08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
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Item Open Access 3D direct laser writing of highly absorptive photoresist for miniature optical apertures(2022) Schmid, Michael D.; Toulouse, Andrea; Thiele, Simon; Mangold, Simon; Herkommer, Alois; Giessen, HaraldThe importance of 3D direct laser writing as an enabling technology increased rapidly in recent years. Complex micro-optics and optical devices with various functionalities are now feasible. Different possibilities to increase the optical performance are demonstrated, for example, multi-lens objectives, a combination of different photoresists, or diffractive optical elements. It is still challenging to create fitting apertures for these micro optics. In this work, a novel and simple way to create 3D-printed opaque structures with a highly absorptive photoresist is introduced, which can be used to fabricate microscopic apertures increasing the contrast of 3D-printed micro optics and enabling new optical designs. Both hybrid printing by combining clear and opaque resists, as well as printing transparent optical elements and their surrounding opaque apertures solely from a single black resist by using different printing thicknesses are demonstrated.Item Open Access 3D printed micro-optics for quantum technology: Optimised coupling of single quantum dot emission into a single-mode fibre(2021) Sartison, Marc; Weber, Ksenia; Thiele, Simon; Bremer, Lucas; Fischbach, Sarah; Herzog, Thomas; Kolatschek, Sascha; Jetter, Michael; Reitzenstein, Stephan; Herkommer, Alois; Michler, Peter; Portalupi, Simone Luca; Giessen, HaraldItem Open Access 3D stimulated Raman spectral imaging of water dynamics associated with pectin-glycocalyceal entanglement(2023) Floess, Moritz; Steinle, Tobias; Werner, Florian; Wang, Yunshan; Wagner, Willi Linus; Steinle, Verena; Liu, Betty; Zheng, Yifan; Chen, Zi; Ackermann, Maximilian; Mentzer, Steven J.; Giessen, HaraldItem Open Access Adaptive piecewise Poly-Sinc methods for ordinary differential equations(2022) Khalil, Omar; El-Sharkawy, Hany; Youssef, Maha; Baumann, GerdWe propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for the approximation. Our work extends the adaptive piecewise Poly-Sinc method to function approximation, for which we derived an a priori error estimate for our adaptive method and showed its exponential convergence in the number of iterations. In this work, we show the exponential convergence in the number of iterations of the a priori error estimate obtained from the piecewise collocation method, provided that a good estimate of the exact solution of the ordinary differential equation at the Sinc points exists. We use a statistical approach for partition refinement. The adaptive greedy piecewise Poly-Sinc algorithm is validated on regular and stiff ordinary differential equations.Item Open Access Algebraic conditions for conformal superintegrability in arbitrary dimension(2024) Kress, Jonathan; Schöbel, Konrad; Vollmer, AndreasWe consider second order (maximally) conformally superintegrable systems and explain how the definition of such a system on a (pseudo-)Riemannian manifold gives rise to a conformally invariant interpretation of superintegrability. Conformal equivalence in this context is a natural extension of the classical (linear) Stäckel transform, originating from the Maupertuis-Jacobi principle. We extend our recently developed algebraic geometric approach for the classification of second order superintegrable systems in arbitrarily high dimension to conformally superintegrable systems, which are presented via conformal scale choices of second order superintegrable systems defined within a conformal geometry. For superintegrable systems on constant curvature spaces, we find that the conformal scales of Stäckel equivalent systems arise from eigenfunctions of the Laplacian and that their equivalence is characterised by a conformal density of weight two. Our approach yields an algebraic equation that governs the classification under conformal equivalence for a prolific class of second order conformally superintegrable systems. This class contains all non-degenerate examples known to date, and is given by a simple algebraic constraint of degree two on a general harmonic cubic form. In this way the yet unsolved classification problem is put into the reach of algebraic geometry and geometric invariant theory. In particular, no obstruction exists in dimension three, and thus the known classification of conformally superintegrable systems is reobtained in the guise of an unrestricted univariate sextic. In higher dimensions, the obstruction is new and has never been revealed by traditional approaches.Item Open Access Analysis of target data-dependent greedy kernel algorithms : convergence rates