Three Lectures on Metastability Under Stochastic Dynamics
Metastability is a phenomenon where a physical, chemical or biological system, under the influence of a noisy dynamics, moves between different regions of its state space on different time scales. On short time scales the system is in a quasi-equilibrium within a single region, while on long time scales it undergoes rapid transitions between quasiequilibria in different regions (see Fig. 1).
biology: folding of proteins;
climatology: effects of global warming;
economics: crashes of financial markets;
materials science: anomalous relaxation in disordered media;
physics: freezing of supercooled liquids.
The task of mathematics is to formulate microscopic models of the relevant underlying dynamics, to prove the occurrence of metastable behavior in these models on macroscopic space-time scales, and to identify the key mechanisms behind the experimentally observed universality in the metastable behavior of whole classes of systems. This is a challenging program!
KeywordsIsing Model Free Particle Simple Random Walk Metastable Behavior Glauber Dynamic
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