278 research outputs found
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
- …