for f-, f· P- and f/P-greedy(2022) Wenzel, Tizian; Santin, Gabriele; Haasdonk, BernardData-dependent greedy algorithms in kernel spaces are known to provide fast converging interpolants, while being extremely easy to implement and efficient to run. Despite this experimental evidence, no detailed theory has yet been presented. This situation is unsatisfactory, especially when compared to the case of the data-independent P-greedy algorithm, for which optimal convergence rates are available, despite its performances being usually inferior to the ones of target data-dependent algorithms. In this work, we fill this gap by first defining a new scale of greedy algorithms for interpolation that comprises all the existing ones in a unique analysis, where the degree of dependency of the selection criterion on the functional data is quantified by a real parameter. We then prove new convergence rates where this degree is taken into account, and we show that, possibly up to a logarithmic factor, target data-dependent selection strategies provide faster convergence. In particular, for the first time we obtain convergence rates for target data adaptive interpolation that are faster than the ones given by uniform points, without the need of any special assumption on the target function. These results are made possible by refining an earlier analysis of greedy algorithms in general Hilbert spaces. The rates are confirmed by a number of numerical examples.Item Open Access Analysis of the fine structure of the D‐exciton shell in cuprous oxide(2021) Heckötter, Julian; Rommel, Patric; Main, Jörg; Aßmann, Marc; Bayer, ManfredThe exciton states in cuprous oxide show a pronounced fine structure splitting associated with the crystal environment and the resulting electronic band structure. High‐resolution spectroscopy reveals an especially pronounced splitting of the yellow D excitons with one state pushed above any other state with the same principal quantum number. This large splitting offset is related to a strong mixing of these D states with the 1S exciton of the green series, as suggested by previously published calculations. Here, a detailed comparison of this theory with experimental data is given, which leads to a complete reassignment of the experimentally observed D exciton lines. The origin of different amounts of green admixture to D‐envelope states is deduced by analyzing the different terms of the Hamiltonian. The yellow-green mixing leads to level repulsion and induces an exchange interaction splitting to D‐envelope states, from which one of them becomes the highest state within each multiplet. Furthermore, the assignment of D exciton states according to their total angular momentum F is given and corrects an earlier description given in a former study.Item Open Access An approach to quantum physics teaching through analog experiments(2022) Aehle, Stefan; Scheiger, Philipp; Cartarius, HolgerWith quantum physics being a particularly difficult subject to teach because of its contextual distance from everyday life, the need for multiperspective teaching material arises. Quantum physics education aims at exploring these methods but often lacks physical models and haptic components. In this paper, we provide two analog models and corresponding teaching concepts that present analogies to quantum phenomena for implementation in secondary school and university classrooms: While the first model focuses on the polarization of single photons and the deduction of reasoning tools for elementary comprehension of quantum theory, the second model investigates analog Hardy experiments as an alternative to Bell’s theorem. We show how working with physical models to compare classical and quantum perspectives has proven helpful for novice learners to grasp the abstract nature of quantum experiments and discuss our findings as an addition to existing quantum physics teaching concepts.Item Open Access Approximation of a two‐dimensional Gross-Pitaevskii equation with a periodic potential in the tight‐binding limit(2024) Gilg, Steffen; Schneider, GuidoThe Gross-Pitaevskii (GP) equation is a model for the description of the dynamics of Bose-Einstein condensates. Here, we consider the GP equation in a two‐dimensional setting with an external periodic potential in the x‐direction and a harmonic oscillator potential in the y‐direction in the so‐called tight‐binding limit. We prove error estimates which show that in this limit the original system can be approximated by a discrete nonlinear Schrödinger equation. The paper is a first attempt to generalize the results from [19] obtained in the one‐dimensional setting to higher space dimensions and more general interaction potentials. Such a generalization is a non‐trivial task due to the oscillations in the external periodic potential which become