Metastability in Stochastic Dynamics

Metastability is a phenomenon that occurs in the dynamics of a multi-stable non-linear system subject to noise. In models of statistical mechanics, it is related to the behavior of macroscopic quantities in the vicinity of a first order phase transition. A signature of metastable systems is the existence of multiple, well separated time scales. While at short time scales the system appears to be in a quasi-equilibrium (metastable state), at longer time scales rapid transitions between meta-stable states occur which are induced by random fluctuations. The understanding of the quantitative aspects of dynamical phase tran-sitions is one of the basic problem encountered in physics. In the first part of the book, we develop the potential theoretic approach to the analysis of metastability with a particular focus on systems in which the entropy is relevant. This approach allows to derive sharp estimates on metastable transitions times and its distribution. In the second part, we apply this method to the random-field Curie-Weiss-Potts model.

Autorentext

studied Mathematics and Physics at the TU Berlin. He wrote his thesis both at the Weierstrass Institute of Applied Analysis and Stochastics in Berlin and the Institute of Applied Mathematics in Bonn and received his PhD in 2012. His major research interests are disordered systems and its dynamical behavior.