Nonadiabatic formulation for radiationless transitions induced by classical lattice vibrations

A semiclassical model for nonadiabatic radiationless transitions is described. Lattice dynamics are introduced as stochastic fluctuations in the separation and coupling of electronic levels. Formulation on the Bloch sphere brings an appealing perspective through the analogy to a magnetic moment moving in fluctuating magnetic field. Numerical solutions are reported which retain nonadiabatic features exactly. For near-adiabatic behavior, out-side crossing regions, a first-order correction to adiabatic dynamics is derived and compared with the exact solution.