April 4, 2003 Colloquium

The concept of energy landscapes relevant for the low temperature thermal behavior of i.e. glasses and spin glasses, metastable chemical compounds, clusters proteins and polymers, but also for evolution biology and for hard optimization problems studied by simulated annealing.

The evolution of all these systems is usually described by a time dependent probability distribution defined over the set of states. The update rule, embodied in simulations by the Metropolis algorithm, is biased in favor of transitions to low energy states, and leads, eventually, to the Boltzmann distribution known from equilibrium statistical mechanics. Global relaxation is hindered and often unobservable in complex landscapes with many valleys. These act as metastable states wherein a state of approximate local equilibrium is established. The system hence retains a memory of the initial configuration produced by a quench for may time scales. Metastability yields a very rich phenomenology, often referred to as aging. A key issue is how the landscape geometry affects the coarse grained dynamics of aging systems.

The talk will give a general introduction to this area, with emphasis on phenomenology and open questions more than on models and answers.