Quantum entanglement and fixed-point bifurcations

How does the classical phase space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state - the ground state - achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.Comment: v2: Structure of the paper changed for clarity, reduced length, now 9 pages with 6 figure

Computing and software

The reality is that the statistical methods used for analysis of data depend upon the availability of software. Analysis of marked animal data is no different than the rest of the statistical field. The methods used for analysis are those that are available in reliable software packages. Thus, the critical importance of having reliable, up–to–date software available to biologists is obvious. Statisticians have continued to develop more robust models, ever expanding the suite of potential analysis methods available. But without software to implement these newer methods, they will languish in the abstract, and not be applied to the problems deserving them. In the Computers and Software Session, two new software packages are described, a comparison of implementation of methods for the estimation of nest survival is provided, and a more speculative paper about how the next generation of software might be structured is presented. Rotella et al. (2004) compare nest survival estimation with different software packages: SAS logistic regression, SAS non–linear mixed models, and Program MARK. Nests are assumed to be visited at various, possibly infrequent, intervals. All of the approaches described compute nest survival with the same likelihood, and require that the age of the nest is known to account for nests that eventually hatch. However, each approach offers advantages and disadvantages, explored by Rotella et al. (2004). Efford et al. (2004) present a new software package called DENSITY. The package computes population abundance and density from trapping arrays and other detection methods with a new and unique approach. DENSITY represents the first major addition to the analysis of trapping arrays in 20 years. Barker & White (2004) discuss how existing software such as Program MARK require that each new model’s likelihood must be programmed specifically for that model. They wishfully think that future software might allow the user to combine pieces of likelihood functions together to generate estimates. The idea is interesting, and maybe some bright young statistician can work out the specifics to implement the procedure. Choquet et al. (2004) describe MSURGE, a software package that implements the multistate capture–recapture models. The unique feature of MSURGE is that the design matrix is constructed with an interpreted language called GEMACO. Because MSURGE is limited to just multistate models, the special requirements of these likelihoods can be provided. The software and methods presented in these papers gives biologists and wildlife managers an expanding range of possibilities for data analysis. Although ease–of–use is generally getting better, it does not replace the need for understanding of the requirements and structure of the models being computed. The internet provides access to many free software packages as well as user–discussion groups to share knowledge and ideas. (A starting point for wildlife–related applications is (http://www.phidot.org)

The Stress-Corrosion Cracking of Austentic Stainless Steels in Aqueous Chloride Solution

The stress-corrosion cracking of 18-8 type steels in hot concentrated magnesium chloride solutionshas been studied. There is an induction period, of which the processes are substantially unaffected hvv stress, followed by a period of rapid crack propagation - as shown by measurements of the electrode potential, the mechanical properties and the extension of direct-loaded wire specimens. The indu-ction period is shortened by increase of applied stress and of temperature, and by cold-work on a fully softened material; it may he indefinitely lengthened by cathodic protection of the metal. Crack propagation is normally at rates of 1-4 mm./hr. ; it is not greatly influenced by increase of applied stress, is somewhat accelerated by increase of temperature, and may be slowed down or stopped cntirely by cathodic protection

High Accuracy Near-infrared Imaging Polarimetry with NICMOS

The findings of a nine orbit calibration plan carried out during HST Cycle 15, to fully determine the NICMOS camera 2 (2.0 micron) polarization calibration to high accuracy, are reported. Recently Ueta et al. and Batcheldor et al. have suggested that NICMOS possesses a residual instrumental polarization at a level of 1.2-1.5%. This would completely inhibit the data reduction in a number of GO programs, and hamper the ability of the instrument to perform high accuracy polarimetry. We obtained polarimetric calibration observations of three polarimetric standards at three spacecraft roll angles separated by ~60deg. Combined with archival data, these observations were used to characterize the residual instrumental polarization in order for NICMOS to reach its full potential of accurate imaging polarimetry at p~1%. Using these data, we place an 0.6% upper limit on the instrumental polarization and calculate values of the parallel transmission coefficients that reproduce the ground-based results for the polarimetric standards. The uncertainties associated with the parallel transmission coefficients, a result of the photometric repeatability of the observations, are seen to dominate the accuracy of p and theta. However, the updated coefficients do allow imaging polarimetry of targets with p~1.0% at an accuracy of +/-0.6% and +/-15deg. This work enables a new caliber of science with HST.Comment: 13 pages, 9 figures, PASP accepte

High Accuracy Imaging Polarimetry with NICMOS

The ability of NICMOS to perform high accuracy polarimetry is currently hampered by an uncalibrated residual instrumental polarization at a level of 1.2-1.5%. To better quantify and characterize this residual we obtained observations of three polarimetric standard stars at three separate space-craft roll angles. Combined with archival data, these observations were used to characterize the residual instrumental polarization to enable NICMOS to reach its full polarimetric potential. Using these data, we calculate values of the parallel transmission coefficients that reproduce the ground-based results for the polarimetric standards. The uncertainties associated with the parallel transmission coefficients, a result of the photometric repeatability of the observations, dominate the accuracy of p and theta. However, the new coefficients now enable imaging polarimetry of targets with p~1.0% at an accuracy of +/-0.6% and +/-15 degrees.Comment: 5 pages, 2 figures. Contributed talk, "Astronomical Polarimetry 2008. Science from Small to Large Telescopes" La Malbaie, Quebec, Canada, 200

Reply to "Comment on 'Decoherence and dissipation of a quantum harmonic oscillator coupled to two-level systems'"

Contrary to the assertion by Mogilevtsev and Shatokhin [preceding paper, Phys. Rev. A 78, 016101 (2008)], we show that the applicability of the Born-Markov master-equation approach in our treatment of the oscillator-spin model depends on the physical situation under study. Heating effects do occur although they may not be accurately captured by second-order perturbation theory inherent in the Born-Markov scheme

Analytical and experimental study of stratification and liquid-ullage coupling, 1 June 1964 - 31 May 1965

Closed-form solution for stratification of subcooled fluids in containers subjected to heating, and for liquid-ullage vapor couplin

Quantum Entanglement and Fixed-Point Bifurcations

How do the classical dynamics of a composite system relate to the entanglement characteristics of the corresponding quantum system? We show that entanglement in nonlinear bipartite systems can be associated with a fixed point bifurcation in the classical description. In a non dissipative system a fixed point corresponds to a quantum stationary state, usually a ground state. Using the example of coupled giant spins we show that, when the fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state achieves a maximum amount of entanglement. By way of contrast, we consider a molecular BEC system that experiences a different kind of bifurcation and does not exhibit a peak in the entanglement corresponding to the bifurcation parameter

Entanglement Sharing and Decoherence in the Spin-Bath

The monogamous nature of entanglement has been illustrated by the derivation of entanglement sharing inequalities - bounds on the amount of entanglement that can be shared amongst the various parts of a multipartite system. Motivated by recent studies of decoherence, we demonstrate an interesting manifestation of this phenomena that arises in system-environment models where there exists interactions between the modes or subsystems of the environment. We investigate this phenomena in the spin-bath environment, constructing an entanglement sharing inequality bounding the entanglement between a central spin and the environment in terms of the pairwise entanglement between individual bath spins. The relation of this result to decoherence will be illustrated using simplified system-bath models of decoherence.Comment: 5 pages, 1 figure v2: 6 pages 2 figures, additional example and reference