74 research outputs found
A conformal scalar dyon black hole solution
An exact solution of Einstein - Maxwell - conformal scalar field equations is
given, which is a black hole solution and has three parameters: scalar charge,
electric charge, and magnetic charge. Switching off the magnetic charge
parameter yields the solution given by Bekenstein. In addition the energy of
the conformal scalar dyon black hole is obtained.Comment: 7 pages, Late
On the consistency of de Sitter vacua
In this paper the consistency of the de Sitter invariant -vacua,
which have been introduced as simple tools to study the effects of
transplanckian physics, is investigated. In particular possible non
renormalization problems are discussed, as well as non standard properties of
Greens functions. We also discuss the non thermal properties of the -vacua and the necessity of to change. The conclusion is that non of
these problems necessarily exclude an application of the -vacua to
inflation.Comment: 12 pages, v2: minor clarifications and corrections to reference
A First-Quantized Formalism for Cosmological Particle Production
We show that the amount of particle production in an arbitrary cosmological
background can be determined using only the late-time positive-frequency modes.
We don't refer to modes at early times, so there is no need for a Bogolubov
transformation. We also show that particle production can be extracted from the
Feynman propagator in an auxiliary spacetime. This provides a first-quantized
formalism for computing particle production which, unlike conventional
Bogolubov transformations, may be amenable to a string-theoretic
generalization.Comment: 18 pages, LaTeX; v2: significantly revised for clarity; conclusions
unchange
RPA vs. exact shell-model correlation energies
The random phase approximation (RPA) builds in correlations left out by
mean-field theory. In full 0-hbar-omega shell-model spaces we calculate the
Hartree-Fock + RPA binding energy, and compare it to exact diagonalization. We
find that in general HF+RPA gives a very good approximation to the ``exact''
ground state energy. In those cases where RPA is less satisfactory, however,
there is no obvious correlation with properties of the HF state, such as
deformation or overlap with the exact ground state wavefunction.Comment: 6 pages, 7 figures, submitted to Phys Rev
Squeezed States in the de Sitter Vacuum
We discuss the treatment of squeezed states as excitations in the Euclidean
vacuum of de Sitter space. A comparison with the treatment of these states as
candidate no-particle states, or alpha-vacua, shows important differences
already in the free theory. At the interacting level alpha-vacua are
inconsistent, but squeezed state excitations seem perfectly acceptable. Indeed,
matrix elements can be renormalized in the excited states using precisely the
standard local counterterms of the Euclidean vacuum. Implications for
inflationary scenarios in cosmology are discussed.Comment: 15 pages, no figures. One new citation in version 3; no other change
Miracles and complementarity in de Sitter space
In this paper we consider a scenario, consisting of a de Sitter phase
followed by a phase described by a scale factor , where
, which can be viewed as an inflationary toy model. It is argued that
this scenario naively could lead to an information paradox. We propose that the
phenomenon of Poincar\'{e} recurrences plays a crucial role in the resolution
of the paradox. We also comment on the relevance of these results to inflation
and the CMBR.Comment: 13 page
Projection and ground state correlations made simple
We develop and test efficient approximations to estimate ground state
correlations associated with low- and zero-energy modes. The scheme is an
extension of the generator-coordinate-method (GCM) within Gaussian overlap
approximation (GOA). We show that GOA fails in non-Cartesian topologies and
present a topologically correct generalization of GOA (topGOA). An RPA-like
correction is derived as the small amplitude limit of topGOA, called topRPA.
Using exactly solvable models, the topGOA and topRPA schemes are compared with
conventional approaches (GCM-GOA, RPA, Lipkin-Nogami projection) for
rotational-vibrational motion and for particle number projection. The results
shows that the new schemes perform very well in all regimes of coupling.Comment: RevTex, 12 pages, 7 eps figure
Temporal Vagueness, Coordination and Communication
How is it that people manage to communicate even when they implicitly differ on the meaning of the terms they use? Take an innocent-sounding expression such as tomorrow morning. What counts as morning? There is a surprising amount of variation across different people.
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
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