Complete time-dependent treatment of a three-level system

Both unitary evolution and the effects of dissipation and decoherence for a general three-level system are of widespread interest in quantum optics, molecular physics, and elsewhere. A previous paper presented a technique for solving the time-dependent operator equations involved but under certain restrictive conditions. We now extend our results to a general three-level system with arbitrary time-dependent Hamiltonians and Lindblad operators. Analytical handling of the SU(3) algebra of the eight operators involved leaves behind a set of coupled first-order differential equations for classical functions. Solution of this set gives a complete solution of the quantum problem, without having to invoke rotating-wave or other approximations. Numerical illustrations are given.Comment: 1 tar.gz file containing a Tex and four eps figure files; unzip with command gunzip RZPRA05.tar.g

Constraint on the early Universe by relic gravitational waves: From pulsar timing observations

Recent pulsar timing observations by the Parkers Pulsar Timing Array and European Pulsar Timing Array teams obtained the constraint on the relic gravitational waves at the frequency $f_*=1/{\rm yr}$, which provides the opportunity to constrain $H_*$, the Hubble parameter when these waves crossed the horizon during inflation. In this paper, we investigate this constraint by considering the general scenario for the early Universe: we assume that the effective (average) equation-of-state $w$ before the big bang nucleosynthesis stage is a free parameter. In the standard hot big-bang scenario with $w=1/3$, we find that the current PPTA result follows a bound H_*\leq 1.15\times10^{-1}\mpl, and the EPTA result follows H_*\leq 6.92\times10^{-2}\mpl. We also find that these bounds become much tighter in the nonstandard scenarios with $w>1/3$. When $w=1$, the bounds become H_*\leq5.89\times10^{-3}\mpl for the current PPTA and H_*\leq3.39\times10^{-3}\mpl for the current EPTA. In contrast, in the nonstandard scenario with $w=0$, the bound becomes H_*\leq7.76\mpl for the current PPTA.Comment: 8 pages, 3 figures, 1 table, PRD in pres

General Design Bayesian Generalized Linear Mixed Models

Linear mixed models are able to handle an extraordinary range of complications in regression-type analyses. Their most common use is to account for within-subject correlation in longitudinal data analysis. They are also the standard vehicle for smoothing spatial count data. However, when treated in full generality, mixed models can also handle spline-type smoothing and closely approximate kriging. This allows for nonparametric regression models (e.g., additive models and varying coefficient models) to be handled within the mixed model framework. The key is to allow the random effects design matrix to have general structure; hence our label general design. For continuous response data, particularly when Gaussianity of the response is reasonably assumed, computation is now quite mature and supported by the R, SAS and S-PLUS packages. Such is not the case for binary and count responses, where generalized linear mixed models (GLMMs) are required, but are hindered by the presence of intractable multivariate integrals. Software known to us supports special cases of the GLMM (e.g., PROC NLMIXED in SAS or glmmML in R) or relies on the sometimes crude Laplace-type approximation of integrals (e.g., the SAS macro glimmix or glmmPQL in R). This paper describes the fitting of general design generalized linear mixed models. A Bayesian approach is taken and Markov chain Monte Carlo (MCMC) is used for estimation and inference. In this generalized setting, MCMC requires sampling from nonstandard distributions. In this article, we demonstrate that the MCMC package WinBUGS facilitates sound fitting of general design Bayesian generalized linear mixed models in practice.Comment: Published at http://dx.doi.org/10.1214/088342306000000015 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Electrical conductivity and thermal dilepton rate from quenched lattice QCD

We report on a continuum extrapolation of the vector current correlation function for light valence quarks in the deconfined phase of quenched QCD. This is achieved by performing a systematic analysis of the influence of cut-off effects on light quark meson correlators at $T\simeq 1.45 T_c$ using clover improved Wilson fermions. We discuss resulting constraints on the electrical conductivity and the thermal dilepton rate in a quark gluon plasma. In addition new results at 1.2 and 3.0 $T_c$ will be presented.Comment: 4 pages, 6 eps figures, to appear in the proceedings of Quark Matter 2011, 23-28 May 2011, Annecy, Franc

