143 research outputs found
Enhanced Convergence and Robust Performance of Randomized Dynamical Decoupling
We demonstrate the advantages of randomization in coherent quantum dynamical
control. For systems which are either time-varying or require decoupling cycles
involving a large number of operations, we find that simple randomized
protocols offer superior convergence and stability as compared to deterministic
counterparts. In addition, we show how randomization always allows to
outperform purely deterministic schemes at long times, including combinatorial
and concatenated methods. General criteria for optimally interpolating between
deterministic and stochastic design are proposed and illustrated in explicit
decoupling scenarios relevant to quantum information storage.Comment: 4 pages, 3 figures, replaced with final versio
Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: An exact vacuum solution in five dimensions
As is well-known, Kerr-Schild metrics linearize the Einstein tensor. We shall
see here that they also simplify the Gauss-Bonnet tensor, which turns out to be
only quadratic in the arbitrary Kerr-Schild function f when the seed metric is
maximally symmetric. This property allows us to give a simple analytical
expression for its trace, when the seed metric is a five dimensional maximally
symmetric spacetime in spheroidal coordinates with arbitrary parameters a and
b. We also write in a (fairly) simple form the full Einstein-Gauss-Bonnet
tensor (with a cosmological term) when the seed metric is flat and the
oblateness parameters are equal, a=b. Armed with these results we give in a
compact form the solution of the trace of the Einstein-Gauss-Bonnet field
equations with a cosmological term and a different than b. We then examine
whether this solution for the trace does solve the remaining field equations.
We find that it does not in general, unless the Gauss-Bonnet coupling is such
that the field equations have a unique maximally symmetric solution.Comment: 10 pages, no figures, references added. Last version for CQ
Un algoritmo secuencial, aleatorio y óptimo para problemas de factibilidad robusta
[ES] En este trabajo (del cual se presentó una versión preliminar en Alamo et al. (2007)) se propone un algoritmo aleatorio para determinar la factibilidad robusta de un conjunto de desigualdades lineales matriciales (Linear Matrix Inequalities, LMI). El algoritmo está basado en la solución de una secuencia de problemas de optimización semidefinida sujetos a un bajo número de restricciones. Se aporta además una cota superior del número máximo de iteraciones que requiere el algoritmo para resolver el problema de factibilidad robusta. Finalmente, los resultados se ilustran mediante un ejemplo numérico. [EN] This paper proposes a randomized algorithm for feasibility of uncertain LMIs. The algorithm is based on the solution of a sequence of semidefinite optimization problems involving a reduced number of constraints. A bound of the maximum number of iterations required by the algorithm is given. Finally, the performance and behaviour of the algorithm are illustrated by means of a numerical example. Los autores agradecen la financiacion del Ministerio de Ciencia e Innovación mediante el proyecto DPI2010-21589-C05-01. Álamo, T.; Tempo, R.; Ramírez, D.; Luque, A.; Camacho, E. (2013). Un algoritmo secuencial, aleatorio y óptimo para problemas de factibilidad robusta. Revista Iberoamericana de Automática e Informática industrial. 10(1):50-61. https://doi.org/10.1016/j.riai.2012.11.005 OJS 50 61 10
Second-Order Formalism for 3D Spin-3 Gravity
A second-order formalism for the theory of 3D spin-3 gravity is considered.
Such a formalism is obtained by solving the torsion-free condition for the spin
connection \omega^a_{\mu}, and substituting the result into the action
integral. In the first-order formalism of the spin-3 gravity defined in terms
of SL(3,R) X SL(3,R) Chern-Simons (CS) theory, however, the generalized
torsion-free condition cannot be easily solved for the spin connection, because
the vielbein e^a_{\mu} itself is not invertible. To circumvent this problem,
extra vielbein-like fields e^a_{\mu\nu} are introduced as a functional of
e^a_{\mu}. New set of affine-like connections \Gamma_{\mu M}^N are defined in
terms of the metric-like fields, and a generalization of the Riemann curvature
tensor is also presented. In terms of this generalized Riemann tensor the
action integral in the second-order formalism is expressed. The transformation
rules of the metric and the spin-3 gauge field under the generalized
diffeomorphims are obtained explicitly. As in Einstein gravity, the new
affine-like connections are related to the spin connection by a certain gauge
transformation, and a gravitational CS term expressed in terms of the new
connections is also presented.Comment: 40 pages, no figures. v2:references added, coefficients of eqs in
apppendix D corrected, minor typos also corrected, v3:Version accepted for
publication in Classical and Quantum Gravit
Black holes in three dimensional higher spin gravity: A review
We review recent progress in the construction of black holes in three
dimensional higher spin gravity theories. Starting from spin-3 gravity and
working our way toward the theory of an infinite tower of higher spins coupled
to matter, we show how to harness higher spin gauge invariance to consistently
generalize familiar notions of black holes. We review the construction of black
holes with conserved higher spin charges and the computation of their partition
functions to leading asymptotic order. In view of the AdS/CFT correspondence as
applied to certain vector-like conformal field theories with extended conformal
symmetry, we successfully compare to CFT calculations in a generalized Cardy
regime. A brief recollection of pertinent aspects of ordinary gravity is also
given.Comment: 49 pages, harvmac, invited contribution to J. Phys. A special volume
on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M.
