Thermalization of a Lipkin-Meshkov-Glick model coupled to a bosonic bath

We derive a Lindblad master equation that approximates the dynamics of a Lipkin-Meshkov-Glick (LMG) model weakly coupled to a bosonic bath. By studying the time evolution of operators under the adjoint master equation we prove that, for large system sizes, these operators attain their thermal equilibrium expectation values in the long-time limit, and we calculate the rate at which these values are approached. Integrability of the LMG model prevents thermalization in the absence of a bath, and our work provides an explicit proof that the bath indeed restores thermalization. Imposing thermalization on this otherwise non-thermalizing model outlines an avenue towards probing the unconventional thermodynamic properties predicted to occur in ultracold-atom-based realizations of the LMG model.Comment: 10 pages, 3 figure

Analysing the relationship between ectomycorrhizal infection and forest decline using marginal models

This statistical survey originates from the problem of discovering which relationship exists between root ectomycorrhizal infection and health status of forest plants. The sampling scheme takes observations from roots that come from sectors around the tree resulting in a hierarchical association structure of the observations. Marginal regression models are used to analyze the mean effect of the ectomycorrhizal state on a response variable proxy for the health degree of the plants

On three-dimensional reconstruction of optically thin solar emission sources

Calculations are given for constructing the three dimensional distribution of optically thin EUV emission sources associated with solar active regions, from two dimensional observations (projections) recorded by the spectroheliograph on the OSO 7 satellite. The relation of the method to other image reconstruction methods is briefly discussed as well as the special requirements imposed in the solar case such as a knowledge of the true solar rotation function. A useful correlation criterion for establishing the physical validity of solutions is given

Cross-sectional Analysis of Longitudinal Data with Missing Values in the Dependent Variables: A Comparison of Weighted Estimating Equations with the Complete Case Analysis

Inference for cross-sectional models using longitudinal data can be drawn with independence estimating equations (Liang and Zeger, 1986). Many studies suffer from missing data. Robins and coworkers proposed to use weighted estimating equations (WEE) in estimating the mean structure, if missing data are present in dependent variables. In this paper the WEE are compared with complete case analyses for binary responses using simulated data. Our results are in accordance with the theoretical findings of Robins and coworkers. The WEE yield consistent estimates, even if the data are missing at random

The Effect of Misspecified Response Probabilities on Parameter Estimates from Weighted Estimating Equations

Inference for the marginal mean using longitudinal data with monotone drop-outs in the response can be drawn with the weighted estimating equations (WEE; Robins, Rotnitzky&Zhao, 1995). Estimation proceeds in two steps. In the first step, a generalised linear model is usually applied to estimate response probabilities. In the second step, parameters of the mean structure are estimated by weighting a response inversely proportional to its estimated observation probability. The parameter estimates of the WEE are asymptotically normal and semiparametric efficient under suitable regularity conditions that include the correct specification of the model for the response probabilities. In this paper, we investigate the effect of misspecifying a) the parameters used to estimate the response probabilities and b) the link function for the response probabilities in a simulation study. We demonstrate that a slightly misspecified model for the response probabilities has an unimportant effect on the parameter estimates of the marginal mean from the WEE. We furthermore show that the choice of the link function has a negligible effect on the estimates of the marginal mean from the WEE. Our results are in line with classical findings for generalised linear models and for generalised estimating equations. Theoretical work should be added to our simulations that allow a quantification of the bias introduced by a misspecification of the model for the response probabilities

Pinpointing the Position of the Post-AGB Star at the Core of RAFGL 2688 using Polarimetric Imaging with NICMOS

We have used infrared polarimetric imaging with NICMOS to determine precisely the position of the star that illuminates (and presumably generated) the bipolar, pre-planetary reflection nebula RAFGL 2688 (the Egg Nebula). The polarimetric data pinpoint the illuminating star, which is not detected directly at wavelengths less than or equal to 2 microns, at a position well within the dark lane that bisects the nebula, 0.55" (about 550 AU) southwest of the infrared peak which was previously detected at the southern tip of the northern polar lobe. The inferred position of the central star corresponds to the geometric center of the tips of the four principle lobes of near-infrared H2 emission; identifying the central star at this position also reveals the strong point symmetric structure of the nebula, as seen both in the intensity and polarization structure of the polar lobes. The polarimetric and imaging data indicate that the infrared peak directly detected in the NICMOS images is a self-luminous source and, therefore, is most likely a distant binary companion to the illuminating star. Although present theory predicts that bipolar structure in pre-planetary and planetary nebulae is a consequence of binary star evolution, the separation between the components of the RAFGL 2688 binary system, as deduced from these observations, is much too large for the presence of the infrared companion to have influenced the structure of the RAFGL 2688 nebula.Comment: 15 pages, 6 figures, to appear in The Astrophysical Journa

Solving Generalised Estimating Equations With Missing Data Using Pseudo Maximum Likelihood Estimation Is Equivalent to Complete Case Analysis

Arminger and Sobel(1990) proposed an approach to estimate mean- and covariance structures in the presence of missing data. These authors claimed that their method based on Pseudo Maximum Likelihood (PML) estimation may be applied if the data are missing at random (MAR) in the sense of Little and Rubin (1987). Rotnitzky and Robins (1995), however, stated that the PML approach may yield inconsistent estimates if the data are (MAR). We show that the adoption of the PML approach for mean- and covariance structures to mean structures in the presence of missing data as proposed by Ziegler (1994) is identical to the complete case (CC) estimator. Nevertheless, the PML approach has the computational advantage in that the association structure remains the same

Relaxation timescales and decay of correlations in a long-range interacting quantum simulator

We study the time evolution of correlation functions in long-range interacting quantum Ising models. For a large class of initial conditions, exact analytic results are obtained in arbitrary lattice dimension, both for ferromagnetic and antiferromagnetic coupling, and hence also in the presence of geometric frustration. In contrast to the nearest-neighbour case, we find that correlations decay like stretched or compressed exponentials in time. Provided the long-range character of the interactions is sufficiently strong, pronounced prethermalization plateaus are observed and relaxation timescales are widely separated. Specializing to a triangular lattice in two spatial dimensions, we propose to utilize these results for benchmarking of a recently developed ion-trap based quantum simulator.Comment: 19 pages, 6 figures; v2: one section removed, appendices added; v3: upper bound corrected + minor corrections; v4: as publishe

A Comparison of Jackknife Estimators of Variance for GEE2

Marginal regression modeling with generalised estimating equations became very popular in the last decade. While the mean structure is of primary interest in first-order generalised estimating equations (GEE1), second-order generalised estimating equations (GEE2) allow the estimation of both the mean and the association structure. It has repeatedly been shown that the usual robust variance estimator for the GEE1 is conservative, especially in small samples. As an alternative, the jackknife estimator of variance can be used. In this discussion paper, we extend the different jackknife estimators of variance to GEE2 models. The variance estimators are compared in a simulation study. While there is only little difference in the variance estimates of the mean structure across simulated models, the results differ substantially with respect to the association structure. The fully iterated jackknife estimator seems to be the most appropriate when focusing on the GEE2