eDissertationen
http://hdl.handle.net/20.500.11811/1627
2020-10-27T07:02:49ZNonequilibrium Dynamics of Correlated Fermi Gases
http://hdl.handle.net/20.500.11811/8733
Nonequilibrium Dynamics of Correlated Fermi Gases
Kombe, Johannes Amani
Strongly correlated quantum systems display a myriad of complex, fascinating behaviour. The competition between charge, spin, orbital, or lattice degrees of freedom and their respective energy scales gives rise to rich and complex emergent phases. More recently, the non-equilibrium properties of correlated quantum many-body systems have come into the focus of active research, with remarkable advances. While the advent of tensor network based simulations on the theoretical side has allowed access to the full time-evolution of the quantum state as it traverses the Hilbert space, the experimental progress in the ultracold atom community has allowed physicists to enter the paradigm of analog quantum simulation. Their tunability and isolation from the environment makes them ideal platforms to emulate and study open problems in condensed matter physics and go beyond the simulational capabilities of state of the art classical simulations.<br />In this thesis, we explore the dynamics of correlated Fermi gases. We develop and present different facets of applicability of radiofrequency modulation techniques to drive the system out of equilibrium. We begin by considering a homogeneous, three-dimensional Fermi gas in the BCS-BEC crossover and develop an off-resonant radiofrequency transfer scheme to excite the Higgs mode of the superfluid. In a subsequent study we investigate the tunability of the coherence between Cooper pairs by tuning the duration of interaction ramps of the internal interaction strength. These works highlight the possibility to externally tune and stabilise complex quantum many-body states away from equilibrium. Using quasi-exact matrix product state simulations, we study the response of an attractively interacting, one-dimensional Fermi-Hubbard model to weak radiofrequency perturbations. We reveal the emergence of two distinct dynamical regimes in the time evolution and are able to relate it back to the underlying excitation spectrum of the system. Finally, we explore the possibility to perform quantum quenches through radiofrequency π-pulses, achieving nearly complete population transfer between different interacting fermionic states. We reveal non-trivial dynamical effects in the pair correlation of the final state, as well as the excitation of a collective trap mode of the system.
2020-10-26T00:00:00ZOn the theory of higher Segal spaces
http://hdl.handle.net/20.500.11811/8705
On the theory of higher Segal spaces
Walde, Tashi
This thesis contains three chapters, each dealing with one particular aspect of the theory of higher Segal spaces introduced by Dyckerhoff and Kapranov:
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(1) By exhibiting the simplex category as an ∞-categorical localization of the dendrex category of Moerdijk and Weiss, we identify the homotopy theory of 2-Segal spaces with that of invertible ∞-operads.
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(2) Inspired by a heuristic analogy with the manifold calculus of Goodwillie and Weiss, we characterize the various higher Segal conditions in terms of purely categorical conditions of higher weak excision on the simplex category and on Connes’ cyclic category.
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(3) We establish a large class of ∞-categorical Morita-equivalences of Dold–Kan type. As an application we describe higher Segal simplicial objects in the additive context as truncated coherent chain complexes; in the stable context, we identify higher Segal Γ-objects with polynomial functors in the sense of Goodwillie.
2020-10-21T00:00:00ZImprovement of hail detection and nowcasting by synergistic combination of information from polarimetric radar, model predictions, and in-situ observations
http://hdl.handle.net/20.500.11811/8701
Improvement of hail detection and nowcasting by synergistic combination of information from polarimetric radar, model predictions, and in-situ observations
Schmidt, Mari Luna
Large hail can pose a major threat to people, infrastructure, and property. While polarimetric radar observations enable us to reliably detect hail, discrimination of hail size and strategies to nowcast and predict hail and its size are still subject of research. At S band hail size discrimination algorithms do already exist, while retrievals from C-band radars, which are more widespread in Europe, remain challenging due to resonance scattering effects from large raindrops which tend to interfere with large hail signatures.
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Advanced nowcasting tools capable of detecting hail and discriminating its size at C band are required to enable earlier and more precise severe weather warnings being issued by weather services in Europe.
In this thesis 16 severe hail events monitored with the polarimetric C-band radar network of the German national meteorological service (<i>Deutscher Wetterdienst</i>, DWD) are investigated together with hail reports from the European Severe Weather Database (ESWD; https://www.eswd.eu/) for precursory information. This data set includes the largest hailstone (14.1 cm in diameter) reported so far in Germany hitting the ground in Undingen on August 6, 2013.
