Fakultät für Mathematik und Physik
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- ItemSystematic Differences in the Source Properties of the Third Gravitational-Wave Catalog(Hannover : Gottfried Wilhelm Leibniz Universität Hannover; Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), 2025) Melching, Max[No abstract available]
- ItemSystematic Errors in Gravitational Waveform Models(Hannover : Gottfried Wilhelm Leibniz Universität Hannover; Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), 2025) Melching, MaxThe field of gravitational waves is about to enter a new era, with instruments such as LISA, the Einstein Telescope, or Cosmic Explorer expected to become operational in the next decade or two. All of these instruments will enable us to measure many interesting properties of the Universe, such as the distribution of spins and masses of black holes or the Hubble constant, with a precision that will be unparalleled in gravitational wave astrophysics. The general expectation is that by the time these instruments begin their life cycles, systematic biases at today’s levels would be the limiting factor on the accuracy with which astrophysical and cosmological parameters can be inferred. This creates a need to eliminate or control those biases by that time. In this thesis, we examine various aspects of this field of waveform systematics, starting with a linear-order description of the topic, the Fisher matrix formalism. In addition to reviewing well-established results, we also cover a recent advancement named alignment, showing that and how it can be expected to outperform the original formula. We then continue to apply the Fisher matrix formalism to two other topics. First, a newly proposed model to describe waveform errors and the induced systematic biases is analyzed. This includes a description of the model itself, along with thoughts on its interplay with some of the existing infrastructure used by the LIGO-Virgo-KAGRA collaborations. After that, both Fisher matrix estimation and parameter estimation are used to study the model. In the second project, we outline how to quantify systematic biases in a catalog of publicly available gravitational wave events. We proceed by comparing Fisher matrix and catalog results, and provide a comprehensive discussion of factors that could potentially contaminate the results of the analysis.
- ItemIntroduction to Numerical Modeling, Discretization, and Solution with Differential Equations Applied to Poro-Elasticity(Hannover : Institutionelles Repositorium der Leibniz Universität Hannover, 2025-08-15) Wick, ThomasThis course is designed for students and peers who had basic classes in calculus, introduction to numerical methods, differential equations, and finite element discretizations. In three lectures, the goal is to provide rigorous concepts for mathematical and numerical methods for continuum mechanics problems with a focus on porous media applications. They range from the linear Biot system up to current research on fluid-filled phase-field fracture in porous media. This Mini-Curso is part of the DAAD (German academic exchange service) program SaCCC : South American Competence Center of Scientific Computing (https://numerics.ovgu.de/sac3/).
- ItemMeasurement-based quantum computation in finite one-dimensional systems: string order implies computational power(Wien : Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2023) Raussendorf, Robert; Yang, Wang; Adhikary, ArnabWe present a new framework for assessing the power of measurement-based quantum computation (MBQC) on short-range entangled symmetric resource states, in spatial dimension one. It requires fewer assumptions than previously known. The formalism can handle finitely extended systems (as opposed to the thermodynamic limit), and does not require translation-invariance. Further, we strengthen the connection between MBQC computational power and string order. Namely, we establish that whenever a suitable set of string order parameters is non-zero, a corresponding set of unitary gates can be realized with fidelity arbitrarily close to unity.
- ItemQuasi-hermitian quantum mechanics and a new class of user-friendly matrix hamiltonians(Bristol : IOP Publ., 2023) Lechtenfeld, Olaf; Znojil, MiloslavIn the conventional Schrödinger's formulation of quantum mechanics the unitary evolution of a state ψ is controlled, in Hilbert space L, by a Hamiltonian h which must be self-adjoint. In the recent, "quasi-Hermitian"reformulation of the theory one replaces h by its isospectral but non-Hermitian avatar H = ω-1 o ω with ω†ω = Θ ≠ I. Although acting in another, manifestly unphysical Hilbert space H, the amended Hamiltonian H ≠ H † can be perceived as self-adjoint with respect to the amended inner-product metric Θ. In our paper motivated by a generic technical "user-unfriendliness"of the non-Hermiticity of H we introduce and describe a specific new family of Hamiltonians H for which the metrics Θ become available in closed form.