Stochastic-trajectories and nonPoisson kinetics in single-molecule spectroscopy

Microscopic correlation-function expressions for the stochastic evolution observed in single molecule spectroscopy are derived using Liouville-space projection operators. The kinetics of a multilevel quantum system coupled to a single collective overdamped Brownian-oscillator coordinate is exactly mapped onto a continuous-time-random-walk (CTRW) involving the transition states(curve-crossing points). Closed expressions are derived for the stochastic trajectories and the nonPoissonian distribution of number of flips. When the oscillator relaxation is fast compared with the reaction rates, the waiting time distribution becomes exponential and the standard Poisson kinetics is recovered. (C) 1999 American Institute of Physics. [S0021-9606(99)01340-9].