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First, an algorithm for correcting anomalously high attenuation in hail-bearing thunderstorms is evaluated using four overlapping C-band radars. Post-processing of polarimetric moments, like spike-filtering of differential phase, is done to reduce noise and improve attenuation corrections. Results illustrate the capability to mitigate attenuation of up to 15 db km<sup>-1</sup> but only small overcorrection in precipitation without hail.
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Second, T-matrix scattering simulations for dry and wet hail are conducted to adjust a fuzzy logic based hail size discrimination algorithm (HSDA) developed for S band for usage at C band. Hereby, dual-layered spheroids are simulated to mimic melting hail. The revised fuzzy logic utilizes an <i>ad-hoc</i> weighting of input variables to improve performance through self-adjustment similar to other unsupervised learning techniques.
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Finally, hail precursors and storm dynamics are investigated in an object-based, precipitation system oriented analysis to develop and evaluate nowcasting tools to detect hail growth and predict the hail's terminal diameter. This analysis utilizes a custom-made cell tracker and exploits the results of the attenuation correction algorithm.
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Results show that sudden increases of the vertical extent of columns of enhanced differential reflectivity Z<sub>DR</sub>, so called Z<sub>DR</sub>-columns, precede peaks of strong signal attenuation most probably linked to hail. Also, strong attenuation was often accompanied by specific differential phase K<sub>DP</sub> above 10 ° km<sup>-1</sup>. It is demonstrated that the intensity of Z<sub>DR</sub>-columns, described e.g. by their maximum Z<sub>DR</sub> value, and the height of Z<sub>DR</sub>-columns above the melting layer, allow for nowcasting hail size at the ground with lead times between 10 and 20 minutes, which can be exploited for warnings.
2020-10-21T00:00:00ZLow Dimensional Gauge Theories and Quantum Geometry
http://hdl.handle.net/20.500.11811/8672
Low Dimensional Gauge Theories and Quantum Geometry
Ninad, Urmi
This thesis explores the connection between supersymmetric gauge theories on curved spaces of dimensions two and three and geometries that arise in string theory. It does so by studying quantum field theoretic objects such as the partition function and correlation functions on the gauge theory and finding links to geometric information of its target space. An exact calculation of the path integral is made possible using the localisation technique for supersymmetric gauge theories.
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A 2d gauge theory with <em>N</em> = (2, 2) supersymmetry on the Ω-deformed two-sphere subject to the A-twist is the first object of study. Here we find that the correlation functions of the twisted chiral field fulfil certain universal and non-trivial relations. These relations can be interpreted as quantum operators that govern the moduli dependence of the ground state of the gauge theory in a Hilbert-space picture. Furthermore, the relations can be imparted a representation as differential operators that are shown to annihilate Givental’s cohomology-valued I-function on the target space of the gauge theory. This is a consequence of the fact that the 2d gauge theory provides an ultraviolet model for quantum cohomology on a manifold. In particular, for gauge theories with Calabi-Yau target spaces, these operators coincide with Picard-Fuchs operators in algebraic geometry. For a certain class of Calabi-Yau manifolds, we turn the argument around and express the Picard-Fuchs operators in terms of a finite number of correlators in the gauge theory.
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In 3d we study <em>N</em> = 2 gauge theories on the solid torus <em>D</em><sup>2</sup> X<sub>q</sub> <em>S</em><sup>1</sup>, where q is the twist in the fibration of <em>D</em><sup>2</sup> over <em>S</em><sup>1</sup>, with Grassmannian manifolds as target spaces. These theories are ultraviolet models for quantum K-theory on their target spaces. We compute the partition function and extract from it Givental’s I-function of permutation symmetric quantum K-theory. This facilitates a calculation of the algebra of Wilson loops which, for different values of the Chern-Simons levels, is shown to be isomorphic to either the quantum K-theoretic ring of Schubert structure sheaves on the Grassmannian or the Verlinde algebra.
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Additionally, we evaluate difference equations that annihilate this I-function. A limit where the <em>S</em><sup>1</sup> contracts to a point, all the computed quantities are shown to coincide with the corresponding objects encountered in 2d.
2020-10-14T00:00:00Z