Integrable systems: From the ice rule to supersymmetric fishnet Feynman diagrams

Diese Dissertation untersucht den Zusammenhang zwischen Modellen der statistischen Physik und Feynman-Diagrammen in Quantenfeldtheorien, anhand einer gemeinsamen Eigenschaft, der Integrabilität. In beiden Fällen betrachten wir integrable Strukturen für periodische Randbedingungen und setzen dabei unseren Fokus auf das Acht- und Sechs-Vertex-Modell, sowie die bi-skalare Fischnetz-Theorie. Letztere ist eine gewisse deformierte Version der N = 4 supersymmetrischen Yang-Mills-Theorie. Wir geben einen Überblick über eine bekannte Anwendung von Integrabilität in diesen Theorien, nämlich die Berechnung der freien Energie im thermodynamischen Limes und ihr Gegenstück in Quantenfeldtheorien, die kritische Kopplungsstärke. Auch wiederholen wir die Berechnung anomaler Dimensionen und Koeffizienten der Operator-Produkt Entwicklung (OPE) in der konformen Fischnetz-Feldtheorie, dessen Ergebnis zu beliebiger Schleifenordnung bestimmt werden kann. Die neuen Erkenntnisse dieser Arbeit umfassen die Ergebnisse zur kritischen Kopplungsstärke für gewisse Modelle mit Fermionen. Genauer handelt es sich dabei um die Brick-Wall-Theorie und die fermionische Fischnetz-Theorie. Darüber hin- aus verallgemeinern wir die Studien integrabler Feynman-Diagramme für supersymmetrische Diagramme. Dank der Entwicklung eines effizienten graphischen Formalismus sind wir in der Lage die kritische Kopplungsstärke von starken Deformationen der N = 4 Super-Yang-Mills-Theorie sowie der ABJM-Theorie zu bestimmen, die sogenannte Super-Brick-Wall- und Superfishnet-Theorie. Desweitern leiten wir nützliche Superraumtechniken her, die uns erlauben die anomale Skalendimension und einen OPE-Koeffizienten zu beliebiger Schleifenordung zu bestimmen. Zudem untersuchen wir die Rand-Integrabilität im Sechs-Vertex-Modell und in Feynman-Diagrammen. Wir präsentieren neue, kastenförmige Randbedingungen für das Sechs-Vertex-Modell und postulieren eine geschlossene Form der Zustandssumme bei beliebiger Gittergröße.This thesis examines the correspondence between models of statistical physics and Feynman graphs of quantum field theories by a common property: integrability. We review integrable structures for periodic boundary conditions on both sides, while focusing on the eight- and six-vertex model and the bi-scalar fishnet theory. The latter is a double-scaled γ-deformations of N = 4 super Yang-Mills theory. Interesting applications of integrability existing in the literature that we reconsider are the computation of the free energy in the thermodynamic limit and its quantum field theory (QFT) counterpart, the critical coupling. In addition, we provide a detailed overview of the calculation of exact anomalous dimensions and operator product expansion (OPE) coefficients in the conformal bi-scalar fishnet theory. The original contributions of this work comprise the results of the critical coupling for models with fermions, the brick wall theory, and the fermionic fishnet theory. Additionally, we extend the study of integrable Feynman graphs to supersymmetric diagrams in superspace. By establishing an efficient graphical formalism, we obtain the critical coupling of double-scaled β-deformations of N = 4 super Yang-Mills theory and Aharony-Bergman-Jafferis-Maldacena theory, the super brick wall and superfishnet theory, respectively. Moreover, we apply superspace methods to the superfishnet theory and find results for anomalous dimensions and an OPE coefficient, which are all-loop exact in the coupling. In addition, we study boundary integrability in the six-vertex model and for Feynman diagrams. We present new box-shaped boundary conditions for the six-vertex model and conjecture a closed form for its partition function at any lattice size. On the QFT side, we find integrable boundary scattering matrices in the form of generalized Feynman diagrams by graphical methods

Toward Green Processing of Perovskite Solar Cells: Protic Ionic Liquids Enable Water‐ and Alcohol‐Based MAPbI3 Precursors Inks for Slot‐Die Coating

