Conserving Approximations in Time-Dependent Density Functional Theory

In the present work we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach to many-body perturbation theory (MBPT) as developed during the sixties and later expanded by us in the mid nineties. Due to this feature the resulting response functions obey a large number of conservation laws such as particle and momentum conservation and sum rules. The quality of the obtained results is governed by the physical processes built in through MBPT but also by the choice of variational expressions. We here present several conserving response functions of different sophistication to be used in the calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio

Total energies from variational functionals of the Green function and the renormalized four-point vertex

We derive variational expressions for the grand potential or action in terms of the many-body Green function $G$ which describes the propagation of particles and the renormalized four-point vertex $\Gamma$ which describes the scattering of two particles in many-body systems. The main ingredient of the variational functionals is a term we denote as the $\Xi$-functional which plays a role analogously to the usual $\Phi$-functional studied by Baym (G.Baym, Phys.Rev. 127, 1391 (1962)) in connection with the conservation laws in many-body systems. We show that any $\Xi$-derivable theory is also $\Phi$-derivable and therefore respects the conservation laws. We further set up a computational scheme to obtain accurate total energies from our variational functionals without having to solve computationally expensive sets of self-consistent equations. The input of the functional is an approximate Green function $\tilde{G}$ and an approximate four-point vertex $\tilde{\Gamma}$ obtained at a relatively low computational cost. The variational property of the functional guarantees that the error in the total energy is only of second order in deviations of the input Green function and vertex from the self-consistent ones that make the functional stationary. The functionals that we will consider for practical applications correspond to infinite order summations of ladder and exchange diagrams and are therefore particularly suited for applications to highly correlated systems. Their practical evaluation is discussed in detail.Comment: 21 pages, 10 figures. Physical Review B (accepted

A deconvolution map-making method for experiments with circular scanning strategies

Aims. To investigate the performance of a deconvolution map-making algorithm for an experiment with a circular scanning strategy, specifically in this case for the analysis of Planck data, and to quantify the effects of making maps using simplified approximations to the true beams. Methods. We present an implementation of a map-making algorithm which allows the combined treatment of temperature and polarisation data, and removal of instrumental effects, such as detector time constants and finite sampling intervals, as well as the deconvolution of arbitrarily complex beams from the maps. This method may be applied to any experiment with a circular scanning-strategy. Results. Low-resolution experiments were used to demonstrate the ability of this method to remove the effects of arbitrary beams from the maps and to demonstrate the effects on the maps of ignoring beam asymmetries. Additionally, results are presented of an analysis of a realistic full-scale simulated data-set for the Planck LFI 30 GHz channel. Conclusions. Our method successfully removes the effects of the beams from the maps, and although it is computationally expensive, the analysis of the Planck LFI data should be feasible with this approach.Comment: 14 pages, 14 figures, accepte

Time correlations in a confined magnetized free-electron gas

The time-dependent pair correlation functions for a degenerate ideal quantum gas of charged particles in a uniform magnetic field are studied on the basis of equilibrium statistics. In particular, the influence of a flat hard wall on the correlations is investigated, both for a perpendicular and a parallel orientation of the wall with respect to the field. The coherent and incoherent parts of the time-dependent structure function in position space are determined from an expansion in terms of the eigenfunctions of the one-particle Hamiltonian. For the bulk of the system, the intermediate scattering function and the dynamical structure factor are derived by taking successive Fourier transforms. In the vicinity of the wall the time-dependent coherent structure function is found to decay faster than in the bulk. For coinciding positions near the wall the form of the structure function turns out to be independent of the orientation of the wall. Numerical results are shown to corroborate these findings.Comment: 25 pages, 14 figures, to be published in Journal of Physics

Optimising the multiplex factor of the frequency domain multiplexed readout of the TES-based microcalorimeter imaging array for the X-IFU instrument on the Athena Xray observatory

