The Center for Nonlinear Studies
2006 Kac Lecture Series
June 12, 13, & 15, 2006
Lecture 1: The Theory of Glasses
Supercooled liquids and glasses can be viewed as aperiodic crystals. Pursuing this view leads to the random first order transition theory of glasses. A liquid in this picture can be thought of as a mosaic of local energy landscapes. The theory explains quantitatively, without adjustable parameters, the super-Arrhenius slowing of dynamics and emergence of nonexponential relaxation in the supercooled liquid regime. The aging regime of glasses is also quantitatively treated. When quantized, the theory yields a description of the two level systems and Boson peak excitations that dominate the low temperature properties of amorphous solids.
Lecture 2: Recent Successes of the Energy Landscape Theory of Protein Folding
Protein folding can be understood as a biased search on a funneled but rugged energy landscape. This picture can be made quantitative using the statistical mechanics of glasses and first order transitions in mesoscopic systems. The funneled nature of the protein energy landscape is a consequence of natural selection. I will discuss how this rather simple picture quantitatively predicts folding mechanism from native structure and sequence. Recent advances using the energy landscape ideas to design algorithms to predict protein structure from sequence will also be reviewed.
Lecture 3: Quantum Many Body Chaos: Energy Flow in Molecules
Regularity and Chaos are well-known antitheses in classical mechanics. The same mathematical conflict occurs in understanding quantum mechanical systems but has been studied much less. I will discuss the quantum theory of how energy flows in moderate-size molecules and its connection with experiment. The implications of these ideas in chemical kinetics and quantum control will be emphasized.