Vorträge in der Woche 15.12.2025 bis 21.12.2025

Dienstag, 16.12.2025: Anosov representations and convex-cocompact groups II

Giacomo Gavelli

Donnerstag, 18.12.2025: Mean-field regimes of the Bose-Hubbard Model

Dr. Shahnaz Farhat (Tübingen)

In the first part, I will talk about the many-body quantum Gibbs state for the Bose–Hubbard model on a finite graph at positive temperature. We scale the interaction with the inverse temperature, corresponding to a mean-field limit where the temperature is of the order of the average particle number. We prove an expansion to any order of the many-body Gibbs state with inverse temperature as a small parameter. The coefficients in the expansion can be calculated as vacuum expectation values using a recursive formula. In the second part of the talk, I will talk about the validity of a mean-field approximation for the dynamics of quantum systems in high dimension, using the Bose–Hubbard model on a square lattice. We prove a trace norm estimate between the one-lattice-site reduced density of the Schrödinger dynamics and the mean-field dynamics in the limit of large dimension.