Quantum Hall Physics - hierarchies and CFT techniques

The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past thirty years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of emerging states of matter would need to be understood in a systematic manner. The first attempts to do this, by Haldane and Halperin, set an agenda for further work which has continued to this day. Since that time the idea of hierarchies of quasiparticles condensing to form new states has been a pillar of our understanding of fractional quantum Hall physics. In the thirty years that have passed since then, a number of new directions of thought have advanced our understanding of fractional quantum Hall states, and have extended it in new and unexpected ways. Among these directions is the extensive use of topological quantum field theories and conformal field theories, the application of the ideas of composite bosons and fermions, and the study of nonabelian quantum Hall liquids. This article aims to present a comprehensive overview of this field, including the most recent developments.Comment: added section on experimental status, 59 pages+references, 3 figure

Microscopic theory of the quantum Hall hierarchy

We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan {\it et. al.}, and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states.Comment: 4 pages, 2 figures. Publishe

Die Greenlight-Laservaporisation der Prostata zur Therapie des benignen Prostatasyndroms: Entwicklung und Stellenwert

Zusammenfassung: Die Greenlight-Laservaporisation hat in den letzten 10Jahren breiten Einsatz in der Therapie des benignen Prostatasyndroms (BPS) gefunden. Neben der Steigerung der Effektivität des Lasers durch eine Erhöhung der maximalen Leistung auf zunächst 80W und später 120W führten auch die guten Ergebnisse der klinischen Evaluationen zu einer zunehmenden Akzeptanz dieses Lasersystems. In der vorliegenden Arbeit werden wesentliche Ergebnisse der klinischen Evaluation der Technik aus den letzten Jahren dargelegt, an denen Schweizer Kliniken maßgeblich beteiligt waren. Hier sind v.a. die geringe peri- und postoperative Morbidität sowie die bisher guten kurz- und mittelfristigen funktionellen Ergebnisse zu nennen. Neben diesen Vorteilen, die v.a. in der nahezu blutungsfreien Durchführung des Eingriffs begründet liegen, werden jedoch ebenso die Nachteile und Limitationen der Laservaporisation beleuchtet, die möglicherweise auch spezifische klinische Nebenwirkungen zur Folge haben. Der zukünftige Stellenwert der Technik wird daher auch vor dem Hintergrund der noch ausstehenden Langzeitdaten weiter evaluiert werden müsse

Transverse Emittance Measurement with the Three-Monitor-Method at the CERN Linac4

This report evaluates the applicability of the Three-Monitor-Method to determine the transverse emittance of the CERN Linac4 160 MeV H- -beam. The Three-Monitor-Method is a linear formalism allowing to calculate transverse emittance values from beam size measurements at three different positions along a beam line, assuming that the transfer matrix elements between these locations are known. It is planned to build two of these measurement systems, which should operate from 2013/14 immediately behind the exit of the linear accelerator in the dump line and close to the end of the transfer line to the PS Booster synchrotron in the LBE line. At first, the mathematical formalism and the simulation tools are briefly introduced. Then, the method is applied for both measurement lines. Results on measurement precisions and systematic errors are presented. Final conclusions are drawn at the end, and a summary of the equipment to be installed or modified will be given

Compositional Performance Modelling with the TIPPtool

Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations

Quantum Hall quasielectron operators in conformal field theory

In the conformal field theory (CFT) approach to the quantum Hall effect, the multi-electron wave functions are expressed as correlation functions in certain rational CFTs. While this approach has led to a well-understood description of the fractionally charged quasihole excitations, the quasielectrons have turned out to be much harder to handle. In particular, forming quasielectron states requires non-local operators, in sharp contrast to quasiholes that can be created by local chiral vertex operators. In both cases, the operators are strongly constrained by general requirements of symmetry, braiding and fusion. Here we construct a quasielectron operator satisfying these demands and show that it reproduces known good quasiparticle wave functions, as well as predicts new ones. In particular we propose explicit wave functions for quasielectron excitations of the Moore-Read Pfaffian state. Further, this operator allows us to explicitly express the composite fermion wave functions in the positive Jain series in hierarchical form, thus settling a longtime controversy. We also critically discuss the status of the fractional statistics of quasiparticles in the Abelian hierarchical quantum Hall states, and argue that our construction of localized quasielectron states sheds new light on their statistics. At the technical level we introduce a generalized normal ordering, that allows us to "fuse" an electron operator with the inverse of an hole operator, and also an alternative approach to the background charge needed to neutralize CFT correlators. As a result we get a fully holomorphic CFT representation of a large set of quantum Hall wave functions.Comment: minor changes, publishe

Ferromagnetic coupling of mononuclear Fe centers in a self-assembled metal-organic network on Au(111)

The magnetic state and magnetic coupling of individual atoms in nanoscale structures relies on a delicate balance between different interactions with the atomic-scale surrounding. Using scanning tunneling microscopy, we resolve the self-assembled formation of highly ordered bilayer structures of Fe atoms and organic linker molecules (T4PT) when deposited on a Au(111) surface. The Fe atoms are encaged in a three-dimensional coordination motif by three T4PT molecules in the surface plane and an additional T4PT unit on top. Within this crystal field, the Fe atoms retain a magnetic ground state with easy-axis anisotropy, as evidenced by X-ray absorption spectroscopy and X-ray magnetic circular dichroism. The magnetization curves reveal the existence of ferromagnetic coupling between the Fe centers

Hierarchy wave functions--from conformal correlators to Tao-Thouless states

Laughlin's wave functions, describing the fractional quantum Hall effect at filling factors $\nu=1/(2k+1)$, can be obtained as correlation functions in conformal field theory, and recently this construction was extended to Jain's composite fermion wave functions at filling factors $\nu=n/(2kn+1)$. Here we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multi-hole states, make the connection to Wen's general classification of abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally we discuss to what extent our wave functions can be described in the language of composite fermions.Comment: 9 page