No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the 2d gluon propagator

We study general properties of the Landau-gauge Gribov ghost form factor sigma(p(2)) for SU(N-c) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d = 3, 4 with respect to the d = 2 case. In particular, considering any (sufficiently regular) gluon propagator D(p(2)) and the one-loop-corrected ghost propagator, we prove in the 2d case that the function sigma(p(2)) blows up in the infrared limit p -> 0 as -D(0) ln(p(2)). Thus, for d = 2, the no-pole condition sigma(p(2)) < 1 (for p(2) > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, D(0) = 0. On the contrary, in d = 3 and 4, sigma(p(2)) is finite also if D(0) > 0. The same results are obtained by evaluating the ghost propagator G(p(2)) explicitly at one loop, using fitting forms for D(p(2)) that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g(2) as a free parameter, the ghost propagator admits a one-parameter family of behaviors (labeled by g(2)), in agreement with previous works by Boucaud et al. In this case the condition sigma(0) <= 1 implies g(2) <= g(c)(2), where g(c)(2) is a "critical" value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g(2) smaller than g(c)(2), while for g(2) = g(c)(2) one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for sigma(p(2)) and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor sigma(p(2)). Using these bounds we find again that only in the d = 2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d = 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d = 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

Dynamic symmetry loss of high-frequency hysteresis loops in single-domain particles with uniaxial anisotropy

Understanding how magnetic materials respond to rapidly varying magnetic fields, as in dynamic hysteresis loops, constitutes a complex and physically interesting problem. But in order to accomplish a thorough investigation, one must necessarily consider the effects of thermal fluctuations. Albeit being present in all real systems, these are seldom included in numerical studies. The notable exceptions are the Ising systems, which have been extensively studied in the past, but describe only one of the many mechanisms of magnetization reversal known to occur. In this paper we employ the Stochastic Landau-Lifshitz formalism to study high-frequency hysteresis loops of single-domain particles with uniaxial anisotropy at an arbitrary temperature. We show that in certain conditions the magnetic response may become predominantly out-of-phase and the loops may undergo a dynamic symmetry loss. This is found to be a direct consequence of the competing responses due to the thermal fluctuations and the gyroscopic motion of the magnetization. We have also found the magnetic behavior to be exceedingly sensitive to temperature variations, not only within the superparamagnetic-ferromagnetic transition range usually considered, but specially at even lower temperatures, where the bulk of interesting phenomena is seen to take place. (C) 2011 Elsevier B.V. All rights reserved.

Geometry of BV quantization and Mathai-Quillen formalism

Il formalismo Mathai-Quillen (MQ) è un metodo per costruire la classe di Thom di un fibrato vettoriale attraverso una forma differenziale di profilo Gaussiano. Lo scopo di questa tesi è quello di formulare una nuova rappresentazione della classe di Thom usando aspetti geometrici della quantizzazione Batalin-Vilkovisky (BV). Nella prima parte del lavoro vengono riassunti i formalismi BV e MQ entrambi nel caso finito dimensionale. Infine sfrutteremo la trasformata di Fourier “odd" considerando la forma MQ come una funzione definita su un opportuno spazio graduato.

