12,149 research outputs found
Interpreting the projective hierarchy in expansions of the real line
We give a criterion when an expansion of the ordered set of real numbers
defines the image of the expansion of the real field by the set of natural
numbers under a semialgebraic injection. In particular, we show that for a
non-quadratic irrational number a, the expansion of the ordered Q(a)-vector
space of real numbers by the set of natural numbers defines multiplication on
the real numbers
Reducing backaction when measuring temporal correlations in quantum systems
Dynamic correlations of quantum observables are challenging to measure due to
measurement backaction incurred at early times. Recent work [P. Uhrich et al.,
Phys. Rev. A, 96:022127 (2017)] has shown that ancilla-based noninvasive
measurements are able to reduce this backaction, allowing for dynamic
correlations of single-site spin observables to be measured. We generalise this
result to correlations of arbitrary spin observables and extend the measurement
protocol to simultaneous noninvasive measurements which allow for real and
imaginary parts of correlations to be extracted from a single set of
measurements. We use positive operator-valued measures to analyse the dynamics
generated by the ancilla-based measurements. Using this framework we prove that
special observables exist for which measurement backaction is of no concern, so
that dynamic correlations of these can be obtained without making use of
ancillas.Comment: 13 page
Flexible shrinkage in high-dimensional Bayesian spatial autoregressive models
This article introduces two absolutely continuous global-local shrinkage
priors to enable stochastic variable selection in the context of
high-dimensional matrix exponential spatial specifications. Existing approaches
as a means to dealing with overparameterization problems in spatial
autoregressive specifications typically rely on computationally demanding
Bayesian model-averaging techniques. The proposed shrinkage priors can be
implemented using Markov chain Monte Carlo methods in a flexible and efficient
way. A simulation study is conducted to evaluate the performance of each of the
shrinkage priors. Results suggest that they perform particularly well in
high-dimensional environments, especially when the number of parameters to
estimate exceeds the number of observations. For an empirical illustration we
use pan-European regional economic growth data.Comment: Keywords: Matrix exponential spatial specification, model selection,
shrinkage priors, hierarchical modeling; JEL: C11, C21, C5
Foreign aid and developing countries' creditworthiness
We explore whether foreign aid affects developing countries' creditworthiness, as proxied by the Institutional Investor's measure of country credit risk. Based on a simple model of international borrowing and lending, we develop the hypothesis that aid reduces the likelihood that borrowers in a given country default on their foreign debt. We then test this hypothesis, using a panel data set that covers a large number of developing countries in the 1980s and 1990s. Our empirical findings support the notion that aid improves countries' standing vis-a-vis international capital markets. However, the strength of this effect differs across types of aid and country groups.
Probabilistic ODE Solvers with Runge-Kutta Means
Runge-Kutta methods are the classic family of solvers for ordinary
differential equations (ODEs), and the basis for the state of the art. Like
most numerical methods, they return point estimates. We construct a family of
probabilistic numerical methods that instead return a Gauss-Markov process
defining a probability distribution over the ODE solution. In contrast to prior
work, we construct this family such that posterior means match the outputs of
the Runge-Kutta family exactly, thus inheriting their proven good properties.
Remaining degrees of freedom not identified by the match to Runge-Kutta are
chosen such that the posterior probability measure fits the observed structure
of the ODE. Our results shed light on the structure of Runge-Kutta solvers from
a new direction, provide a richer, probabilistic output, have low computational
cost, and raise new research questions.Comment: 18 pages (9 page conference paper, plus supplements); appears in
Advances in Neural Information Processing Systems (NIPS), 201
Probing unitary two-time correlations in a neutral atom quantum simulator
Measuring unitarily-evolved quantum mechanical two-time correlations is
challenging in general. In a recent paper [P.~Uhrich {\em et al.}, Phys.\
Rev.~A {\bf 96}, 022127 (2017)], a considerable simplification of this task has
been pointed out to occur in spin- lattice models, bringing such
measurements into reach of state-of-the-art or near-future quantum simulators
of such models. Here we discuss the challenges of an experimental
implementation of measurement schemes of two-time correlations in quantum gas
microscopes or microtrap arrays. We propose a modified measurement protocol
that mitigates these challenges, and we rigorously estimate the accuracy of the
protocols by means of Lieb-Robinson bounds. On the basis of these bounds we
identify a parameter regime in which the proposed protocols allow for accurate
measurements of the desired two-time correlations.Comment: 15 pages, 2 figure
Many-Body Quantum Optics with Decaying Atomic Spin States: (, ) Dicke model
We provide a theory for quantum-optical realizations of the open Dicke model
with internal, atomic spin states subject to spontaneous emission with rate
. This introduces a second decay channel for excitations to
irreversibly dissipate into the environment, in addition to the photon loss
with rate , which is composed of individual atomic decay processes and
a collective atomic decay mechanism. The strength of the latter is determined
by the cavity geometry. We compute the mean-field non-equilibrium steady states
for spin and photon observables in the long-time limit, .
Although does not conserve the total angular momentum of the spin
array, we argue that our solution is exact in the thermodynamic limit, for the
number of atoms . In light of recent and upcoming
experiments realizing superradiant phase transitions using internal atomic
states with pinned atoms in optical lattices, our work lays the foundation for
the pursuit of a new class of open quantum magnets coupled to quantum light.Comment: 17 pages, 6 figures; added appendix for the derivation of a
collective atomic decay mechanism in a Lindblad formalism; version as
published in Physical Review
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