Halide perovskite solar cells are approaching commercialization, with solution processing emerging as a key method for large‐scale production. This study introduces a significant advancement: using non‐toxic solvents like water and alcohol in perovskite precursor inks facilitated by the protic ionic liquid methylammonium propionate (MAP). MAP effectively dissolves perovskite precursors such as lead acetate and methylammonium iodide, enabling the first stable water‐based perovskite precursor ink suitable for one‐step slot‐die coating. This new ink formulation contrasts with conventional dimethylformamide (DMF) and dimethylsulfoxide (DMSO)‐based inks, as evidenced by in‐situ grazing incidence wide‐angle X‐ray scattering (GIWAXS), which revealed an intermediate‐free liquid‐to‐solid transition. In‐situ mass spectrometry also showed that organic molecules evaporate during annealing, resulting in a crystalline perovskite phase. Optimization of the solvent mixture to H2O/IPA/MAP enabled successful slot‐die coating, yielding perovskite solar cells with an efficiency of up to 10%. This eco‐friendly ink reduces toxicity and environmental impact compared to DMF‐based inks, offering a longer shelf life and the possibility of using the ink in ambient conditions. This pioneering work represents the first report of a water‐based green ink formulation for one‐step thin film coating at room‐temperature conditions by slot‐die coating, highlighting its potential for sustainable commercial applications.Alianza SÉNECAVIPER Lab ProjectFundación Séneca 10.13039/100007801Helmholtz‐Gemeinschaft 10.13039/501100001656HORIZON EUROPE Reforming and enhancing the European Research and Innovation system 10.13039/100018707Deutsche Forschungsgemeinschaft 10.13039/501100001659Peer Reviewe

Biarticular gastrocnemii muscles increase their joint energy transfer potential at high running speeds

The involvement of energy transfer mechanisms between the ankle and the knee joint by the biarticular gastrocnemii muscles at high running speeds is currently unknown. During running at seven speeds (3.0–8.5 m s−1), the ankle and knee joint kinematics as well as the electromyographic activity of the gastrocnemius medialis and lateralis were captured. By means of the ankle–knee joint coupling angles, we determined the energy transfer potential between the two joints as the fraction of contact time where the joint angles are in-phase. At speeds above 6.0 m s−1, the ankle-to-knee joint energy transfer potential during the first part of stance and the knee-to-ankle energy transfer potential during the second part of stance were increased by 37% and 12%, respectively. This was accompanied by a 2.8-fold and 2.0-fold increase of the gastrocnemii muscle activation. The findings demonstrate a speed-dependent modification of the ankle–knee joint coordination towards an in-phase pattern in combination with an increase in muscle activation, which enhances the possibility of energy transfer between the two joints by the biarticular gastrocnemii muscles. An increased energy transfer from the knee to the ankle joint is probably necessary to increase the power output at the ankle joint, required for the highest running speeds.Peer Reviewe

Electrical Conductivity as a Tracer for Seasonal Reverse Flow and Transport of Trace Organic Contaminants in River Spree

Climate change, population growth, urbanisation and water pollution will exacerbate the closely linked challenges of water quantity and water quality. The River Spree in Berlin, Germany, experiences recurrent low flow conditions in summer with seasonal flow reversals in certain sections of the river. This reverse flow leads to the transport of treated wastewater to upstream sections of River Spree and possibly to the introduction of treated wastewater into Lake Müggelsee, which is located upstream of the city centre and important for drinking water production via bank filtration in Berlin. A better understanding of the flow and contaminant dynamics in River Spree is required, but field data on the reverse flow are still lacking. In 2022 and 2023, we collected surface water samples to quantify major ions and trace organic contaminants. Over a period of nine months in 2023, we also measured the specific electrical conductivity at six locations with a temporal resolution of five minutes. During summer, the specific electrical conductivity increased at the sampling locations in River Spree upstream of the mouth of the wastewater‐impaired River Erpe. The specific electrical conductivity proved to be an indicative parameter for the seasonal dynamics of reverse flow periods. During reverse flow, we observed increased concentrations of wastewater‐derived trace organic contaminants, many of which correlated positively with the specific electrical conductivity. Strong differences in the reverse flow intensity between 2022 and 2023 indicate that both precipitation and discharge of the River Spree upstream of Lake Müggelsee have a strong influence on the reverse flow. This study demonstrates the applicability of easy‐to‐measure specific electrical conductivity as a proxy for hydrological conditions and chemical water quality.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Bundesministerium für Bildung und Forschung http://dx.doi.org/10.13039/501100002347Peer Reviewe

