Localization in the quantum Hall regime

The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced. Descriptions in terms of equivalent tight-binding Hamiltonians, and the 2D Dirac model, are outlined. Evidences for the universal critical behavior of the localization length are summarized. A short review of the supersymmetric critical field theory is provided. The interplay between edge states and bulk localization properties is investigated. For a system with finite width and with short-range randomness, a sudden breakdown of the two-point conductance from $ne^{2}/h$ to 0 ($n$ integer) is predicted if the localization length exceeds the distance between the edges.Comment: 16 pages, to be published in Physica E, Proceedings of the Symposium "Quantum Hall Effect: Past, Present and Future

Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach

We consider the network model of the integer quantum Hall effect transition. By generalizing the real--space renormalization group procedure for the classical percolation to the case of quantum percolation, we derive a closed renormalization group (RG) equation for the universal distribution of conductance of the quantum Hall sample at the transition. We find an approximate solution of the RG equation and use it to calculate the critical exponent of the localization length and the central moments of the conductance distribution. The results obtained are compared with the results of recent numerical simulations.Comment: 17 pages, RevTex, 7 figure

Intelligente Vernetzung zur autonomen Fräsbearbeitung von Strukturbauteilen - Ergebnisbericht des BMBF Verbundprojektes TensorMill

Digitalisierte Prozesse können zukünftig zu einer intelligenten Fertigung beitragen, um den Herausforderungen einer intelligent vernetzten, autonomen Fertigung von sicherheitsrelevanten Integralbauteilen zu begegnen. Die Herausforderungen hierbei liegen insbesondere in der Aufzeichnung und Extraktion von nutzerrelevanten Daten zur Steigerung der Produktivität bei der Fertigung von sicherheitsrelevanten Integralbauteilen für die Luft- und Raumfahrtbranche. An diesem Punkt hat das Verbundforschungsprojekt „TensorMill“ angesetzt. Ziel des Projekts war es, die Produktivität in der spanenden Fertigung sicherheitsrelevanter Integralbauteile durch die Entwicklung und den Aufbau einer intelligent, vernetzten, autonomen Fertigung zu erhöhen und die Prozesssicherheit zu verbessern. Die intelligente Fertigung soll dabei in der Lage sein, auf möglichst viele Situationen im Fertigungsprozess mit Hilfe von künstlicher Intelligenz (KI) zu reagieren. Für die Implementierung der KI-basierten Lösungen sind im Projekt fortschrittliche Methoden und Vorgehensweisen entstanden, welche es ermöglichen, die Daten von Produktionsmitteln in einer einfachen Form nutzbar zu machen, damit diese einen Mehrwert für Hersteller und Anwender bringen. Die aufbereiteten Daten dienten schließlich der Umsetzung von KI-basierten Lösungen zur prozessparallelen Qualitätsprognose und Werkzeugzustandserkennung. Darüber hinaus wurde ein entwickeltes cyber-physisches Spannsystem entwickelt, um neuartige Ansätze zur Abdrängungskompensation und Echtzeitbewertung der Prozessstabilität zu erforschen

Integer Quantum Hall Effect in Double-Layer Systems

We consider the localization of independent electron orbitals in double-layer two-dimensional electron systems in the strong magnetic field limit. Our study is based on numerical Thouless number calculations for realistic microscopic models and on transfer matrix calculations for phenomenological network models. The microscopic calculations indicate a crossover regime for weak interlayer tunneling in which the correlation length exponent appears to increase. Comparison of network model calculations with microscopic calculations casts doubt on their generic applicability.Comment: 14 pages, 12 figures included, RevTeX 3.0 and epsf. Additional reference

Scaling Theory of the Integer Quantum Hall Effect

The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are disorder-induced localization-delocalization transitions. While experimental and analytical approaches are surveyed, the main emphasis is on numerical studies, which successfully describe the experiments. The theoretical models for disordered systems are described in detail. An overview of the finite-size scaling theory and its relation to Anderson localization is given. The field-theoretical approach to the localization problem is outlined. Numerical methods for the calculation of scaling quantities, in particular the localization length, are detailed. The properties of local observables at the localization-delocalization transition are discussed in terms of multifractal measures. Finally, the results of extensive numerical investigations are compared with experimental findings.Comment: 96 pages, REVTeX 3, 28 figures, Figs. 8-24, 26-28 appended as uuencoded compressed tarred PostScript files. Submitted to Rev. Mod. Phys

Identification of methylated genes in salivary gland adenoid cystic carcinoma xenografts using global demethylation and methylation microarray screening

Salivary gland adenoid cystic carcinoma (ACC) is a rare head and neck malignancy without molecular biomarkers that can be used to predict the chemotherapeutic response or prognosis of ACC. The regulation of gene expression of oncogenes and tumor suppressor genes (TSGs) through DNA promoter methylation may play a role in the carcinogenesis of ACC. To identify differentially methylated genes in ACC, a global demethylating agent, 5-aza-2′-deoxycytidine (5-AZA) was utilized to unmask putative TSG silencing in ACC xenograft models in mice. Fresh xenografts were passaged, implanted in triplicate in mice that were treated with 5-AZA daily for 28 days. These xenografts were then evaluated for genome-wide DNA methylation patterns using the Illumina Infinium HumanMethylation27 BeadChip array. Validation of the 32 candidate genes was performed by bisulfite sequencing (BS-seq) in a separate cohort of 6 ACC primary tumors and 6 normal control salivary gland tissues. Hypermethylation was identified in the HCN2 gene promoter in all 6 control tissues, but hypomethylation was found in all 6 ACC tumor tissues. Quantitative validation of HCN2 promoter methylation level in the region detected by BS-seq was performed in a larger cohort of primary tumors (n=32) confirming significant HCN2 hypomethylation in ACCs compared with normal samples (n=10; P=0.04). HCN2 immunohistochemical staining was performed on an ACC tissue microarray. HCN2 staining intensity and H-score, but not percentage of the positively stained cells, were significantly stronger in normal tissues than those of ACC tissues. With our novel screening and sequencing methods, we identified several gene candidates that were methylated. The most significant of these genes, HCN2, was actually hypomethylated in tumors. However, promoter methylation status does not appear to be a major determinant of HCN2 expression in normal and ACC tissues. HCN2 hypomethylation is a biomarker of ACC and may play an important role in the carcinogenesis of ACC