Consistent-histories and dipolar-basis representation of nonlinear response functions

By expanding optical response functions in the eigenstates of the dipole operator (rather than of the Hamiltonian), we obtain a path-integral representation that lends itself more readily to classical simulations. Connection is made to stochastic (consistent-histories) theories of quantum dynamics of single quantum systems by computing the entire probability distribution of the observed polarization (rather than merely its expectation value). The weight of each Liouville space path contributing to the optical response is complex, and cannot be recast using the joint probabilities used in the consistent-histories approach.