Browsing by Author "Reiff, Johannes"
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Item Open Access Advances in transition-state theory and applications to driven systems(2023) Reiff, Johannes; Main, Jörg (Prof. Dr.)Chemical reactions are often described via the motion of an effective particle on a Born–Oppenheimer potential-energy surface. In this picture, trajectories typically turn from reactants to products when crossing a rank-1 saddle on the energy surface. The geometric properties of this bottleneck and its associated transition state play an important role for the dynamics of activated trajectories, i. e., trajectories that cross near threshold energy. Transition state theory is a well-established framework that can be used to analyze the dynamics near the rank-1 saddle. It focuses particularly on the determination of rates via the flux through the transition state, which has been investigated since the early 20th century and continues to be of relevance today. In this work, we focus mainly on the geometrical formulation of transition state theory. This description formalizes the distinction between reactants and products by defining a dividing surface in phase space based on the hyperbolic dynamics near the saddle. Specifically, a formally exact dividing surface can be constructed by anchoring it to the saddle's normally hyperbolic invariant manifold. This invariant manifold and its associated stable and unstable manifolds determine the fate of activated trajectories, and so they are of great interest in the field of chemical reaction kinetics. This dissertation is concerned with the development and application of numerical methods in the framework of transition state theory. We address the emergent dynamics of time-dependent chemical and physical model systems under periodic external driving of the transition barrier. In particular, we focus on the structure of the normally hyperbolic invariant manifold, its associated decay rates, and whether these rates can somehow be connected to Kramers's notion of escape rates. The range of models we investigate includes two simple but prototypical test cases with one and two driven saddles as well as the LiCN → LiNC isomerization reaction. We further show how transition state theory can be applied to celestial-mechanics, where it can be used to optimize orbits of satellites with respect to fuel consumption while accounting for time-dependent perturbations from the moon. The systems are mostly treated deterministically, but we also make use of the (generalized) Langevin equation when examining the absolute LiCN isomerization rates. In this context, we ask the fundamental question of how to define a rate, which is especially important at high temperatures.Item Open Access Beschreibung PT-symmetrischer Bose-Einstein-Kondensate mit einem Vier-Mulden-Potential und der Bogoliubov-Backreaction-Methode(2016) Reiff, JohannesNicht-hermitesche Hamiltonoperatoren mit PT-Symmetrie erlauben die elegante Beschreibung offener Quantensysteme. Die Arbeit untersucht die Realisierung eines PT-symmetrischen Zweimuldensystems durch die Einbettung in ein hermitesches Viermuldensystem mithilfe der Bogoliubov-Backreaction-Methode.Item Open Access Dynamik und Trennflächen für getriebene Systeme mit zwei zeitabhängigen Sattelpunkten(2018) Reiff, JohannesDie Arbeit untersucht chemische Reaktionen in zeitlich getriebenen Systemen mit zwei Sattelpunkten mithilfe der Transition State Theory.