  Correlation-function expressions are derived for the coherent nonlinear
response of molecules to three resonant ultrafast pulses in the x-ray regime.
The ability to create two-core-hole states with controlled attosecond timing in
four-wave-mixing and pump probe techniques should open up new windows into the
response of valence electrons, which are not available from incoherent x-ray
Raman and fluorescence techniques. Closed expressions for the necessary
four-point correlation functions are derived for the electron-boson model by
using the second order cumulant expansion to describe the fluctuating
potentials. The information obtained from multidimensional nonlinear techniques
could be used to test and refine this model, and establish an anharmonic
oscillator picture for electronic excitations.
