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Einladung zum Vortrag (Zoom) von Herrn Prof. Dr. Wolfgang König (Technische Universität Berlin) am 24.04.2024 - 15:30 Uhr im Rahmen des Forschungsseminars Analysis
[24.04.2024]Im Rahmen des Forschungsseminars Analysis hält am Mittwoch, den 24. April 2024, um 15:30 Uhr,
Herr Prof. Dr. Wolfgang König (Technische Universität Berlin) einen Vortrag zum Thema
Off-diagonal long-range order for the free Bose gas via the Feynman-Kac formula
Abstract: We consider the path-integral representation of the ideal Bose gas under various boundary conditions. We show that Bose–Einstein condensation occurs at the famous critical density threshold, by proving that its 1-particle-reduced density matrix exhibits off-diagonal long-range order above that threshold, but not below. Our proofs are based on the well-known Feynman–Kac formula and a representation in terms of a crucial Poisson point process. Furthermore, in the condensation regime, we derive a law of large numbers with strong concentration for the number of particles in short loops.
In contrast to the situation for free boundary conditions, where the entire condensate sits in just one loop, for all other boundary conditions we obtain the limiting Poisson–Dirichlet distribution for the collection of the lengths of all long loops.
Our proofs are new and purely probabilistic (apart from a standard eigenvalue expansion), using elementary tools like Markov’s inequality, Poisson point processes, combinatorial formulas for cardinalities of particular partition sets, and asymptotics for random walks with Pareto-distributed steps.
Der Vortrag findet im Rahmen eines Zoom-Meetings statt. Bei Interesse an den Zugangsdaten bitte bei Herrn PD Dr. habil. Joachim Kerner (joachim.kerner) melden.
