Nancy Makri

We strive to advance theoretical understanding of quantum mechanical processes in large molecules and the condensed phase. Full solution of the Schrödinger equation is feasible only for small molecules, as the required numerical effort increases exponentially with the number of particles. We develop new theoretical approaches and simulation methods based on Feynman’s path integral formulation of quantum dynamics and its semiclassical limit.

Methodology. The path integral representation avoids storage of multidimensional wave functions at the cost of introducing auxiliary integration variables at each time step. Evaluating the resulting multidimensional integrals presents a challenge: the number of paths grows exponentially with time, while importance sampling fails due to phase cancellation.

We developed the first rigorous methodology for following the dynamics of a quantum particle interacting with a polyatomic medium. A path integral represents the subsystem of interest, while the collective effects of the environment are evaluated in the semiclassical approximation using trajectories in combined forward-backward time to alleviate the phase cancellation problem. Through dephasing effects, the medium helps shorten the range of temporal correlations, allowing an exact decomposition of the path sum into an iterative scheme that circumvents the need for global summation over astronomical numbers of paths. The method allows a faithful description of all aspects of quantum mechanical processes in condensed phase environments and, if the environment consists of harmonic phonon modes, yields the exact quantum mechanical result.

Reaction Rates. We have performed path integral calculations to benchmark adiabatic and nonadiabatic reaction rates in generic dissipative environments and to explore the interplay between coherence and dissipation at low temperatures. Our simulation of hydrogen diffusion in silicon identified important tunneling contributions and an inverse isotope effect.

Photosynthesis. Our path integral simulations helped resolve a long-standing controversy concerning the primary charge separation mechanism. Further, we have been exploring the energy transfer process in light-harvesting complexes using the path integral representation of quantum statistical mechanics.

Quantum Control. We are investigating the possibility of using coherent light to manipulate exciton tunneling and transport in nanostructures. We have identified novel mechanisms for sustaining charge localization or inducing coherent oscillations in semiconductor double-quantum wells.