singular in the tight‐binding limit and cause some irregularity of the solutions which are harder to handle in higher space dimensions. To overcome these difficulties, we work in anisotropic Sobolev spaces. Moreover, additional non‐resonance conditions have to be satisfied in the two‐dimensional case.Item Open Access An approximation of solutions to heat equations defined by generalized measure theoretic Laplacians(2020) Ehnes, Tim; Hambly, BenWe consider the heat equation defined by a generalized measure theoretic Laplacian on [0, 1]. This equation describes heat diffusion in a bar such that the mass distribution of the bar is given by a non-atomic Borel probabiliy measure μ, where we do not assume the existence of a strictly positive mass density. We show that weak measure convergence implies convergence of the corresponding generalized Laplacians in the strong resolvent sense. We prove that strong semigroup convergence with respect to the uniform norm follows, which implies uniform convergence of solutions to the corresponding heat equations. This provides, for example, an interpretation for the mathematical model of heat diffusion on a bar with gaps in that the solution to the corresponding heat equation behaves approximately like the heat flow on a bar with sufficiently small mass on these gaps.Item Open Access Arrays of individually controllable optical tweezers based on 3D-printed microlens arrays(2020) Schäffner, Dominik; Preuschoff, Tilman; Ristok, Simon; Brozio, Lukas; Schlosser, Malte; Giessen, Harald; Birkl, GerhardItem Open Access Axisymmetric spheroidal squirmers and self-diffusiophoretic particles(2020) Pöhnl, Ruben; Popescu, Mihail Nicolae; Uspal, William E.We study, by means of an exact analytical solution, the motion of a spheroidal, axisymmetric squirmer in an unbounded fluid, as well as the low Reynolds number hydrodynamic flow associated to it. In contrast to the case of a spherical squirmer - for which, e.g. the velocity of the squirmer and the magnitude of the stresslet associated with the flow induced by the squirmer are respectively determined by the amplitudes of the first two slip (‘squirming’) modes - for the spheroidal squirmer each squirming mode either contributes to the velocity, or contributes to the stresslet. The results are straightforwardly extended to the self-phoresis of axisymmetric, spheroidal, chemically active particles in the case when the phoretic slip approximation holds.Item Open Access Bell-state measurement exceeding 50% success probability with linear optics(2023) Bayerbach, Matthias J.; D’Aurelio, Simone E.; Loock, Peter van; Barz, StefanieItem Open Access Brauer graph algebras are closed under derived equivalence(2022) Antipov, Mikhail; Zvonareva, AlexandraIn this paper the class of Brauer graph algebras is proved to be closed under derived equivalence. For that we use the rank of the maximal torus of the identity component Out0(A)of the group of outer automorphisms of a symmetric stably biserial algebra A .Item Open Access A brief review of capillary number and its use in capillary desaturation curves(2022) Guo, Hu; Song, Kaoping; Hilfer, R.Capillary number, understood as the ratio of viscous force to capillary force, is one of the most important parameters in enhanced oil recovery (EOR). It continues to attract the interest of scientists and engineers, because the nature and quantification of macroscopic capillary forces remain controversial. At least 41 different capillary numbers have been collected here from the literature. The ratio of viscous and capillary force enters crucially into capillary desaturation experiments. Although the ratio is length scale dependent, not all definitions of capillary number depend on length scale, indicating potential inconsistencies between various applications and publications. Recently, new numbers have appeared and the subject continues to be actively discussed. Therefore, a short review seems appropriate and pertinent.Item Open Access Centers of Hecke algebras of complex reflection groups(2023) Chavli, Eirini; Pfeiffer, GötzWe provide a dual version of the Geck-Rouquier Theorem (Geck and Rouquier in Finite Reductive Groups (Luminy, 1994), Progr. Math., vol. 141, Birkhäuser Boston, Boston, pp. 251–272, 1997) on the center of an Iwahori-Hecke algebra, which also covers the complex case. For the eight complex reflection groups of rank 2, for which the symmetrising trace conjecture is known to be true, we provide a new faithful matrix model for their Hecke algebra H . These models enable concrete calculations inside H . For each of the eight groups, we compute an explicit integral basis of the center of H .Item Open Access Character of doped holes in Nd1-xSrxNiO2(2021) Plienbumrung, Tharathep; Schmid, Michael Thobias; Daghofer, Maria; Oleś, Andrzej M.We investigate