BCS Theory in the Weak Magnetic Field Regime for Systems with Nonzero Flux and Exponential Estimates on the Adiabatic Theorem in Extended Quantum Lattice Systems

In the main part of this PhD thesis, we consider a periodically realized microscopic superconductor described by BCS theory, which is subject to external electromagnetic fields. We show that the superconductor is properly described by Ginzburg--Landau theory in the macroscopic and weak magnetic field limit. The main novelty of our results is to allow for a non-vanishing magnetic flux through the unit cell of the lattice of periodicity. These main results are supplemented by various unpublished notes in the field of BCS theory. Furthermore, we preface the presentation of these results with a comprehensive introduction suitable for master's or PhD students. Thereby, we hope to contribute to filling the gap of missing introductory literature in the field. The thesis comprises a second topic, in which we provide ideas for setting up quantum lattice systems in order to prove exponential estimates for the adiabatic theorem. These notes are the result of studies in this field, which have been conducted during a research stay at the University of British Columbia (UBC) in Vancouver, Canada.Comment: PhD thesi

BCS theory in the weak magnetic field regime for systems with nonzero flux and exponential estimates on the adiabatic theorem in extended quantum lattice systems

In the main part of this PhD thesis, we consider a periodically realized microscopic superconductor described by BCS theory, which is subject to external electromagnetic fields. We show that the superconductor is properly described by Ginzburg--Landau theory in the macroscopic and weak magnetic field limit. The main novelty of our results is to allow for a non-vanishing magnetic flux through the unit cell of the lattice of periodicity. These main results are supplemented by various unpublished notes in the field of BCS theory. Furthermore, we preface the presentation of these results with a comprehensive introduction suitable for master's or PhD students. Thereby, we hope to contribute to filling the gap of missing introductory literature in the field. The thesis comprises a second topic, in which we provide ideas for setting up quantum lattice systems in order to prove exponential estimates for the adiabatic theorem. These notes are the result of studies in this field, which have been conducted during a research stay at the University of British Columbia (UBC) in Vancouver, Canada.Comment: PhD thesi

Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields

We consider the Bardeen-Cooper-Schrieffer (BCS) free energy functional with weak and macroscopic external electric and magnetic fields and derive the Ginzburg-Landau functional. We also provide an asymptotic formula for the BCS critical temperature as a function of the external fields. This extends our previous results in arXiv:2105.05623 for the constant magnetic field to general magnetic fields with a nonzero magnetic flux through the unit cell.Comment: 82 pages, 1 figure. arXiv admin note: text overlap with arXiv:2105.0562

PUBA: Privacy-Preserving User-Data Bookkeeping and Analytics

In this paper we propose Privacy-preserving User-data Bookkeeping & Analytics (PUBA), a building block destined to enable the implementation of business models (e.g., targeted advertising) and regulations (e.g., fraud detection) requiring user-data analysis in a privacy-preserving way. In PUBA, users keep an unlinkable but authenticated cryptographic logbook containing their historic data on their device. This logbook can only be updated by the operator while its content is not revealed. Users can take part in a privacy-preserving analytics computation, where it is ensured that their logbook is up-to-date and authentic while the potentially secret analytics function is verified to be privacy-friendly. Taking constrained devices into account, users may also outsource analytic computations (to a potentially malicious proxy not colluding with the operator).We model our novel building block in the Universal Composability framework and provide a practical protocol instantiation. To demonstrate the flexibility of PUBA, we sketch instantiations of privacy-preserving fraud detection and targeted advertising, although it could be used in many more scenarios, e.g. data analytics for multi-modal transportation systems. We implemented our bookkeeping protocols and an exemplary outsourced analytics computation based on logistic regression using the MP-SPDZ MPC framework. Performance evaluations using a smartphone as user device and more powerful hardware for operator and proxy suggest that PUBA for smaller logbooks can indeed be practical

Benchmarking a DEM‐CFD Model of an Optical Belt Sorter by Experimental Comparison

A DEM-CFD (discrete element method - computational fluid dynamics) model of an optical belt sorter was extensively compared with experiments of a laboratory-scale sorter to assess the model\u27s accuracy. Brick and sand-lime brick were considered as materials. First, the transport characteristics on the conveyor belt, involving mass flow, lateral particle distribution and proximity, were compared. Second, sorting results were benchmarked for varying mixture proportions at differing mass flows. It was found that the numerical model is able to reproduce the experimental results with high accuracy

