数学物理
Quantum-mechanical observables for spatial and spacetime localization are considered from a lattice-theoretic perspective. It is shown that when replacing the lattice of all complex orthogonal projections underlying the Born rule by the…
Lagrangian multiforms provide a variational framework for describing integrable hierarchies. This thesis presents two approaches for systematically constructing Lagrangian one-forms, which cover the case of finite-dimensional integrable…
We characterise non-Hermitian Fabry-P\'erot resonances in high-contrast resonator systems and study the properties of their associated resonant modes from continuous differential models. We consider two non-Hermitian effects: the…
We derive the zero order approximation of a charged particle under the influence of a strong magnetic field in a mathematically rigorous manner and clarify in which sense this approximation is valid. We use this to further rigorously derive…
We investigate properties of the image and kernel of the Biot-Savart operator in the context of stellarator designs for plasma fusion. We first show that for any given coil winding surface (CWS) the image of the Biot-Savart operator is…
In the present work we present a general framework which guarantees the existence of optimal domains for isoperimetric problems within the class of $C^{1,1}$-regular domains satisfying a uniform ball condition as long as the desired…
We study the Fluctuation Theorem (FT) for entropy production in chaotic discrete-time dynamical systems on compact metric spaces, and extend it to empirical measures, all continuous potentials, and all weak Gibbs states. In particular, we…
We provide a mathematically rigorous derivation of the first order expansion of the motion of a charged particle in a strong magnetic field. In contrast to the derivations that can be found in the physics literature we solely assume…
We investigate thermalization and symmetry-breaking in a nonlinear stochastic Klein-Gordon equation on a spatial lattice, taking into account damping, nonlinear interaction, and stochastic forcing terms reduced by a perturbative solution…
We study wave scattering by a finite transversal strip in a discrete square-lattice waveguide with Dirichlet boundary conditions imposed on the strip and the waveguide walls. The setting is motivated as a discrete analogue of the classical…
The Kepler problem in classical mechanics exhibits a rich structure of conserved quantities, highlighted by the Laplace--Runge--Lenz (LRL) vector. Through Noether's theorem in reverse, the LRL vector gives rise to a corresponding…
A special class of (complex) para-Hermite Einstein spaces is analyzed. For this class of spaces the self-dual Weyl tensor is type-[D] in the Petrov-Penrose classification. The anti-self-dual Weyl tensor is algebraically degenerate,…
In this paper, first we revisit the formal integration of Lie algebras, which give rise to braces in some special cases. Then we establish the formal integration theory for complete Rota-Baxter Lie algebras, that is, we show that there is a…
This article introduces a novel framework for developing quantum algorithms for the Lattice Boltzmann Method (LBM) applied to the advection-diffusion equation. We formulate the collision-streaming evolution of the LBM as a compact…
We perform the quantization of Teukolsky scalars of spin $0$, $\pm 1$, and $\pm 2$ within the algebraic approach to quantum field theory. We first discuss the classical phase space, from which we subsequently construct the algebra. This…
This paper develops a bridge between bi-Hamiltonian structures of Poisson-Lie type, contact Hamiltonian dynamics, and the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) formalism for quantum open systems. On the classical side, we consider…
We extend a previous result [Sutter et al., J. Phys. A: Math. Theor. 57, 475202 (2024)] to give an explicit form of the set of $v$-representable densities on the one-dimensional torus with any fixed number of particles in contact with a…
We develop a systematic framework for the model reduction of multivariate geometric Brownian motions (GBMs), a fundamental class of stochastic processes with broad applications in mathematical finance, population biology, and statistical…
We propose a geometric model predictive control framework for quantum systems subject to smoothness and state constraints. By formulating quantum state evolution intrinsically on the projective Hilbert space, we penalize covariant…
We determine the isometry group of the $n$-qubit state space with respect to the quantum Wasserstein distance induced by the so-called symmetric transport cost for all $n \in \mathbb{N}.$ It turns out that the isometries are precisely the…