Non-Kramers Freezing and Unfreezing of Tunneling in the Biaxial Spin Model

The ground state tunnel splitting for the biaxial spin model in the magnetic field, H = -D S_{x}^2 + E S_{z}^2 - g \mu_B S_z H_z, has been investigated using an instanton approach. We find a new type of spin instanton and a new quantum interference phenomenon associated with it: at a certain field, H_2 = 2SE^{1/2}(D+E)^{1/2}/(g \mu_B), the dependence of the tunneling splitting on the field switches from oscillations to a monotonic growth. The predictions of the theory can be tested in Fe_8 molecular nanomagnets.Comment: 7 pages, minor changes, published in EP

Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory

We show that it is possible to adapt to nonparametric disturbance auto-correlation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency-domain generalized least squares. When the collective memory in regressors and disturbances is sufficiently strong, ordinary least squares is not only asymptotically inefficient but asymptotically non-normal and has a slow rate of convergence, whereas generalized least squares is asymptotically normal and Gauss-Markov efficient with standard convergence rate. Despite the anomalous behaviour of nonparametric spectrum estimates near a spectral pole, we are able to justify a standard construction of frequency-domain generalized least squares, earlier considered in case of short memory disturbances. A small Monte Carlo study of finite sample performance is included.Time series regression, long memory, adaptive estimation.

On recent SFR calibrations and the constant SFR approximation

Star Formation Rate (SFR) inferences are based in the so-called constant SFR approximation, where synthesis models are require to provide a calibration; we aims to study the key points of such approximation to produce accurate SFR inferences. We use the intrinsic algebra used in synthesis models, and we explore how SFR can be inferred from the integrated light without any assumption about the underling Star Formation history (SFH). We show that the constant SFR approximation is actually a simplified expression of more deeper characteristics of synthesis models: It is a characterization of the evolution of single stellar populations (SSPs), acting the SSPs as sensitivity curve over different measures of the SFH can be obtained. As results, we find that (1) the best age to calibrate SFR indices is the age of the observed system (i.e. about 13Gyr for z=0 systems); (2) constant SFR and steady-state luminosities are not requirements to calibrate the SFR; (3) it is not possible to define a SFR single time scale over which the recent SFH is averaged, and we suggest to use typical SFR indices (ionizing flux, UV fluxes) together with no typical ones (optical/IR fluxes) to correct the SFR from the contribution of the old component of the SFH, we show how to use galaxy colors to quote age ranges where the recent component of the SFH is stronger/softer than the older component. Particular values of SFR calibrations are (almost) not affect by this work, but the meaning of what is obtained by SFR inferences does. In our framework, results as the correlation of SFR time scales with galaxy colors, or the sensitivity of different SFR indices to sort and long scale variations in the SFH, fit naturally. In addition, the present framework provides a theoretical guide-line to optimize the available information from data/numerical experiments to improve the accuracy of SFR inferences.Comment: A&A accepted, 13 pages, 4 Figure

Gaussian Estimation of Parametric Spectral Density with Unknown Pole

We consider a parametric spectral density with power-law behaviour about a fractional pole at the unknown frequency w. The case of unknown w, especially w = 0, is standard in the long memory literature. When w is unknown, asymptotic distribution theory for estimates of parameters, including the (long) memory parameter, is significantly harder. We study a form of Gaussian estimate. We establsih n-consistency of the estimate of w, and discuss its (non-standard) limiting distributional behaviour. For the remaining parameter estimates, we establish Vn-consistency and asymptotic normality.Long-range dependence, unknown pole.