| This thesis addresses a number of problems associated with dynamics on rough energy landscapes. The first half presents new methodologies for the calculation of reaction rates and mechanisms with the remaining portion devoted to the dynamics and thermodynamics of glassy systems. After the introduction in chapter 1, chapter 2 presents a complementary set of methods for the efficient calculation of approximate but accurate quantum rates. These methods can be applied to complex systems without a preconceived knowledge of the reaction coordinate and are tested on a seven atom noble gas cluster. In chapter 3, a method for the calculation of global and multiple reaction paths is presented and tested on the difficult problem of water diffusing on an ice surface. Chapter 4 describes a method for improving the efficiency of transition state location, which is tested on a wide variety of model and physical systems. In chapter 5, the focus shifts to glassy systems. Here, evidence is presented to suggest that previous claims regarding the presence or lack of a thermodynamic transition near the Kauzmann temperature must be reevaluated. Further, fundamental difficulties are brought to light regarding the common notion that systems can be equilibrated at glassy temperatures using non-local Monte Carlo methods. In chapter 6, we investigate the deep connections between mean-field theory, mode-coupling theory, and the landscape picture of the glass transition. It is found that the temperature where the full wavevector dependent mode-coupling equations predict a loss of ergodicity coincides with the temperature where finite sized mean-field spin glass models display non-mean-field α-relaxation effects. This temperature also corresponds to the onset temperature at which the system begins to explore a restricted landscape as the glass transition approaches. Lastly, chapter 7 discusses in detail the search for structural signatures of glassy behavior. The response to an instantaneous shear deformation and the compressibility are shown to display important trends as a liquid is supercooled. |
