Vorträge in der Woche 22.07.2024 bis 28.07.2024
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Donnerstag, 25.07.2024: Foliations of asymptotically Schwarzschildean lightcones by surfaces of constant spacetime mean curvature
Dr. Markus Wolff (KTH Royal Institute of Technology Stockholm)
We construct asymptotic foliations of asymtotically Schwarzschildean lightcones by surfaces of constant spacetime mean curvature (STCMC). For a surface in an ambient spacetime, the spacetime mean curvature is defined as the (Lorentzian) length of the co-dimension 2 mean curvature vector. Asymtotic foliations of asymptotically flat spacelike hypersurfaces by STCMC surfaces have previously been constructed by Cederbaum-Sakovich. Our construction is motivated by the approach of Huisken-Yau for the Riemannian setting in employing a geometric flow. We show that initial data within a sufficient a-priori class converges exponentially to an STCMC surface under area preserving null mean curvature flow. We further show that the resulting STCMC surfaces form an asymptotic foliation. This is joint work with Klaus Kröncke.
| Uhrzeit: | 14:00 |
| Ort: | Seminarraum S09 (C6H05) and virtual via zoom, for zoom link please contact Martina Neu |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Carla Cederbaum, Gerhard Huisken, zusammen mit Jan Metzger (Potsdam) |
Donnerstag, 25.07.2024: Emergence of a second law of thermodynamics in isolated quantum systems
Florian Meier (TU Wien)
The second law of thermodynamics states that the entropy of an isolated system can only increase over time. This appears to conflict with the reversible evolution of isolated quantum systems under the Schrödinger equation, which preserves the von Neumann entropy. Nonetheless, one finds that with respect to many observables, expectation values approach a fixed value - their equilibrium value. This raises the main question we address in this seminar: in what sense does the entropy of an isolated quantum system increase over time? For classical systems, one introduces the assumption of a low entropy initial state along with the concept of ignorance about the microscopic details of the physical system, leading to a statistical interpretation of the second law. By considering the observables through which we examine quantum systems, both these assumptions can be incorporated, building upon recent studies of the equilibration on average of observables. While the statistical behavior of observable expectation values is well-established, a quantitative connection to entropy increase has been lacking so far. In deriving novel bounds for the equilibration of observables, and considering the entropy of the system relative to observables, we recover a variant of the second law: the entropy with respect to a given observable tends towards its equilibrium value in the course of the system's unitary evolution. The presentation is structured to build up to the main result pedagogically and with illustrative examples where we observe entropy increasing up to equilibrium values, as well as fluctuations which expose the underlying reversible evolution in accordance with the derived bounds.
| Uhrzeit: | 14:30 |
| Ort: | online - wenn Sie Zugang haben wollen, schicken Sie bitte eine Nachricht an Elena Kabagema-Bilan |
| Gruppe: | Oberseminar Mathematical Physics |
| Einladender: | Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka |