University of Vienna

About: University of Vienna is a education organization based out in Vienna, Austria. It is known for research contribution in the topics: Population & Context (language use). The organization has 44686 authors who have published 95840 publications receiving 2907492 citations.

Mathematical Methods in Quantum Mechanics

Abstract: Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators Part 1 of the book is a concise introduction to the spectral theory of unbounded operators Only those topics that will be needed for later applications are covered The spectral theorem is a central topic in this approach and is introduced at an early stage Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution Position, momentum, and angular momentum are discussed via algebraic methods Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required In particular, no functional analysis and no Lebesgue integration theory are assumed It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature This new edition has additions and improvements throughout the book to make the presentation more student friendly

Feasible Entanglement Purification for Quantum Communication

Abstract: The distribution of entangled states between distant locations will be essential for the future large scale realization of quantum communication schemes such as quantum cryptography and quantum teleportation. Because of the unavoidable noise in the quantum communication channel, the entanglement between two particles is more and more degraded the further they propagate. Entanglement purification is thus essential to distill highly entangled states from less entangled ones. Existing general purification protocols are based on the quantum controlled-NOT (CNOT) or similar quantum logic operations, which are very difficult to implement experimentally. Present realizations of CNOT gates are much too imperfect to be useful for long-distance quantum communication. Here we present a feasible scheme for the entanglement purification of general mixed entangled states, which does not require any CNOT operations, but only simple linear optical elements. Since the perfection of such elements is very high, the local operations necessary for purification can be performed with the required precision. Our procedure is within the reach of current technology and should significantly simplify the implementation of long-distance quantum communication.

Scientific foundations for an IUCN Red List of ecosystems.

Abstract: An understanding of risks to biodiversity is needed for planning action to slow current rates of decline and secure ecosystem services for future human use. Although the IUCN Red List criteria provide an effective assessment protocol for species, a standard global assessment of risks to higher levels of biodiversity is currently limited. In 2008, IUCN initiated development of risk assessment criteria to support a global Red List of ecosystems. We present a new conceptual model for ecosystem risk assessment founded on a synthesis of relevant ecological theories. To support the model, we review key elements of ecosystem definition and introduce the concept of ecosystem collapse, an analogue of species extinction. The model identifies four distributional and functional symptoms of ecosystem risk as a basis for assessment criteria: A) rates of decline in ecosystem distribution; B) restricted distributions with continuing declines or threats; C) rates of environmental (abiotic) degradation; and D) rates of disruption to biotic processes. A fifth criterion, E) quantitative estimates of the risk of ecosystem collapse, enables integrated assessment of multiple processes and provides a conceptual anchor for the other criteria. We present the theoretical rationale for the construction and interpretation of each criterion. The assessment protocol and threat categories mirror those of the IUCN Red List of species. A trial of the protocol on terrestrial, subterranean, freshwater and marine ecosystems from around the world shows that its concepts are workable and its outcomes are robust, that required data are available, and that results are consistent with assessments carried out by local experts and authorities. The new protocol provides a consistent, practical and theoretically grounded framework for establishing a systematic Red List of the world’s ecosystems. This will complement the Red List of species and strengthen global capacity to report on and monitor the status of biodiversity

Lesions of the acetabular labrum: accuracy of MR imaging and MR arthrography in detection and staging.

Abstract: PURPOSE: To determine the accuracy of magnetic resonance (MR) imaging and MR arthrography in the detection and staging of lesions of the acetabular labrum. MATERIALS AND METHODS: Fifty-seven hips of 56 patients with chronic hip pain and a strong clinical suspicion of labral lesions were examined with a three-dimensional gradient-echo sequence in the coronal oblique and sagittal oblique projections before and after the intraarticular injection of gadopentetate dimeglumine. The labra were evaluated on the basis of morphology, signal intensity, the presence or absence of a tear, and their attachment to the acetabulum. Twenty-two of the hips underwent surgical intervention, and 35 hips were treated conservatively. RESULTS: Twenty of the 22 labra with surgical proof were staged accurately with MR arthrography. On the conventional MR images, only eight of the 22 labra were staged correctly. Whereas the sensitivity of MR arthrography was 90% and its accuracy was 91%, the sensitivity of MR imaging was 30% and its...

Measurement and imaging of birefringence and optic axis orientation by phase resolved polarization sensitive optical coherence tomography

Abstract: We present an improved method of polarization sensitive optical coherence tomography that enables measurement and imaging of backscattered intensity, birefringence, and fast optic axis orientation simultaneously with only one single A-scan per transverse measurement location. While intensity and birefringence data are obtained in a conventional way, the optic axis orientation is determined from the phase difference recorded in two orthogonal polarization channels. We report on accuracy and precision of the method by measuring birefringence and optic axis orientation of well defined polarization states in a technical object and present maps of birefringence and, what we believe for the first time, of optic axis orientation in biological tissue.