Athena is a space-based X-ray observatory intended for exploration of the hot and energetic universe. One of the science instruments on Athena will be the X-ray Integrated Field Unit (X-IFU), which is a cryogenic X-ray spectrometer, based on a large cryogenic imaging array of Transition Edge Sensors (TES) based microcalorimeters operating at a temperature of 100mK. The imaging array consists of 3800 pixels providing 2.5 eV spectral resolution, and covers a field of view with a diameter of of 5 arc minutes. Multiplexed readout of the cryogenic microcalorimeter array is essential to comply with the cooling power and complexity constraints on a space craft. Frequency domain multiplexing has been under development for the readout of TES-based detectors for this purpose, not only for the X-IFU detector arrays but also for TES-based bolometer arrays for the Safari instrument of the Japanese SPICA observatory. This paper discusses the design considerations which are applicable to optimise the multiplex factor within the boundary conditions as set by the space craft. More specifically, the interplay between the science requirements such as pixel dynamic range, pixel speed, and cross talk, and the space craft requirements such as the power dissipation budget, available bandwidth, and electromagnetic compatibility will be discussed

Waiting and Residence Times of Brownian Interface Fluctuations

We report on the residence times of capillary waves above a given height $h$ and on the typical waiting time in between such fluctuations. The measurements were made on phase separated colloid-polymer systems by laser scanning confocal microscopy. Due to the Brownian character of the process, the stochastics vary with the chosen measurement interval $\Delta t$. In experiments, the discrete scanning times are a practical cutoff and we are able to measure the waiting time as a function of this cutoff. The measurement interval dependence of the observed waiting and residence times turns out to be solely determined by the time dependent height-height correlation function $g(t)$. We find excellent agreement with the theory presented here along with the experiments.Comment: 5 figure

Rotation periods of late-type stars in the young open cluster IC 2602

We present the results of a monitoring campaign aimed at deriving rotation periods for a representative sample of stars in the young (30 Myr) open cluster IC 2602. Rotation periods were derived for 29 of 33 stars monitored. The periods derived range from 0.2d (one of the shortest known rotation periods of any single open cluster star) to about 10d (which is almost twice as long as the longest period previously known for a cluster of this age). We are able to confirm 8 previously known periods and derive 21 new ones, delineating the long period end of the distribution. Despite our sensitivity to longer periods, we do not detect any variables with periods longer than about 10d. The combination of these data with those for IC 2391, an almost identical cluster, leads to the following conclusions: 1) The fast rotators in a 30 Myr cluster are distributed across the entire 0.5 < B-V < 1.6 color range. 2) 6 stars in our sample are slow rotators, with periods longer than 6d. 3) The amplitude of variability depends on both the color and the period. The dependence on the latter might be important in understanding the selection effects in the currently available rotation period database and in planning future observations. 4) The interpretation of these data in terms of theoretical models of rotating stars suggests both that disk-interaction is the norm rather than the exception in young stars and that disk-locking times range from zero to a few Myr.Comment: 23 pages, 8 figures, accepted for publication in the Astrophysical Journa

Electrochemical methods for speciation of trace elements in marine waters. Dynamic aspects

The contribution of electrochemical methods to the knowledge of dynamic speciation of toxic trace elements in marine waters is critically reviewed. Due to the importance of dynamic considerations in the interpretation of the electrochemical signal, the principles and recent developments of kinetic features in the interconversion of metal complex species will be presented. As dynamic electrochemical methods, only stripping techniques (anodic stripping voltammetry and stripping chronopotentiometry) will be used because they are the most important for the determination of trace elements. Competitive ligand ex- change-adsorptive cathodic stripping voltammetry, which should be considered an equilibrium technique rather than a dynamic method, will be also discussed because the complexing parameters may be affected by some kinetic limitations if equilibrium before analysis is not attained and/or the flux of the adsorbed complex is in fluenced by the lability of the natural complexes in the water sample. For a correct data interpretation and system characterization the comparison of results obtained from different techniques seems essential in the articulation of a serious discussion of their meaning

Normal modes of a quasi-one-dimensional multi-chain complex plasma

We studied equally charged particles, suspended in a complex plasma, which move in a plane and interact with a screened Coulomb potential (Yukawa type) and with an additional external confining parabolic potential in one direction, that makes the system quasi-one-dimensional (Q1D). The normal modes of the system are studied in the presence of dissipation. We also investigated how a perpendicular magnetic field couples the phonon modes with each other. Two different ways of exciting the normal modes are discussed: 1) a uniform excitation of the Q1D lattice, and 2) a local forced excitation of the system in which one particle is driven by e.g. a laser. Our results are in very good agreement with recent experimental findings on a finite single chain system (Phys. Rev. Lett. {\bf 91}, 255003 (2003)). Predictions are made for the normal modes of multi-chain structures in the presence of damping.Comment: 15 pages, 14 figures, accepted for publication on PR