INTENTAS - an entanglement-enhanced atomic sensor for microgravity

The INTENTAS project aims to develop an atomic sensor utilizing entangled Bose-Einstein condensates (BECs) in a microgravity environment. This key achievement is necessary to advance the capability for measurements that benefit from both entanglement-enhanced sensitivities and extended interrogation times. The project addresses significant challenges related to size, weight, and power management (SWaP) specific to the experimental platform at the Einstein-Elevator in Hannover. The design ensures a low-noise environment essential for the creation and detection of entanglement. Additionally, the apparatus features an innovative approach to the all-optical creation of BECs, providing a flexible system for various configurations and meeting the requirements for rapid turnaround times. Successful demonstration of this technology in the Einstein-Elevator will pave the way for a future deployment in space, where its potential applications will unlock high-precision quantum sensing.Open Access funding enabled and organized by Projekt DEAL.Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR) (4202)Peer Reviewe

Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions

Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen–Specker and non-Kochen–Specker contextual sets. Traditionally, their representation has been predominantly operator-based, mainly focusing on specific constructs in dimensions ranging from three to eight. However, nearly all of these constructs can be represented as low-dimensional hypergraphs. This study demonstrates how to generate contextual hypergraphs in any dimension using various methods, particularly those that do not scale in complexity with increasing dimensions. Furthermore, we introduce innovative examples of hypergraphs extending to dimension 32. Our methodology reveals the intricate structural properties of hypergraphs, enabling precise quantifications of contextuality. Additionally, we investigate several promising applications of hypergraphs in quantum communication and quantum computation, paving the way for future breakthroughs in the field.Supported by the Ministry of Science and Education of Croatia through the Center of Excellence for Advanced Materials and Sensing Devices (CEMS) funding and by MSE grants No. KK.01.1.1.01.0001 and 533-19-15-0022. Also supported by the Humboldt Foundation, Germany. Computational support was provided by the Zagreb University Computing Centre.Ministry of Science and Education of CroatiaHumboldt Foundation, GermanyZagreb University Computing CentrePeer Reviewe

Beyond liquids, beyond oxides: sulfur and sulfides in solid-state lithium batteries

Lithium-Festkörperbatterien (SSB) könnten durch höhere Energiedichte und erhöhte Sicherheit die Energiespeicherung revolutionieren, doch Herausforderungen hemmen ihre Nutzung. Einige davon, wie die begrenzte elektrochemische Stabilität der Festelektrolyte (SE) und die Schwierigkeit, ein effizientes Leitungsnetz innerhalb der Elektroden zu etablieren, lassen sich durch den Einsatz neuartiger Kathoden lösen oder zumindest abmildern. In dieser Arbeit wurden TiS2 und Schwefel untersucht, da beide eine starke Synergie mit einem Festkörperdesign erwarten lassen. Eine TiS2-SSB würde von der hohen elektronischen und ionischen Leitfähigkeit dieser Verbindung profitieren, während eine Schwefel-SSB durch die Unterdrückung des „Shuttle-Effekts“ des SE Vorteile aufweisen würde. Die begrenzte elektrochemische Stabilität des SE könnte wiederum durch die moderaten Redoxpotenziale beider Materialien positiv beeinflusst werden. TiS2-SSBs wurden optimiert, und ihr Reaktionsweg wurde durch operando XPS aufgeklärt. Anschließend wurden die Eigenschaften von TiS2 selbst versuchsweise durch Einlagerung von Fe und Mn in seine Struktur verbessert. TiS2 erwies sich insgesamt als vielversprechende Kathode für SSBs. Darüber hinaus ist es aufgrund seiner Fähigkeit, ohne leitende Zusätze zu funktionieren, für theoretische und experimentelle Analysen besonders nützlich. Die Untersuchung der Schwefelkathode konzentrierte sich auf die bislang nicht vollständig verstandene spontane Festkörperadsorption von Schwefel an Kohlenstoff. Erstmals war es möglich, die thermodynamischen Parameter zu quantifizieren und eine Erklärung für die Ursachen vorzuschlagen. Anschließend wurden S-SSBs zusammengebaut, um das Verhalten während des Zyklus zu beobachten. Obwohl noch offene Fragen bestehen, lassen sich potenzielle Anwendungen bei der Herstellung sowie Vorteile während des Zyklus ableiten. Beide Materialien haben sich als vielversprechend erwiesen und könnten in praktischen Geräten erhebliche Anwendung finden.Lithium solid state batteries (SSBs), thanks to their expected higher energy density and safety, could revolutionise energy storage and help to decarbonise our societies. However, their use is still hampered by several unresolved issues. Some of these, such as the limited electrochemical stability of the solid electrolytes (SE) and the difficulty of creating and maintaining an efficient conduction network in the electrodes, can be solved or alleviated by using novel cathodes. This work studied two active materials that are expected to have a strong synergy with a solid-state design, TiS2 and sulfur. Indeed, a TiS2 SSB would benefit from the high electronic and ionic conductivity of this compound, while a sulfur SSB would benefit from the suppression of the “shuttle effect” offered by the SE, whose limited electrochemical stability would in turn benefit from the moderate redox potentials of both materials. Li-TiS2 SSBs were optimised and their reaction pathway was elucidated by operando XPS. Then, the properties of TiS2 itself were tentatively improved by intercalating Fe and Mn into its structure. TiS2 proved to be a promising cathode for SSBs. What's more, its ability to function without conductive additives makes it particularly useful for theoretical and experimental analysis. Sulfur cathodes have been studied focusing on the analysis of the previously reported but largely unexplained spontaneous solid-solid adsorption of sulfur on carbon. Using a mixture of experimental and mathematical methods, it was possible for the first time to quantify its thermodynamic parameters and propose an explanation of its causes. Li-S batteries were then assembled to observe the phenomenon during cycling. Although several questions remain to be answered, possible applications in manufacturing and benefits during cycling are proposed. Both materials confirmed their promise and could find significant applications in practical devices

