often focused on the loudest
event(s) in searching for detections and in determining upper limits on
astrophysical populations. Typical upper limits have been reported on event
rates and event amplitudes which can then be translated into constraints on
astrophysical populations. We describe the mathematical construction of such
upper limits.Comment: 8 pages, 1 figur
On quantum error-correction by classical feedback in discrete time
We consider the problem of correcting the errors incurred from sending
quantum information through a noisy quantum environment by using classical
information obtained from a measurement on the environment. For discrete time
Markovian evolutions, in the case of fixed measurement on the environment, we
give criteria for quantum information to be perfectly corrigible and
characterize the related feedback. Then we analyze the case when perfect
correction is not possible and, in the qubit case, we find optimal feedback
maximizing the channel fidelity.Comment: 11 pages, 1 figure, revtex
From Black Strings to Black Holes
Using recently developed numerical methods, we examine neutral compactified
non-uniform black strings which connect to the Gregory-Laflamme critical point.
By studying the geometry of the horizon we give evidence that this branch of
solutions may connect to the black hole solutions, as conjectured by Kol. We
find the geometry of the topology changing solution is likely to be nakedly
singular at the point where the horizon radius is zero. We show that these
solutions can all be expressed in the coordinate system discussed by Harmark
and Obers.Comment: 6 pages, 5 figures, RevTe
Caged Black Holes: Black Holes in Compactified Spacetimes II - 5d Numerical Implementation
We describe the first convergent numerical method to determine static black
hole solutions (with S^3 horizon) in 5d compactified spacetime. We obtain a
family of solutions parametrized by the ratio of the black hole size and the
size of the compact extra dimension. The solutions satisfy the demanding
integrated first law. For small black holes our solutions approach the 5d
Schwarzschild solution and agree very well with new theoretical predictions for
the small corrections to thermodynamics and geometry. The existence of such
black holes is thus established. We report on thermodynamical (temperature,
entropy, mass and tension along the compact dimension) and geometrical
measurements. Most interestingly, for large masses (close to the
Gregory-Laflamme critical mass) the scheme destabilizes. We interpret this as
evidence for an approach to a physical tachyonic instability. Using
extrapolation we speculate that the system undergoes a first order phase
transition.Comment: 42 pages, 19 eps figures; v2: 3 references added, version to appear
in Phys.Rev.
Adaptive single-shot phase measurements: The full quantum theory
The phase of a single-mode field can be measured in a single-shot measurement
by interfering the field with an effectively classical local oscillator of
known phase. The standard technique is to have the local oscillator detuned
from the system (heterodyne detection) so that it is sometimes in phase and
sometimes in quadrature with the system over the course of the measurement.
This enables both quadratures of the system to be measured, from which the
phase can be estimated. One of us [H.M. Wiseman, Phys. Rev. Lett. 75, 4587
(1995)] has shown recently that it is possible to make a much better estimate
of the phase by using an adaptive technique in which a resonant local
oscillator has its phase adjusted by a feedback loop during the single-shot
measurement. In Ref.~[H.M. Wiseman and R.B. Killip, Phys. Rev. A 56, 944] we
presented a semiclassical analysis of a particular adaptive scheme, which
yielded asymptotic results for the phase variance of strong fields. In this
paper we present an exact quantum mechanical treatment. This is necessary for
calculating the phase variance for fields with small photon numbers, and also
for considering figures of merit other than the phase variance. Our results
show that an adaptive scheme is always superior to heterodyne detection as far
as the variance is concerned. However the tails of the probability distribution
are surprisingly high for this adaptive measurement, so that it does not always
result in a smaller probability of error in phase-based optical communication.Comment: 17 pages, LaTeX, 8 figures (concatenated), Submitted to Phys. Rev.
Static Axisymmetric Vacuum Solutions and Non-Uniform Black Strings
We describe new numerical methods to solve the static axisymmetric vacuum
Einstein equations in more than four dimensions. As an illustration, we study
the compactified non-uniform black string phase connected to the uniform
strings at the Gregory-Laflamme critical point. We compute solutions with a
ratio of maximum to minimum horizon radius up to nine. For a fixed
compactification radius, the mass of these solutions is larger than the mass of
the classically unstable uniform strings. Thus they cannot be the end state of
the instability.Comment: 48 pages, 13 colour figures; v2: references correcte
In-loop squeezing is real squeezing to an in-loop atom
Electro-optical feedback can produce an in-loop photocurrent with arbitrarily
low noise. This is not regarded as evidence of `real' squeezing because
squeezed light cannot be extracted from the loop using a linear beam splitter.
Here I show that illuminating an atom (which is a nonlinear optical element)
with `in-loop' squeezed light causes line-narrowing of one quadrature of the
atom's fluorescence. This has long been regarded as an effect which can only be
produced by squeezing. Experiments on atoms using in-loop squeezing should be
much easier than those with conventional sources of squeezed light.Comment: 4 pages, 2 figures, submitted to PR
Multiple-copy state discrimination: Thinking globally, acting locally
We theoretically investigate schemes to discriminate between two
nonorthogonal quantum states given multiple copies. We consider a number of
state discrimination schemes as applied to nonorthogonal, mixed states of a
qubit. In particular, we examine the difference that local and global
optimization of local measurements makes to the probability of obtaining an
erroneous result, in the regime of finite numbers of copies , and in the
asymptotic limit as . Five schemes are considered:
optimal collective measurements over all copies, locally optimal local
measurements in a fixed single-qubit measurement basis, globally optimal fixed
local measurements, locally optimal adaptive local measurements, and globally
optimal adaptive local measurements. Here, adaptive measurements are those for
which the measurement basis can depend on prior measurement results. For each
of these measurement schemes we determine the probability of error (for finite
) and scaling of this error in the asymptotic limit. In the asymptotic
limit, adaptive schemes have no advantage over the optimal fixed local scheme,
and except for states with less than 2% mixture, the most naive scheme (locally
optimal fixed local measurements) is as good as any noncollective scheme. For
finite , however, the most sophisticated local scheme (globally optimal
adaptive local measurements) is better than any other noncollective scheme, for
any degree of mixture.Comment: 11 pages, 14 figure
Using weak values to experimentally determine "negative probabilities" in a two-photon state with Bell correlations
Bipartite quantum entangled systems can exhibit measurement correlations that
violate Bell inequalities, revealing the profoundly counter-intuitive nature of
the physical universe. These correlations reflect the impossibility of
constructing a joint probability distribution for all values of all the
different properties observed in Bell inequality tests. Physically, the
impossibility of measuring such a distribution experimentally, as a set of
relative frequencies, is due to the quantum back-action of projective
measurements. Weakly coupling to a quantum probe, however, produces minimal
back-action, and so enables a weak measurement of the projector of one
observable, followed by a projective measurement of a non-commuting observable.
By this technique it is possible to empirically measure weak-valued
probabilities for all of the values of the observables relevant to a Bell test.
The marginals of this joint distribution, which we experimentally determine,
reproduces all of the observable quantum statistics including a violation of
the Bell inequality, which we independently measure. This is possible because
our distribution, like the weak values for projectors on which it is built, is
not constrained to the interval [0, 1]. It was first pointed out by Feynman
that, for explaining singlet-state correlations within "a [local] hidden
variable view of nature ... everything works fine if we permit negative
probabilities". However, there are infinitely many such theories. Our method,
involving "weak-valued probabilities", singles out a unique set of
probabilities, and moreover does so empirically.Comment: 9 pages, 3 figure
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