charge distribution in the recently discovered high-𝑇𝑐 superconductors, layered nickelates. With increasing value of charge-transfer energy, we observe the expected crossover from the cuprate to the local triplet regime upon hole doping. We find that the 𝑑-𝑝 Coulomb interaction 𝑈𝑑𝑝 makes Zhang-Rice singlets less favorable, while the amplitude of local triplets at Ni ions is enhanced. By investigating the effective two-band model with orbitals of 𝑥2-𝑦2 and s symmetries we show that antiferromagnetic interactions dominate for electron doping. The screened interactions for the s band suggest the importance of rare-earth atoms in superconducting nickelates.Item Open Access Charge-order phase transition in the quasi one-dimensional organic conductor (TMTTF)2NO3(2020) Majer, Lena N.; Miksch, Björn; Lesseux, Guilherme Gorgen; Untereiner, Gabriele; Dressel, MartinLow-dimensional organic conductors show a rich phase diagram, which has, despite all efforts, still some unexplored regions. Charge ordered phases present in many compounds of the (TMTTF)2X family are typically studied with their unique electronic properties in mind. An influence on the spin arrangement is, however, not expected at first glance. Here, we report temperature and angle dependent electron spin resonance (ESR) measurements on the quasi one-dimensional organic conductor (TMTTF)2NO3. We found that the (TMTTF)2NO3 compound develops a peculiar anisotropy with a doubled periodicity (ab′-plane) of the ESR linewidth below about TCO=(250±10) K. This behavior is similar to observations in the related compounds (TMTTF)2X (X=PF6, SbF6 and AsF6), where it has been attributed to relaxation processes of magnetically inequivalent sites in the charge-ordered state. For the structural analogous (TMTTF)2ClO4, known for the absence of charge order, such angular dependence of the ESR signal is not observed. Therefore, our ESR measurements lead us to conclude that a charge-order phase is stabilized in the title compound below TCO≈250 K.Item Open Access Classical interaction potentials for diverse materials from ab initio data : a review of potfit(2015) Brommer, Peter; Kiselev, Alexander; Schopf, Daniel; Beck, Philipp; Roth, Johannes; Trebin, Hans-RainerForce matching is an established technique to generate effective potentials for molecular dynamics simulations from first-principles data. This method has been implemented in the open source code potfit. Here, we present a review of the method and describe the main features of the code. Particular emphasis is placed on the features added since the initial release: interactions represented by analytical functions, differential evolution as optimization method, and a greatly extended set of interaction models. Beyond the initially present pair and embedded-atom method potentials, potfit can now also optimize angular dependent potentials, charge and dipolar interactions, and electron-temperature-dependent potentials. We demonstrate the functionality of these interaction models using three example systems: phonons in type I clathrates, fracture of α-alumina, and laser-irradiated silicon.Item Open Access CO2-induced drastic decharging of dielectric surfaces in aqueous suspensions(2024) Vogel, Peter; Beyer, David; Holm, Christian; Palberg, ThomasWe study the influence of airborne CO2 on the charge state of carboxylate stabilized polymer latex particles suspended in aqueous electrolytes. We combine conductometric experiments interpreted in terms of Hessinger's conductivity model with Poisson-Boltzmann cell (PBC) model calculations with charge regulation boundary conditions. Without CO2, a minority of the weakly acidic surface groups are dissociated and only a fraction of the total number of counter-ions actually contribute to conductivity. The remaining counter-ions exchange freely with added other ions like Na+, K+ or Cs+. From the PBC-calculations we infer a corresponding pKa of 4.26 as well as a renormalized charge in reasonably good agreement with the number of freely mobile counter-ions. Equilibration of salt- and CO2-free suspensions against ambient air leads to a drastic de-charging, which exceeds by far the expected effects of to dissolved CO2 and its dissociation products. Further, no counter-ion-exchange is observed. To reproduce the experimental findings, we have to assume an effective pKa of 6.48. This direct influence of CO2 on the state of surface group dissociation explains our recent finding of a CO2-induced decrease of the ζ-potential and supports the suggestion of an additional charge regulation caused by molecular CO2. Given the importance of charged surfaces in contact with aqueous electrolytes, we anticipate that our observations bear substantial theoretical challenges and important implications for applications ranging from desalination to bio-membranes.