Events Archive

Freitag, 06.12.2019: Campus Bockenheim, Robert-Mayer-Straße 10, Raum 711 groß, 7. OG

15.15 Uhr Simone Warzel (TU München): Quantum spin glasses: a mathematical challenge

The theory of classical mean-field spin glasses is a well-established and celebrated field within probability theory. The addition of a constant perpendicular magnetic field introduces a non-commuting term into the energy of such spin glasses and hence causes quantum effects. The main aim of this talk is to give an overview over some of the motivations for the study of quantum spin glasses. I will also review some first mathematical results in this field. Among them is a derivation of the key features of the thermal phase diagram of the simplest of all mean-field spin glasses, the quantum random energy model.

16.15-16.45 Uhr Kaffeepause

16.15 Uhr Matthias Erbar (Bonn): A variational characterization of the Sine_ß point process

The one-dimensional log gas in finite volume is a system of particles interacting via a repulsive logarithmic potential and confined by some external field. When the number of particles goes to infinity, their macroscopic empirical distribution approaches a deterministic limit shape. When zooming in one sees microscopic fluctuations around this limit which are described in the limit by a stationary point process, the Sine_ß process constructed by Valko and Virag. Leblé and Serfaty have established a large deviation principle for the microscopic configurations governed by a rate function which is the sum of a specific entropy and a renormalized interaction energy. Thus the typical microscopic behavior of the gas is described by the minimizers of this free energy functional, one of which is the Sine_ß process. We show that this is indeed the unique minimizer. Our argument is based on optimal transport of random point configurations and exploits strict displacement convexity in the free energy functional. Joint work with Martin Huesmann and Thomas Leblé.

Im Anschluss gemeinsame Nachsitzung.