Detuning Properties of RF Phase Modulation in the Electron Storage Ring KARA

In electron storage rings, it is possible to increase the electron bunch length by applying a phase modulation on the radio frequency accelerating field by choosing appropriate parameters for the modulation. Such a bunch lengthening effect improves beam parameters such as the beam lifetime, which can help us to get better beam stability. The dependence of the bunch lengthening on the modulation frequency, the so-called detuning property, tends to have a peak with asymmetric slopes around it. The modulation amplitude and the beam current also affect the properties of the detuning condition of such bunch lengthening. We have investigated the detuning property with systematic measurements at the electron storage ring KARA. The experimental results agree with the theoretical model and the simulation results

Detuning Properties of RF Phase Modulation in the Electron Storage Ring KARA

In electron storage rings, it is possible to increase the electron bunch length by applying a phase modulation on the radio frequency accelerating field by choosing appropriate parameters for the modulation. Such a bunch lengthening effect improves beam parameters such as the beam lifetime, which can help us to get better beam stability. The dependence of the bunch lengthening on the modulation frequency, the so-called detuning property, tends to have a peak with asymmetric slopes around it. The modulation amplitude and the beam current also affect the properties of the detuning condition of such bunch lengthening. We have investigated the detuning property with systematic measurements at the electron storage ring KARA. The experimental results agree with the theoretical model and the simulation results

Machine learning based multiobject tracking for sensor based sorting

Sensor-based sorting provides state-of-the-art solutions for sorting of granular materials. Current systems useline-scanning sensors, which yields a single observation of each object only and no information about their movement. Recent works show that using an area-scan camera bears the potential to decrease both the error in characterization and separation. Using a multiobject tracking system, this enables an estimate of the followed paths as well as the parametrization of an individual motion model per object. While previous works focus on physically-motivated motion models, it has been shown that state-of-the-art machine learning methods achieve an increased prediction accuracy. In this paper, we present the development of a neural network-based multiobject tracking system and its integration into a laboratory-scale sorting system. Preliminary results show that the novel system achieves results comparable to a highly optimized Kalman filter-based one. A benefit lies in avoiding tiresome manual tuning of parameters of the motion model, as the novel approach allows learning its parameters by provided examples due to its data-driven nature

Simulation study and experimental validation of a neural network-based predictive tracking system for sensor-based sorting

Die sensorgestützte Sortierung bietet zukunftsweisende Lösungen für die Trennung von körnigen Materialien. Die derzeit in solchen Systemen verwendeten Zeilensensoren liefern nur eine einzige Beobachtung jedes Objekts und keine Daten über dessen Bewegung. Jüngsten Studien zufolge hat die Verwendung einer Flächenkamera das Potenzial, sowohl den Charakterisierungs- als auch den Trennungsfehler in einem Sortierprozess zu verringern. Ein prädiktiver Tracking-Ansatz auf der Grundlage von Kalman-Filtern ermöglicht die Schätzung der verfolgten Pfade und die Parametrisierung eines individuellen Bewegungsmodells für jedes Objekt in einem Multiobjekt-Tracking-System. Während sich frühere Studien auf physikalisch motivierte Bewegungsmodelle konzentrierten, hat sich gezeigt, dass moderne Ansätze des maschinellen Lernens genauere Vorhersagen ermöglichen. In diesem Beitrag beschreiben wir die Entwicklung eines prädiktiven Trackingsystems auf Basis neuronaler Netze. Der neue Algorithmus wird auf ein experimentelles Sortiersystem und auf ein numerisches Modell des Sortierers angewendet. Zwar erreicht der neue Ansatz noch nicht ganz die Sortierqualität der bestehenden Ansätze, jedoch ermöglicht er die Anwendung von prädiktivem Tracking, ohne dass hierfür Expertenwissen oder ein grundlegendes Verständnis der Parametrisierung des Partikelbewegungsmodells erforderlich sind

Magnetism and Metallicity in Moir\'e Transition Metal Dichalcogenides

The ability to control the properties of twisted bilayer transition metal dichalcogenides in situ makes them an ideal platform for investigating the interplay of strong correlations and geometric frustration. Of particular interest are the low energy scales, which make it possible to experimentally access both temperature and magnetic fields that are of the order of the bandwidth or the correlation scale. In this manuscript we analyze the moir\'e Hubbard model, believed to describe the low energy physics of an important subclass of the twisted bilayer compounds. We establish its magnetic and the metal-insulator phase diagram for the full range of magnetic fields up to the fully spin polarized state. We find a rich phase diagram including fully and partially polarized insulating and metallic phases of which we determine the interplay of magnetic order, Zeeman-field, and metallicity, and make connection to recent experiments.Comment: 7 (+9) pages, 4 (+8) figure