Uncertainty Relations for Angular Momentum

In this work we study various notions of uncertainty for angular momentum in the spin-s representation of SU(2). We characterize the "uncertainty regions'' given by all vectors, whose components are specified by the variances of the three angular momentum components. A basic feature of this set is a lower bound for the sum of the three variances. We give a method for obtaining optimal lower bounds for uncertainty regions for general operator triples, and evaluate these for small s. Further lower bounds are derived by generalizing the technique by which Robertson obtained his state-dependent lower bound. These are optimal for large s, since they are saturated by states taken from the Holstein-Primakoff approximation. We show that, for all s, all variances are consistent with the so-called vector model, i.e., they can also be realized by a classical probability measure on a sphere of radius sqrt(s(s+1)). Entropic uncertainty relations can be discussed similarly, but are minimized by different states than those minimizing the variances for small s. For large s the Maassen-Uffink bound becomes sharp and we explicitly describe the extremalizing states. Measurement uncertainty, as recently discussed by Busch, Lahti and Werner for position and momentum, is introduced and a generalized observable (POVM) which minimizes the worst case measurement uncertainty of all angular momentum components is explicitly determined, along with the minimal uncertainty. The output vectors for the optimal measurement all have the same length r(s), where r(s)/s goes to 1 as s tends to infinity.Comment: 30 pages, 22 figures, 1 cut-out paper model, video abstract available on https://youtu.be/h01pHekcwF

Quantum-Classical hybrid systems and their quasifree transformations

The focus of this work is the description of a framework for quantum-classical hybrid systems. The main emphasis lies on continuous variable systems described by canonical commutation relations and, more precisely, the quasifree case. Here, we are going to solve two main tasks: The first is to rigorously define spaces of states and observables, which are naturally connected within the general structure. Secondly, we want to describe quasifree channels for which both the Schrödinger picture and the Heisenberg picture are well defined. We start with a general introduction to operator algebras and algebraic quantum theory. Thereby, we highlight some of the mathematical details that are often taken for granted while working with purely quantum systems. Consequently, we discuss several possibilities and their advantages respectively disadvantages in describing classical systems analogously to the quantum formalism. The key takeaway is that there is no candidate for a classical state space or observable algebra that can be put easily alongside a quantum system to form a hybrid and simultaneously fulfills all of our requirements for such a partially quantum and partially classical system. Although these straightforward hybrid systems are not sufficient enough to represent a general approach, we use one of the candidates to prove an intermediate result, which showcases the advantages of a consequent hybrid ansatz: We provide a hybrid generalization of classical diffusion generators where the exchange of information between the classical and the quantum side is controlled by the induced noise on the quantum system. Then, we present solutions for our initial tasks. We start with a CCR-algebra where some variables may commute with all others and hence generate a classical subsystem. After clarifying the necessary representations, our hybrid states are given by continuous characteristic functions, and the according state space is equal to the state space of a non-unital C*-algebra. While this C*-algebra is not a suitable candidate for an observable algebra itself, we describe several possible subsets in its bidual which can serve this purpose. They can be more easily characterized and will also allow for a straightforward definition of a proper Heisenberg picture. The subsets are given by operator-valued functions on the classical phase space with varying degrees of regularity, such as universal measurability or strong*-continuity. We describe quasifree channels and their properties, including a state-channel correspondence, a factorization theorem, and some basic physical operations. All this works solely on the assumption of a quasifree system, but we also show that the more famous subclass of Gaussian systems fits well within this formulation and behaves as expected

Integration erneuerbarer Energiequellen in das Schweizer Verteilnetz: Möglichkeiten von Microgrids

Die Literaturstudie wurde von den Elektrizitätswerken des Kantons Zürich (EKZ) im Rahmen ihrer Hochschulförderung finanziell unterstützt.Microgrids sind eine vielversprechende Möglichkeit, die zunehmende Anzahl EE-Anlagen verhältnismässig kostengünstig in das bestehende Stromnetz zu integrieren. Viele technische Komponenten befinden sich jedoch noch in der Entwicklungsphase und werden erst in der Zukunft wirtschaftlich einsetzbar sein. Trotzdem werden derzeit schon verschiedene grosse Microgrids in Pilotprojekten weltweit implementiert. Offiziell und langfristig ins Netz integriert wurden bisher meist nur kleine Microgrids, typischerweise zur rudimentären Stromversorgung oder auf Gebäude- oder Campus-Ebene. Die Rolle der Verteilnetzbetreiber wird sich mit der Einführung von Microgrids erheblich ändern und erweitern, da sie damit aktiver in das Stromgeschehen eingreifen können. In der Schweiz werden die gesetzlichen Rahmenbedingungen für die Einbindung von Microgrids momentan erst noch ausgearbeitet, welche die möglichen Implementierungen von Microgrids, beispielsweise über Vergütungsanreize, in den nächsten Jahren stark beeinflussen können

INVESTIGATION OF LUNAR METEORITE NWA 3163 AND COMPARISONS WITH SHOCKED ANORTHOSITES FROM THE MISTASTIN LAKE IMPACT STRUCTURE, LABRADOR