Twist-noncommutative field theories and integrability

Integrable Deformationen bilden eine perfekte Landschaft, um neue integrable Modelle zu konstruieren. Im Bereich der AdS/CFT-Korrespondenz spielte die Integrabilität eine wichtige Rolle für Präzisionstests der Korrespondenz zwischen der =4 Super-Yang-Mills-Theorie und dem AdS₅ × S⁵ Superstring. In jüngster Zeit haben integrable Deformationen Aufmerksamkeit erregt, insbesondere auf der Stringtheorie-Seite der Korrespondenz, zum Beispiel in Form von homogenen Yang-Baxter-Deformationen. Es wurde vermutet, dass die dualen Feldtheorien letzterer durch Drinfel'd getwistete Versionen von =4 SYM gegeben sind, einschließlich nicht-kommutativer Deformationen mit nicht-kommutativen Raumzeitkoordinaten. In dieser Arbeit werden Eichtheorien auf getwisteten nichtkommutativen Räumen konstruiert. Es wird gezeigt, dass die Eichinvarianz den Twist einschränkt, der aus Poincar\'e Erzeugern aufgebaut werden muss. Weiterhin konstruieren wir die Kopplung der nichtkommutativen Eichtheorie an alle Arten von adjungierter und fundamentaler Materie, was eine Deformation von =4 SYM ermöglicht. Wir beweisen weiter, dass die deformierte Theorie invariant unter getwisteter (2,2|4) Symmetrie ist. Auf Quantenlevel entwickeln wir ein planares Äquivalenztheorem für planare Feynmandiagramme zwischen der undeformierten und der deformierten Theorie und führen eichinvariante Operatoren für bestimmte Deformationen ein, die vor allem aus der Perspektive der Integrabilität interessant sind. Für diese Operatoren bilden wir Ein-Schleifen Quantenkorrekturen der Zweipunktfunktionen auf Reshetikhin-getwistete (2,2|4)-Spinketten ab.Integrable deformations form a perfect landscape to construct new integrable models. In the realm of the AdS/CFT correspondence, integrability has played an important role in precision tests of the correspondence between the =4 super Yang-Mills (SYM) theory and the AdS₅ × S⁵ superstring. Recently, integrable deformations, particularly in the form of homogeneous Yang-Baxter deformations, have received attention on the string theory side of the correspondence. It has been conjectured that the field theory duals of these deformations are given by Drinfel'd twisted versions of =4 SYM, including noncommutative deformations of the spacetime. In this thesis, we construct gauge theories on twist-noncommutative spaces. It will be shown that gauge invariance restricts the twist to the Poincar\'e algebra. Furthermore, we construct the coupling of noncommutative gauge theory to various types of adjoint and fundamental matter, enabling a deformation of =4 SYM. We demonstrate that the deformed theory is invariant under twisted (2,2|4) symmetry. Moreover, we develop an equivalence theorem for planar Feynman diagrams between the undeformed and deformed theories and introduce gauge invariant operators for particular deformations, which are highly relevant to integrability. For these operators, we relate the one-loop two-point functions to the Reshetikhin twist of the (2,2|4) spin chain