The two-dimensional frustrated Heisenberg model on the orthorhombic lattice

We discuss new high-field magnetization data recently obtained by Tsirlin et al. for layered vanadium phosphates in the framework of the square-lattice model. Our predictions for the saturation fields compare exceptionally well to the experimental findings, and the strong bending of the curves below saturation agrees very well with the experimental field dependence. Furthermore we discuss the remarkably good agreement of the frustrated Heisenberg model on the square lattice in spite of the fact that the compounds described with this model actually have a lower crystallographic symmetry. We present results from our calculations on the thermodynamics of the model on the orthorhombic (i.e., rectangular) lattice, in particular the temperature dependence of the magnetic susceptibility. This analysis also sheds light on the discussion of magnetic frustration and anisotropy of a class of iron pnictide parent compounds, where several alternative suggestions for the magnetic exchange models were proposed.Comment: 4 pages, 3 figures, accepted for publication in Journal of Physics: Conference Serie

High-quality positrons from a multi-proton bunch driven hollow plasma wakefield accelerator

By means of hollow plasma, multiple proton bunches work well in driving nonlinear plasma wakefields and accelerate electrons to energy frontier with preserved beam quality. However, the acceleration of positrons is different because the accelerating structure is strongly charge dependent. There is a discrepancy between keeping a small normalized emittance and a small energy spread. This results from the conflict that the plasma electrons used to provide focusing to the multiple proton bunches dilute the positron bunch. By loading an extra electron bunch to repel the plasma electrons and meanwhile reducing the plasma density slightly to shift the accelerating phase with a conducive slope to the positron bunch, the positron bunch can be accelerate to 400 GeV (40% of the driver energy) with an energy spread as low as 1% and well preserved normalized emittance. The successful generation of high quality and high energy positrons paves the way to the future energy frontier lepton colliders.Comment: 14 pages, 5 figure

Outlier Detection Using Nonconvex Penalized Regression

This paper studies the outlier detection problem from the point of view of penalized regressions. Our regression model adds one mean shift parameter for each of the $n$ data points. We then apply a regularization favoring a sparse vector of mean shift parameters. The usual $L_1$ penalty yields a convex criterion, but we find that it fails to deliver a robust estimator. The $L_1$ penalty corresponds to soft thresholding. We introduce a thresholding (denoted by $\Theta$) based iterative procedure for outlier detection ($\Theta$-IPOD). A version based on hard thresholding correctly identifies outliers on some hard test problems. We find that $\Theta$-IPOD is much faster than iteratively reweighted least squares for large data because each iteration costs at most $O(np)$ (and sometimes much less) avoiding an $O(np^2)$ least squares estimate. We describe the connection between $\Theta$-IPOD and $M$-estimators. Our proposed method has one tuning parameter with which to both identify outliers and estimate regression coefficients. A data-dependent choice can be made based on BIC. The tuned $\Theta$-IPOD shows outstanding performance in identifying outliers in various situations in comparison to other existing approaches. This methodology extends to high-dimensional modeling with $p\gg n$, if both the coefficient vector and the outlier pattern are sparse

Spatially resolved femtosecond pump-probe study of topological insulator Bi2Se3

Carrier and phonon dynamics in Bi2Se3 crystals are studied by a spatially resolved ultrafast pump-probe technique. Pronounced oscillations in differential reflection are observed with two distinct frequencies, and are attributed to coherent optical and acoustic phonons, respectively. The rising time of the signal indicates that the thermalization and energy relaxation of hot carriers are both sub-ps in this material. We found that the thermalization and relaxation time decreases with the carrier density. The expansion of the differential reflection profile allows us to estimate an ambipolar carrier diffusion coefficient on the order of 500 square centimeters per second. A long-term slow expansion of the profile shows a thermal diffusion coefficient of 1.2 square centimeters per second.Comment: 8 pages, 6 figure