Multidimensional Quantum Dynamics via Path Integral Methods
Quantum mechanical effects such as tunneling and phase coherence are important in many chemical and biological phenomena. Many such processes remain poorly understood because--unlike classical mechanical methods--the numerical effort required to solve the non-local quantum equations of motion grows exponentially with the number of particles involved. At present, accurate quantum mechanical calculations are possible only for small (up to three- or four-atom) systems, while larger systems are dealt with by approximations. The proposed research will focus on the further development and application of an efficient method suitable for investigating the dynamics of polyatomic quantum mechanical systems.
Professor Makri's approach is based on Feynman's path integral formalism; according to the latter, the probability amplitude for a quantum mechanical process is obtained by summing the probability amplitudes along all conceivable paths. Feynman's method is extremely useful in equilibrium statistical mechanics, but the Monte Carlo techniques that must be used to evaluate the path integral numerically are not well-behaved if dynamical information is sought. The advantage of our formulation is the choice of a physically meaningful reference system, which accelerates the convergence rate of the path integral by orders of magnitude.
A number of intriguing questions can be investigated using Professor Makri's approach. Recent experiments on the kinetics of hydrogen diffusion on metal surfaces have revealed an "anomalous" isotope dependence at low temperature which implies a complex man-body tunneling mechanism. The dynamics of electron tunneling in semiconductor materials and in the photosynthetic reaction center involves a complicated interplay between quantum coherence and dissipative effects. These effects also determine the characteristics of intramolecular energy flow and are therefore important in laser control experiments.