Vasilie
Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity
The theory of massive gravity in three dimensions recently proposed by
Bergshoeff, Hohm and Townsend (BHT) is considered. At the special case when the
theory admits a unique maximally symmetric solution, a conformally flat space
that contains black holes and gravitational solitons for any value of the
cosmological constant is found. For negative cosmological constant, the black
hole is characterized in terms of the mass and the "gravitational hair"
parameter, providing a lower bound for the mass. For negative mass parameter,
the black hole acquires an inner horizon, and the entropy vanishes at the
extremal case. Gravitational solitons and kinks, being regular everywhere, are
obtained from a double Wick rotation of the black hole. A wormhole solution in
vacuum that interpolates between two static universes of negative spatial
curvature is obtained as a limiting case of the gravitational soliton with a
suitable identification. The black hole and the gravitational soliton fit
within a set of relaxed asymptotically AdS conditions as compared with the ones
of Brown and Henneaux. In the case of positive cosmological constant the black
hole possesses an event and a cosmological horizon, whose mass is bounded from
above. Remarkably, the temperatures of the event and the cosmological horizons
coincide, and at the extremal case one obtains the analogue of the Nariai
solution, . A gravitational soliton is also obtained
through a double Wick rotation of the black hole. The Euclidean continuation of
these solutions describes instantons with vanishing Euclidean action. For
vanishing cosmological constant the black hole and the gravitational soliton
are asymptotically locally flat spacetimes. The rotating solutions can be
obtained by boosting the previous ones in the plane.Comment: Talk given at the "Workshop on Gravity in Three Dimensions," 14-24
April 2009, ESI, Vienna. 30 pages, 6 figures. V2: minor changes and section 6
slightly improved. Last version for JHE
Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes
Field theories with anisotropic scaling in 1+1 dimensions are considered. It
is shown that the isomorphism between Lifshitz algebras with dynamical
exponents z and 1/z naturally leads to a duality between low and high
temperature regimes. Assuming the existence of gap in the spectrum, this
duality allows to obtain a precise formula for the asymptotic growth of the
number of states with a fixed energy which depends on z and the energy of the
ground state, and reduces to the Cardy formula for z=1. The holographic
realization of the duality can be naturally inferred from the fact that
Euclidean Lifshitz spaces in three dimensions with dynamical exponents and
characteristic lengths given by z, l, and 1/z, l/z, respectively, are
diffeomorphic. The semiclassical entropy of black holes with Lifshitz
asymptotics can then be recovered from the generalization of Cardy formula,
where the ground state corresponds to a soliton. An explicit example is
provided by the existence of a purely gravitational soliton solution for BHT
massive gravity, which precisely has the required energy that reproduces the
entropy of the analytic asymptotically Lifshitz black hole with z=3.
Remarkably, neither the asymptotic symmetries nor central charges were
explicitly used in order to obtain these results.Comment: 17 pages, no figures, references corrected and update
Analysis of Stochastic Strategies in Bacterial Competence: A Master Equation Approach
Competence is a transiently differentiated state that certain bacterial cells reach when faced with a stressful environment. Entrance into competence can be attributed to the excitability of the dynamics governing the genetic circuit that regulates this cellular behavior. Like many biological behaviors, entrance into competence is a stochastic event. In this case cellular noise is responsible for driving the cell from a vegetative state into competence and back. In this work we present a novel numerical method for the analysis of stochastic biochemical events and use it to study the excitable dynamics responsible for competence in Bacillus subtilis. Starting with a Finite State Projection (FSP) solution of the chemical master equation (CME), we develop efficient numerical tools for accurately computing competence probability. Additionally, we propose a new approach for the sensitivity analysis of stochastic events and utilize it to elucidate the robustness properties of the competence regulatory genetic circuit. We also propose and implement a numerical method to calculate the expected time it takes a cell to return from competence. Although this study is focused on an example of cell-differentiation in Bacillus subtilis, our approach can be applied to a wide range of stochastic phenomena in biological systems
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Studies of electron and proton isochoric heating for fast ignition
Isochoric heating of inertially confined fusion plasmas by laser driven MeV electrons or protons is an area of great topical interest in the inertial confinement fusion community, particularly with respect to the fast ignition (FI) proposal to use this technique to initiate burn in a fusion capsule. Experiments designed to investigate electron isochoric heating have measured heating in two limiting cases of interest to fast ignition, small planar foils and hollow cones. Data from Cu K{alpha} fluorescence, crystal x-ray spectroscopy of Cu K shell emission, and XUV imaging at 68eV and 256 eV are used to test PIC and Hybrid PIC modeling of the interaction. Isochoric heating by focused proton beams generated at the concave inside surface of a hemi-shell and from a sub hemi-shell inside a cone have been studied with the same diagnostic methods plus imaging of proton induced K{alpha}. Conversion efficiency to protons has also been measured and modeled. Conclusions from the proton and electron heating experiments will be presented. Recent advances in modeling electron transport and innovative target designs for reducing igniter energy and increasing gain curves will also be discussed
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