Ballistic transport in random magnetic fields with anisotropic long-ranged correlations

We present exact theoretical results about energetic and dynamic properties of a spinless charged quantum particle on the Euclidean plane subjected to a perpendicular random magnetic field of Gaussian type with non-zero mean. Our results refer to the simplifying but remarkably illuminating limiting case of an infinite correlation length along one direction and a finite but strictly positive correlation length along the perpendicular direction in the plane. They are therefore ``random analogs'' of results first obtained by A. Iwatsuka in 1985 and by J. E. M\"uller in 1992, which are greatly esteemed, in particular for providing a basic understanding of transport properties in certain quasi-two-dimensional semiconductor heterostructures subjected to non-random inhomogeneous magnetic fields

Functional Methods in Stochastic Systems

Field-theoretic construction of functional representations of solutions of stochastic differential equations and master equations is reviewed. A generic expression for the generating function of Green functions of stochastic systems is put forward. Relation of ambiguities in stochastic differential equations and in the functional representations is discussed. Ordinary differential equations for expectation values and correlation functions are inferred with the aid of a variational approach.Comment: Plenary talk presented at Mathematical Modeling and Computational Science. International Conference, MMCP 2011, Star\'a Lesn\'a, Slovakia, July 4-8, 201

Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second part, see math-ph/0105046. To appear in Reviews in Mathematical Physic

Phase Diagram for Anderson Disorder: beyond Single-Parameter Scaling

The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams in all physical dimensions, a plethora of additional, weaker Anderson transitions are found, characterized by the long-distance behavior of states. Critical disorders are found for Anderson transitions at which the asymptotically dominant sector of augmented space changes for all states at the same disorder. At fixed disorder, critical energies are also found at which the localization properties of states are singular. Under the approximation of single-parameter scaling, this phase diagram reduces to the widely-accepted one in 1, 2 and 3 dimensions. In two dimensions, in addition to the Anderson transition at infinitesimal disorder, there is a transition between two localized states, characterized by a change in the nature of wave function decay.Comment: 51 pages including 4 figures, revised 30 November 200

Towards Cross-Provider Analysis of Transparency Information for Data Protection

Transparency and accountability are indispensable principles for modern data protection, from both, legal and technical viewpoints. Regulations such as the GDPR, therefore, require specific transparency information to be provided including, e.g., purpose specifications, storage periods, or legal bases for personal data processing. However, it has repeatedly been shown that all too often, this information is practically hidden in legalese privacy policies, hindering data subjects from exercising their rights. This paper presents a novel approach to enable large-scale transparency information analysis across service providers, leveraging machine-readable formats and graph data science methods. More specifically, we propose a general approach for building a transparency analysis platform (TAP) that is used to identify data transfers empirically, provide evidence-based analyses of sharing clusters of more than 70 real-world data controllers, or even to simulate network dynamics using synthetic transparency information for large-scale data-sharing scenarios. We provide the general approach for advanced transparency information analysis, an open source architecture and implementation in the form of a queryable analysis platform, and versatile analysis examples. These contributions pave the way for more transparent data processing for data subjects, and evidence-based enforcement processes for data protection authorities. Future work can build upon our contributions to gain more insights into so-far hidden data-sharing practices.Comment: technical repor

Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field

We obtain lower and upper bounds on the heat kernel and Green functions of the Schroedinger operator in a random Gaussian magnetic field and a fixed scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic upper bounds and the Jensen inequality for the lower bound. We show that if the covariance of the electromagnetic (vector) potential is increasing at large distances then the lower bound is decreasing exponentially fast for large distances and a large time.Comment: some technical improvements, new references, to appear in Journ.Phys.

Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials

We study a non-relativistic charged particle on the Euclidean plane R^2 subject to a perpendicular constant magnetic field and an R^2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the Hilbert space L^2(R^2) is restricted to the eigenspace of a single but arbitrary Landau level. For a wide class of Gaussian random potentials we rigorously prove that the associated restricted integrated density of states is absolutely continuous with respect to the Lebesgue measure. We construct explicit upper bounds on the resulting derivative, the restricted density of states. As a consequence, any given energy is seen to be almost surely not an eigenvalue of the restricted random Landau Hamiltonian.Comment: 16 pages, to appear in "Journal of Mathematical Physics

Spielformen im Spielfilm : zur Medienmorphologie des Kinos nach der Postmoderne

Die aktuelle Konjunktur exzentrischen Erzählens im gegenwärtigen Kino ist längst nicht mehr bloß die Illustration einer condition postmoderne, sie verweist vielmehr auf die Hybridisierung von Erzählung und Spiel im digitalen Medienumbruch. Insbesondere im massenattraktiven Spielfilm stehen nicht mehr die selten gewordenen Identifikationsofferten im Zentrum des Interesses und die Zuschauer sorgen sich auch nicht um Interpretationshypothesen, sondern sie finden Vergnügen an Erzählrätseln und verfolgen neugierig das Spiel mit unterschiedlichen Plotvarianten oder paradoxalen Welten. In den Beiträgen dieses Bandes werden Formen dieser Hybridisierung exemplarisch aufgeschlüsselt und genealogisch nachvollzogen

Dynamics of the spin-half Heisenberg chain at intermediate temperatures

Combining high-temperature expansions with the recursion method and quantum Monte Carlo simulations with the maximum entropy method, we study the dynamics of the spin-1/2 Heisenberg chain at temperatures above and below the coupling J. By comparing the two sets of calculations, their relative strengths are assessed. At high temperatures, we find that there is a low-frequency peak in the momentum integrated dynamic structure factor, due to diffusive long-wavelength modes. This peak is rapidly suppressed as the temperature is lowered below J. Calculation of the complete dynamic structure factor S(k,w) shows how the spectral features associated with the two-spinon continuum develop at low temperatures. We extract the nuclear spin-lattice relaxation rate 1/T1 from the w-->0 limit, and compare with recent experimental results for Sr2CuO3 and CuGeO3. We also discuss the scaling behavior of the dynamic susceptibility, and of the static structure factor S(k) and the static susceptibility X(k). We confirm the asymptotic low-temperature forms S(pi)~[ln(T)]^(3/2) and X(pi)~T^(-1)[ln(T)]^(1/2), expected from previous theoretical studies.Comment: 15 pages, Revtex, 14 PostScript figures. 2 new figures and related discussion of the recursion method at finite temperature adde

Percutaneous coronary revascularization in patients with formerly "refractory angina pectoris in end-stage coronary artery disease" – Not "end-stage" after all

<p>Abstract</p> <p>Background</p> <p>Patients with refractory angina pectoris in end-stage coronary artery disease represent a severe condition with a higher reduction of life-expectancy and quality of life as compared to patients with stable coronary artery disease. It was the purpose of this study to invasively re-evaluate highly symptomatic patients with formerly diagnosed refractory angina pectoris in end-stage coronary artery disease for feasible options of myocardial revascularization.</p> <p>Methods</p> <p>Thirty-four Patients formerly characterized as having end stage coronary artery disease with refractory angina pectoris were retrospectively followed for coronary interventions.</p> <p>Results</p> <p>Of those 34 patients 21 (61.8%) were eventually revascularized with percutaneous interventional revascularization (PCI). Due to complex coronary morphology (angulation, chronic total occlusion) PCI demanded an above-average amount of time (66 ± 42 minutes, range 25–206 minutes) and materials (contrast media 247 ± 209 ml, range 50–750 ml; PCI guiding wires 2.0 ± 1.4, range 1–6 wires). Of PCI patients 7 (33.3%) showed a new lesion as a sign of progression of atherosclerosis. Clinical success rate with a reduction to angina class II or lower was 71.4% at 30 days. Surgery was performed in a total of8 (23.5%) patients with a clinical success rate of 62.5%. Based on an intention-to-treat 2 patients of originally 8 (25%) demonstrated clinical success. Mortality during follow-up (1–18 months) was 4.8% in patients who underwent PCI, 25% in patients treated surgically and 25% in those only treated medically.</p> <p>Conclusion</p> <p>The majority of patients with end-stage coronary artery disease can be treated effectively with conventional invasive treatment modalities. Therefore even though it is challenging and demanding PCI should be considered as a first choice before experimental interventions are considered.</p