Variational Perturbation Theory for the Ground-State Wave Function

We evaluate perturbatively the density matrix in the low-temperature limit and thus the ground-state wave function of the anharmonic oscillator up to second order in the coupling constant. We then employ Kleinert's variational perturbation theory to determine the ground-state wave function for all coupling strengths.Comment: The article is a contribution to the book "Fluctuating Paths and Fields - Dedicated to Hagen Kleinert on the Occasion of His 60th Birthday", Eds. Wolfhard Janke, Axel Pelster, Hans-Juergen Schmidt, and Michael Bachmann (World Scientific, Singapore, 2001), p. 315-32

Modelling Correlations in Portfolio Credit Risk

The risk of a credit portfolio depends crucially on correlations between the probability of default (PD) in different economic sectors. Often, PD correlations have to be estimated from relatively short time series of default rates, and the resulting estimation error hinders the detection of a signal. We present statistical evidence that PD correlations are well described by a (one-)factorial model. We suggest a method of parameter estimation which avoids in a controlled way the underestimation of correlation risk. Empirical evidence is presented that, in the framework of the CreditRisk+ model with integrated correlations, this method leads to an increased reliability of the economic capital estimate.Comment: 5 pages, 4 figure

A Simple Method for the Correction of Fermentation Losses Measured in Laboratory Silos

Dry matter (DM) losses caused by formation of gaseous fermentation products can be measured by different methods. The most common method (A) is measuring the difference between the DM input and output of a silo. Other methods are based on the measurement of the fermentation gases which spontaneously leave the silo, either directly by collecting them (B) in a special absorbent like KOH or, much more easily, by weighing the filled silo at the beginning and the end of the fermentation process (C). The figures obtained by B and C are substantially smaller than those by A. This difference represents a certain amount of CO2 which is retained within the silage. The objective of this paper is to deduce a procedure for estimating the amount of this retained CO2 so that the results obtained by method C (or B) can be corrected

Developing Organic Electrochemical Electronics from Fundamentals to Integrated Circuit Components

Heutzutage werden riesige Datenmengen zwischen Endgeräten und Cloud-Servern verschoben. Cloud-Computing war nach Bloomberg bereits für 1% des weltweiten Stromverbrauchs im Jahr 2021 verantwortlich. Darüber hinaus kann die monopolartige Speicherung personenbezogener Daten schwerwiegende Auswirkungen auf die Gesellschaften unserer Welt haben. Um persönlichen Datenschutz und einen nachhaltigen Energieverbrauch zu gewährleisten, bedarf es einer Datenverarbeitung direkt am Endgerät; bezeichnet als Edge Computing. In diesem Zuge wird die Nachfrage nach individuell gestalteten Edge-Geräten rapide ansteigen. Der neu entstehende Markt bietet der organischen elektrochemischen Elektronik eine große Chance, vor allem für bioelektronische Anwendungen; allerdings muss die Chipintegration verbessert werden. In dieser Arbeit habe ich elektrochemische organische Elektronik für die Integration in Computersysteme untersucht. Insbesondere habe ich einen festen, photostrukturierbaren Elektrolyten entwickelt, der die Integration von OECTs ohne Kreuzkommunikation zwischen Bauteilen ermöglicht. Die OECTs arbeiten bei Spannungen unter 1V und schalten mit einem großen An/Aus-Verhältnis von 5 Größenordnungen und einer Unterschwellenschwingung nahe des thermodynamischen Minimums von 60mV/Dekade. Darüber hinaus wurden bei der Untersuchung der Hysterese des Bauelements drei verschiedene Hystereseregime identifiziert. Anschließend untersuchte ich die Schaltdynamik des OECTs und demonstrierte ein Top-Gate-OECT mit einer maximalen Betriebsfrequenz von 1 kHz. Beim Versuch, die komplexe Wechselwirkung zwischen Ionen und Elektronen in integrierten OECTs zu verstehen, habe ich einen grundlegenden elektrochemischen Mechanismus identifiziert. Die Abhängigkeit dieses Mechanismus’ von der Gate-Größe und der Drain-Überlapplänge wurde aufgezeigt und dieses Wissen zur Optimierung elektrochemischer Inverter genutzt. Zur Darstellung von OECT-basierten Schaltungskomponenten habe ich verschiedene Halbleiter verwendet und entsprechende Inverter hergestellt. Schließlich wurde die Hysterese eines einzigen ambipolaren Inverters zur Demonstration eines dynamischen Klinkenschalters genutzt. Im Rahmen dieser Arbeit habe ich die OECT-Technologie von den Anfängen bis hin zu integrierten Schaltkreiskomponenten entwickelt. Ich glaube, dass diese Arbeit ein Startschuss für Wissenschaftler und Ingenieure sein wird, um die OECT-Technologie in der realen Welt des Edge Computing einzusetzen.Nowadays, vast amounts of data are shuttled between end-user devices and cloud servers. This cloud computing paradigm was, according to Bloomberg, already responsible for 1% of the world’s electricity usage in 2021. Moreover, the monopoly-like storage of personal data can have a severe impact on the world’s societies. To guarantee data privacy and sustainable energy consumption in future, data computation directly at the end-user site is mandatory. This computing paradigm is called edge computing. Owing to the vast amount of end-user-specific applications, the demand for individually designed edge devices will rapidly increase. In this newly approaching market, organic electrochemical electronics offer a great opportunity, especially for bioelectronic applications; however, the integration into low-power-consuming systems has to be improved. In this work, I investigated electrochemical organic electronics for their integration into computational systems. In particular, I developed a solid photopatternable electrolyte that allows integrating organic electrochemical transistors (OECTs) without cross-talk between adjacent devices. The OECTs operate at voltages below 1 V, and exhibit a large on/off ratio of 5 orders of magnitude and a subthreshold-swing close to the thermodynamic minimum of 60mV/dec. Moreover, investigating the device’s hysteresis, three distinct hysteresis regimes were identified; the RC-time-dominated regime I, the retention time governed regime II, and the time-independent stable regime III. I then examined the OECT’s switching dynamics and, subsequently, demonstrated a top-gate device with a maximum operating frequency of 1 kHz. Trying to understand the complex interaction between ions and electrons in integrated OECTs, I disclosed a fundamental electrochemical mechanism and named it the electrochemical electrode coupling (EEC). The EEC’s dependence on gate size and drain overlap length was rigorously shown, and this knowledge was used to optimize electrochemical inverters. Yet, to exemplify OECT-based circuit components, I employed various semiconductors and fabricated five inverters, each with its unique advantage. Finally, the ambipolar inverter’s hysteresis was used to demonstrate a single-device dynamic latch, a basic in-memory computational element. In this thesis, I developed the OECT technology from an infancy stage to integrated circuit components. I believe that this work will be a starting signal for scientists and engineers to bring the OECT technology into real-world edge computing

A rule of thumb for the economic capital of a large credit portfolio

We derive approximate formulae for the credit value-at-risk and the economic capital of a large credit portfolio. The representation allows to change the risk horizon quickly and avoids simulation or numerical procedures. The Poisson mixture model is equivalent to CreditRisk+ and uses the same parameters