Scan Time Dependence of Single Molecule Optical Lines in Polymers and Glasses

Analysis of various theories for optical bands of a guest molecule in fluctuating environment is carried out. It is shown that any proper dynamical theory for such a system must include initial conditions for two level systems (TLSs) of a solvent. True choice of the initial conditions can be carried out with the help of quantum mechanics principles. Our dynamic theory gives a theoretical basis for a “sudden jump model” which is used in many stochastic theories. Our theory describes the scan time dependence of single molecule optical lines in more comprehensive fashion than any existing stochastic theory is able to carry out. Experimental data on temporal line broadening of single molecule optical lines are treated with the help of our dynamical theory.