Response functions at the single molecule level

In what follows we will simplify notation in several ways, one of which is to drop the superscript on the transverse electric field. Let us assume for the moment that only a single chromophore molecule exists, so that 

Both ji and are generally vectors and V is their scalar product, however again to simplify notation we will suppress this aspect in the formulation below. 

Our starting point is the equation of motion (10.21) for the density operator p of the overall system in the interaction representation 

The notation is kept for p in order to distinguish between p(t) in the Schrodinger representation and p/ (i) in the interaction representation. Any other operator A will appear as such in the Schrodinger representation, and as A(t) in the interaction representation. 

This equation can be iterated (similar to the solution (2.76) ofEq. (2.73)) to give the interaction representation of the density operator at time to starting from some time tp in the past 

---