Minimal Model for Disorder-induced Missing Moment of Inertia in Solid 4^4He

The absence of a missing moment inertia in clean solid $^4$He suggests that the minimal experimentally relevant model is one in which disorder induces superfluidity in a bosonic lattice. To this end, we explore the relevance of the disordered Bose-Hubbard model in this context. We posit that a clean array $^4$He atoms is a self-generated Mott insulator, that is, the $^4$He atoms constitute the lattice as well as the `charge carriers'. With this assumption, we are able to interpret the textbook defect-driven supersolids as excitations of either the lower or upper Hubbard bands. In the experiments at hand, disorder induces a closing of the Mott gap through the generation of mid-gap localized states at the chemical potential. Depending on the magnitude of the disorder, we find that the destruction of the Mott state takes place for $d+z>4$ either through a Bose glass phase (strong disorder) or through a direct transition to a superfluid (weak disorder). For $d+z<4$, disorder is always relevant. The critical value of the disorder that separates these two regimes is shown to be a function of the boson filling, interaction and the momentum cut off. We apply our work to the experimentally observed enhancement $^3$He impurities has on the onset temperature for the missing moment of inertia. We find quantitative agreement with experimental trends.Comment: 9 pages, 5 figures: Extended version of previous paper in which the pase diagram for the disordered Bose-Hubbard model is computed using mean-field theory and one-loop RG. The criterion for the Bose glass is derived explicitly. (a few typos are corrected

Improved Coefficient and Variance Estimation in Stable First-Order Dynamic Regression Models

In dynamic regression models the least-squares coefficient estimators are biased in finite samples, and so are the usual estimators for the disturbance variance and for the variance of the coefficient estimators. By deriving the expectation of the initial terms in an expansion of the usual expression for the asymptotic coefficient variance estimator and by comparing these with an approximation to the true variance we find an approximation to the bias in variance estimation from which a bias corrected estimator for the variance readily follows. This is also achieved for a bias corrected coefficient estimator and allows to compare analytically the second-order approximation to the mean squared error of the least-squares estimator and its counterpart for the first-order bias corrected coefficient estimator. Two rather strong results on efficiency gains through bias correction for AR(1) models follow. Illustrative simulation results on the magnitude of bias in coefficient and variance estimation and on the scope for effective bias correction and efficiency improvement are presented for some relevant particular cases of the ARX(1) class of models.

Lorentz Violation and Synchrotron Radiation

We consider the radiation emitted by an ultrarelativistic charged particle moving in a magnetic field, in the presence of an additional Lorentz-violating interaction. In contrast with prior work, we treat a form of Lorentz violation that is represented by a renormalizable operator. Neglecting the radiative reaction force, the particle's trajectory can be determined exactly. The resulting orbit is generally noncircular and does not lie in the place perpendicular to the magnetic field. We do not consider any Lorentz violation in the electromagnetic sector, so the radiation from the accelerated charge can be determined by standard means, and the radiation spectrum will exhibit a Lorentz-violating directional dependence. Using data on emission from the Crab nebula, we can set a bound on a particular combination of Lorentz-violating coefficients at the $6\times10^{-20}$ level.Comment: 14 page

Excitation of the molecular gas in the nuclear region of M82

We present high-resolution HIFI spectroscopy of the nucleus of the archetypical starburst galaxy M 82. Six ^(12)CO lines, 2 ^(13)CO lines and 4 fine-structure lines have been detected. Besides showing the effects of the overall velocity structure of the nuclear region, the line profiles also indicate the presence of multiple components with different optical depths, temperatures, and densities in the observing beam. The data have been interpreted using a grid of PDR models. It is found that the majority of the molecular gas is in low density (n = 10^(3.5) cm^(-3)) clouds, with column densities of N_H = 10^(21.5) cm^(-2) and a relatively low UV radiation field (G_0 = 10^2). The remaining gas is predominantly found in clouds with higher densities (n = 10^5 cm^(-3)) and radiation fields (G_0 = 10^(2.75)), but somewhat lower column densities (N_H = 10^(21.2) cm^(-2)). The highest J CO lines are dominated by a small (1% relative surface filling) component, with an even higher density (n = 10^6 cm^(-3)) and UV field (G_0 = 10^(3.25)). These results show the strength of multi-component modelling for interpretating the integrated properties of galaxies