Lunar granulites are believed to be metamorphosed polymict impact breccias that have the potential to yield new information on the origin and evolution of the lunar crust and its impact history. A major challenge in studying these rocks is to elucidate the metamorphic environment and processes that gave rise to the enigmatic granulitic textures. Presented here is the first comparison of the metamorphic characteristics of lunar meteorite NWA 3163 with shock-metamorphosed and heated anorthosites at the Mistastin Lake impact structure of northern Labrador. The Mistastin Lake impact structure is a 36 ± 4 Ma, 28 km diameter feature situated at the north-eastern end of the Mesoproterozoic Mistastin Batholith composed of anorthosites, granites and lesser amounts of gabbro. Petrographic observations suggest that the majority of the feldspar within samples from the central uplift has been transformed to diaplectic glass (maskelynite). Samples from clasts within impact melt rock appear to have undergone some degree of devitrification, most likely because of thermal metamorphism due to the heat of the impact melt. A comparison of these shock features, maskelynite distribution and grain boundary characteristics as shown with Backscatter Imaging (BSE), colour Cathodoluminesence (CL) and Energy Dispersive X-Ray Spectrometry (EDS) spectra with those of NWA 3163 have determined that no samples retrieved from Mistastin exhibit textures similar to those found in lunar granulites. This result was unexpected and warrants additional studies of lunar granulites. Using CL to identify metamorphic textures, NWA 3163 has been found to be a poikiolitic granoblastic granulite

Quantum-Classical Hybrid Systems and their Quasifree Transformations

We study continuous variable systems, in which quantum and classical degrees of freedom are combined and treated on the same footing. Thus all systems, including the inputs or outputs to a channel, may be quantum-classical hybrids. This allows a unified treatment of a large variety of quantum operations involving measurements or dependence on classical parameters. The basic variables are given by canonical operators with scalar commutators. Some variables may commute with all others and hence generate a classical subsystem. We systematically study the class of "quasifree" operations, which are characterized equivalently either by an intertwining condition for phase-space translations or by the requirement that, in the Heisenberg picture, Weyl operators are mapped to multiples of Weyl operators. This includes the well-known Gaussian operations, evolutions with quadratic Hamiltonians, and "linear Bosonic channels", but allows for much more general kinds of noise. For example, all states are quasifree. We sketch the analysis of quasifree preparation, measurement, repeated observation, cloning, teleportation, dense coding, the setup for the classical limit, and some aspects of irreversible dynamics, together with the precise salient tradeoffs of uncertainty, error, and disturbance. Although the spaces of observables and states are infinite dimensional for every non-trivial system that we consider, we treat the technicalities related to this in a uniform and conclusive way, providing a calculus that is both easy to use and fully rigorous.Comment: 63 pages, 6 figure

Quantum-Classical Hybrid Systems and their Quasifree Transformations

We study continuous variable systems, in which quantum and classical degrees of freedom are combined and treated on the same footing. Thus all systems, including the inputs or outputs to a channel, may be quantum-classical hybrids. This allows a unified treatment of a large variety of quantum operations involving measurements or dependence on classical parameters. The basic variables are given by canonical operators with scalar commutators. Some variables may commute with all others and hence generate a classical subsystem. We systematically study the class of "quasifree" operations, which are characterized equivalently either by an intertwining condition for phase-space translations or by the requirement that, in the Heisenberg picture, Weyl operators are mapped to multiples of Weyl operators. This includes the well-known Gaussian operations, evolutions with quadratic Hamiltonians, and "linear Bosonic channels", but allows for much more general kinds of noise. For example, all states are quasifree. We sketch the analysis of quasifree preparation, measurement, repeated observation, cloning, teleportation, dense coding, the setup for the classical limit, and some aspects of irreversible dynamics, together with the precise salient tradeoffs of uncertainty, error, and disturbance. Although the spaces of observables and states are infinite dimensional for every non-trivial system that we consider, we treat the technicalities related to this in a uniform and conclusive way, providing a calculus that is both easy to use and fully rigorous

State-independent Uncertainty Relations and Entanglement Detection in Noisy Systems

Quantifying quantum mechanical uncertainty is vital for the increasing number of experiments that reach the uncertainty limited regime. We present a method for computing tight variance uncertainty relations, i.e., the optimal state-independent lower bound for the sum of the variances for any set of two or more measurements. The bounds come with a guaranteed error estimate, so results of preassigned accuracy can be obtained straightforwardly. Our method also works for postive-operator-valued measurements. Therefore, it can be used for detecting entanglement in noisy environments, even in cases where conventional spin squeezing criteria fail because of detector noise

Hier baut der Fachreferent : Die Präsenzmodule des Projekts Informationskompetenz

Sind Sie der Meinung, dass die Studierenden Ihres Fachbereichs keinen Plan bei ihrer Informationsrecherche haben? Wollten Sie dem schon lange abhelfen und einen Informationskompetenz (IK)-Kurs anbieten, aber sehen sich bislang in Anbetracht des enormen Planungsaufwandes nicht in der Lage, einen solchen Kurs zu realisieren? Um zumindest den Planungsberg entscheidend zu verkleinern, stellt das Projekt Informationskompetenz der Bibliothek der Universität Konstanz allen Interessierten ein modulares Baukastensystem für einen Modellkurs zur Verfügung

Vom Bestandsaufbau zu Flatrates, vom Closed Access zum Open Access. Erwerbung an der Universitätsbibliothek Tübingen von 2010 bis heute

13 Jahre Erwerbung an der Universitätsbibliothek Tübingen – was soll sich da schon großartig verändert haben? Über Jahrzehnte, wenn nicht noch länger, war der Erwerbungs- und Erschließungsprozess unverändert überschaubar: Einer titelbezogenen Auswahl folgte die Bestellung beim Buchhändler und nach Eingang der Bände oder Hefte wurden diese inventarisiert, katalogisiert, mit Signaturschildern ausgestattet und an ihren Standort gebracht, wo sie anschließend den Nutzerinnen und Nutzern zum Lesen vor Ort oder zur Ausleihe nach Hause zur Verfügung standen. Das war nicht mehr ganz der Zustand 2010 – E-Journals und E-Books hatten Einzug gehalten und auch erste Konsortialverträge für Datenbanken und größere E-Journal-Pakete waren bereits abgeschlossen worden – bei E-Journals in der Regel noch auf Subskriptionen aufsetzend