Magnetization dynamics in spin valves

Key technology applications like magnetoresistive sensors or the Magnetic Random Access Memory (MRAM) require reproducible magnetic switching mechanisms. i.e. predefined remanent states. At the same time advanced magnetic recording schemes push the magnetic switching time into the gyromagnetic regime. According to the Landau-Lifschitz-Gilbert formalism, relevant questions herein are associated with magnetic excitations (eigenmodes) and damping processes in confined magnetic thin film structures.rnObjects of study in this thesis are antiparallel pinned synthetic spin valves as they are extensively used as read heads in today’s magnetic storage devices. In such devices a ferromagnetic layer of high coercivity is stabilized via an exchange bias field by an antiferromagnet. A second hard magnetic layer, separated by a non-magnetic spacer of defined thickness, aligns antiparallel to the first. The orientation of the magnetization vector in the third ferromagnetic NiFe layer of low coercivity - the freelayer - is then sensed by the Giant MagnetoResistance (GMR) effect. This thesis reports results of element specific Time Resolved Photo-Emission Electron Microscopy (TR-PEEM) to image the magnetization dynamics of the free layer alone via X-ray Circular Dichroism (XMCD) at the Ni-L3 X-ray absorption edge.rnThe ferromagnetic systems, i.e. micron-sized spin valve stacks of typically deltaR/R = 15% and Permalloy single layers, were deposited onto the pulse leading centre stripe of coplanar wave guides, built in thin film wafer technology. The ferromagnetic platelets have been applied with varying geometry (rectangles, ellipses and squares), lateral dimension (in the range of several micrometers) and orientation to the magnetic field pulse to study the magnetization behaviour in dependence of these magnitudes. The observation of magnetic switching processes in the gigahertz range became only possible due to the joined effort of producing ultra-short X-ray pulses at the synchrotron source BESSY II (operated in the so-called low-alpha mode) and optimizing the wave guide design of the samples for high frequency electromagnetic excitation (FWHM typically several 100 ps). Space and time resolution of the experiment could be reduced to d = 100 nm and deltat = 15 ps, respectively.rnIn conclusion, it could be shown that the magnetization dynamics of the free layer of a synthetic GMR spin valve stack deviates significantly from a simple phase coherent rotation. In fact, the dynamic response of the free layer is a superposition of an averaged critically damped precessional motion and localized higher order spin wave modes. In a square platelet a standing spin wave with a period of 600 ps (1.7 GHz) was observed. At a first glance, the damping coefficient was found to be independent of the shape of the spin-valve element, thus favouring the model of homogeneous rotation and damping. Only by building the difference in the magnetic rotation between the central region and the outer rim of the platelet, the spin wave becomes visible. As they provide an additional efficient channel for energy dissipation, spin waves contribute to a higher effective damping coefficient (alpha = 0.01). Damping and magnetic switching behaviour in spin valves thus depend on the geometry of the element. Micromagnetic simulations reproduce the observed higher-order spin wave mode.rnBesides the short-run behaviour of the magnetization of spin valves Permalloy single layers with thicknesses ranging from 3 to 40 nm have been studied. The phase velocity of a spin wave in a 3 nm thick ellipse could be determined to 8.100 m/s. In a rectangular structure exhibiting a Landau-Lifschitz like domain pattern, the speed of the field pulse induced displacement of a 90°-Néel wall has been determined to 15.000 m/s.rn

Efficient calculation of gluon amplitudes with n legs and an implementation of parton showers using the dipole formalism

The conventional way to calculate hard scattering processes in perturbation theory using Feynman diagrams is not efficient enough to calculate all necessary processes - for example for the Large Hadron Collider - to a sufficient precision. Two alternatives to order-by-order calculations are studied in this thesis.rnrnIn the first part we compare the numerical implementations of four different recursive methods for the efficient computation of Born gluon amplitudes: Berends-Giele recurrence relations and recursive calculations with scalar diagrams, with maximal helicity violating vertices and with shifted momenta. From the four methods considered, the Berends-Giele method performs best, if the number of external partons is eight or bigger. However, for less than eight external partons, the recursion relation with shifted momenta offers the best performance. When investigating the numerical stability and accuracy, we found that all methods give satisfactory results.rnrnIn the second part of this thesis we present an implementation of a parton shower algorithm based on the dipole formalism. The formalism treats initial- and final-state partons on the same footing. The shower algorithm can be used for hadron colliders and electron-positron colliders. Also massive partons in the final state were included in the shower algorithm. Finally, we studied numerical results for an electron-positron collider, the Tevatron and the Large Hadron Collider.

