Short wavelength radio observations of Saturn's rings

Passive radio observations are discussed from 1 mm to 2 cm wavelengths. The interferometric technique was used to observe the brightness of the rings. The reflectivity and disk temperature are also considered. The differences between radio and radar observations are examined and discussed

Bargmann transform, Zak transform, and coherent states

It is well known that completeness properties of sets of coherent states associated with lattices in the phase plane can be proved by using the Bargmann representation or by using the kq representation which was introduced by J. Zak. In this paper both methods are considered, in particular, in connection with expansions of generalized functions in what are called Gabor series. The setting consists of two spaces of generalized functions (tempered distributions and elements of the class S*) which appear in a natural way in the context of the Bargmann transform. Also, a thorough mathematical investigation of the Zak transform is given. This paper contains many comments and complements on existing literature; in particular, connections with the theory of interpolation of entire functions over the Gaussian integers are given

Regulating the infrared by mode matching: A massless scalar in expanding spaces with constant deceleration

In this paper we consider a massless scalar field, with a possible coupling $\xi$ to the Ricci scalar in a $D$ dimensional FLRW spacetime with a constant deceleration parameter $q=\epsilon-1$, $\epsilon=-{\dot{H}}/{H^2}$. Correlation functions for the Bunch-Davies vacuum of such a theory have long been known to be infrared divergent for a wide range of values of $\epsilon$. We resolve these divergences by explicitly matching the spacetime under consideration to a spacetime without infrared divergencies. Such a procedure ensures that all correlation functions with respect to the vacuum in the spacetime of interest are infrared finite. In this newly defined vacuum we construct the coincidence limit of the propagator and as an example calculate the expectation value of the stress energy tensor. We find that this approach gives both in the ultraviolet and in the infrared satisfactory results. Moreover, we find that, unless the effective mass due to the coupling to the Ricci scalar $\xi R$ is negative, quantum contributions to the energy density always dilute away faster, or just as fast, as the background energy density. Therefore, quantum backreaction is insignificant at the one loop order, unless $\xi R$ is negative. Finally we compare this approach with known results where the infrared is regulated by placing the Universe in a finite box. In an accelerating universe, the results are qualitatively the same, provided one identifies the size of the Universe with the physical Hubble radius at the time of the matching. In a decelerating universe however, the two schemes give different late time behavior for the quantum stress energy tensor. This happens because in this case the length scale at which one regulates the infrared becomes sub-Hubble at late times.Comment: 55 pages, 6 figure

Observations of the binary pulsar system PSR B1718-19 -- The Role of Tidal Circularisation

We present optical and infrared observations taken with the Very Large Telescope of the eclipsing binary pulsar system PSR B1718-19. The candidate companion of the pulsar, identified earlier in Hubble Space Telescope observations, has been detected in all three bands, R, I, and J. These detections allowed us to derive constraints on temperature, radius, and mass, pointing to a companion that has expanded to a radius between one of a main sequence star and one at the Roche-limit. We focus on the role of tidal circularisation in the system, which will have transformed the initially eccentric orbit expected from formation scenarios into the nearly circular orbit presently observed. Based on simple energy balance arguments, we are able to draw a picture of the companion's evolution resulting from the energy deposition in the star due to circularisation. In this picture, our measurement of the companion's parameters is consistent with the expected initial eccentricity. However, with the present understanding of tidal dissipation it remains difficult to account for the short time in which the system was circularised.Comment: 10 pages, 6 figures, accepted for publication in Astronomy and Astrophysic

Microscopic dynamics of supercooled liquids from first principles

Glasses are solid materials whose constituent atoms are arranged in a disordered manner. The transition from a liquid to a glass remains one of the most poorly understood phenomena in condensed matter physics, and still no fully microscopic theory exists that can describe the dynamics of supercooled liquids in a quantitative manner over all relevant time scales. Here we present such a theoretical framework that yields near-quantitative accuracy for the time-dependent correlation functions of a supercooled system over a broad density range. Our approach requires only simple static structural information as input and is based entirely based on first principles. Owing to this first-principles nature, the framework offers a unique platform to study the relation between structure and dynamics in glass-forming matter, and paves the way towards a systematically correctable and ultimately fully quantitative theory of microscopic glassy dynamics

Characterization and computation of canonical tight windows for Gabor frames

Let $(g_{nm})_{n,m\in Z}$ be a Gabor frame for $L_2(R)$ for given window $g$. We show that the window $h^0=S^{-1/2} g$ that generates the canonically associated tight Gabor frame minimizes $\|g-h\|$ among all windows $h$ generating a normalized tight Gabor frame. We present and prove versions of this result in the time domain, the frequency domain, the time-frequency domain, and the Zak transform domain, where in each domain the canonical $h^0$ is expressed using functional calculus for Gabor frame operators. Furthermore, we derive a Wiener-Levy type theorem for rationally oversampled Gabor frames. Finally, a Newton-type method for a fast numerical calculation of \ho is presented. We analyze the convergence behavior of this method and demonstrate the efficiency of the proposed algorithm by some numerical examples

Correlation of eigenstates in the critical regime of quantum Hall systems

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, $\alpha_0\approx 2.28$, gives an almost complete characterization of the critical behavior of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.Comment: 17 pages, 9 Postscript figure