Mathematical and Numerical Aspects of Quantum Dynamics

Understanding nonadiabatic interactions at a metal surface: Surface Hopping and Electronic Friction

Joseph Subotnik

University of Pennsylvania

In this talk, I will highlight our recent adventures into the nonadiabatic dynamics as present with electron transfer at a metal surface. I will show (i) how electronic friction arises as a first order correction to the Born Oppenheimer approximation in the limit of small velocity, andI (ii) how surface hopping emerges from perturbation theory in the limit of weak coupling. Lastly, I will highlight how these limits can be unified by extrapolation, though without any mathematical rigor. Finally, time withstanding, I will bring up several curious results that question the exact small parameter that is assumed in each of these derivations.