Workshop »Advances in General Relativity« Mitschnitt einer Veranstaltung des Internationalen Erwin Schrödinger Instituts für Mathematik und Physik (ESI) am Dienstag, dem 29. August 2017 im Boltzmann-Hörsaal des Internationalen Erwin Schrödinger Instituts für Mathematik und Physik (ESI) Teil 5: Piotr Bizoń: From AdS to BEC Kamera: Johannes Sauer, Daniel Winkler Schnitt: Daniel Winkler Abstract: The long-time behavior of nonlinear dispersive waves subject to spatial confinement can be very rich and complex because, in contrast to unbounded domains, waves cannot disperse to infinity and keep self-interacting for all times. If, in addition, the linear spectrum around the ground state is fully resonant, then the nonlinearity can produce significant effects for arbitrarily small perturbations. The weak field dynamics of such systems can be approximated by solutions of the corresponding infinite-dimensional time-averaged Hamiltonian systems, which govern resonant interactions between the modes. A major mathematical challenge in this context is to describe the energy transfer between the modes. I will discuss this problem for three different models of confinement: the Einstein equation with negative cosmological constant describing weakly turbulent behavior of small perturbations of the anti-de Sitter (AdS) spacetime, a nonlinear wave equation on a compact manifold (like the cubic wave equation on the 3-sphere), and the nonlinear Schroedinger equation with a trapping potential describing the dynamics of Bose-Einstein condensates (BEC). Some intriguing parallels between these systems will be emphasized. Piotr Bizoń ist Professor für Theoretische Physik an der Jagiellonen-Universität Krakau. INHALT ====== Kapitel Titel Position --------------------------------------------------------------------- 1. Vorspann 00:00:00 2. Specially confined Hamiltonian systems 00:00:10 3. Example: Wave equation on the 3-sphere 00:10:10 4. Time averaging. Resonant system 00:13:53 5. Other Hamiltonian systems 00:18:52 6. Finite-dimensional invariant manifolds 00:24:45 7. Lowest Landau level equation 00:33:30 8. Vortices in Bose-Einstein-Condensates 00:39:03 9. Anti-de Sitter spacetime in d + 1 dimensions 00:41:41 10. From Klein-Gordon on AdS to Gross-Pitaevskii 00:54:00

Anti-de-Sitter-Raum, Bose-Einstein-Kondensat

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