Statistical mechanics formalism and methods for the analysis of real networks

This thesis provides a thoroughly theoretical background in network theory and shows novel applications to real problems and data. In the first chapter a general introduction to network ensembles is given, and the relations with “standard” equilibrium statistical mechanics are described. Moreover, an entropy measure is considered to analyze statistical properties of the integrated PPI-signalling-mRNA expression networks in different cases. In the second chapter multilayer networks are introduced to evaluate and quantify the correlations between real interdependent networks. Multiplex networks describing citation-collaboration interactions and patterns in colorectal cancer are presented. The last chapter is completely dedicated to control theory and its relation with network theory. We characterise how the structural controllability of a network is affected by the fraction of low in-degree and low out-degree nodes. Finally, we present a novel approach to the controllability of multiplex networks

Accessible information in a two-qubit system through the quantum steering ellipsoids formalism

Capire come ottenere l'informazione accessibile, cioè quanta informazione classica si può estrarre da un processo quantistico, è una delle questioni più intricate e affascinanti nell'ambito della teoria dell'informazione quantistica. Nonostante l'importanza della nozione di informazione accessibile non esistono metodi generali per poterla calcolare, esistono soltanto dei limiti, i più famosi dei quali sono il limite superiore di Holevo e il limite inferiore di Josza-Robb-Wootters. La seguente tesi fa riferimento a un processo che coinvolge due parti, Alice e Bob, che condividono due qubits. Si considera il caso in cui Bob effettua misure binarie sul suo qubit e quindi indirizza lo stato del qubit di Alice in due possibili stati. L'obiettivo di Alice è effettuare la misura ottimale nell'ottica di decretare in quale dei due stati si trova il suo qubit. Lo strumento scelto per studiare questo processo va sotto il nome di 'quantum steering ellipsoids formalism'. Esso afferma che lo stato di un sistema di due qubit può essere descritto dai vettori di Bloch di Alice e Bob e da un ellissoide nella sfera di Bloch di Alice generato da tutte le possibili misure di Bob. Tra tutti gli stati descritti da ellissoidi ce ne sono alcuni che manifestano particolari proprietà, per esempio gli stati di massimo volume. Considerando stati di massimo volume e misure binarie si è riuscito a trovare un limite inferiore all'informazione accessibile per un sistema di due qubit migliore del limite inferiore di Josza-Robb-Wootters. Un altro risultato notevole e inaspettato è che l'intuitiva e giustificata relazione 'distanza tra i punti nell'ellissoide - mutua informazione' non vale quando si confrontano coppie di punti ''vicine'' tra loro e lontane dai più distanti.

50th anniversary of the Judd–Ofelt theory: An experimentalist's view of the formalism and its application

The theory on the intensities of 4f-4f transitions introduced by B.R. Judd and G.S. Ofelt in 1962 has become a center piece in rare-earth optical spectroscopy over the past five decades. Many fundamental studies have since explored the physical origins of the Judd–Ofelt theory and have proposed numerous extensions to the original model. A great number of studies have applied the Judd–Ofelt theory to a wide range of rare-earth doped materials, many of them with important applications in solid-state lasers, optical amplifiers, phosphors for displays and solid state lighting, upconversion and quantum-cutting materials, and fluorescent markers. This paper takes the view of the experimentalist who is interested in appreciating the basic concepts, implications, assumptions, and limitations of the Judd–Ofelt theory in order to properly apply it to practical problems. We first present the formalism for calculating the wavefunctions of 4f electronic states in a concise form and then show their application to the calculation and fitting of 4f-4f transition intensities. The potential, limitations and pitfalls of the theory are discussed, and a detailed case study of LaCl3:Er3+ is presented.

Confirmanden-Unterricht für Israeliten, zunächst für die Schulen des Rabbinatsbezirks Landau

von Elias Grünebaum

Eenige blikken in de negentiende aflevering van het "Beredeneerd Hebr. - en Chald. - Nederl. - Woordenboek bewerkt naar de Grammaticale en Lexicale Werken von Fürst, Landau, Gesenius, Vater en anderen, door I. Waterman"

Philip Elte

Leshon Rabanan (Leschon Rabbanan) : oder gedrängtes, vollständiges aramäisch-chaldäisch-deutsches Handwörterbuch als Hilfsmittel zur Erlernung des Thalmuds, der Thargumim und Midraschim nach dem Aruch, Mussaphia, Buxtorf und Landau ; mit einem Anhange

bearb. u. hrsg. von J. H. Dessauer