The Non-Equilibrium Generalized Anharmonic Solution

In order to evaluate the remaining integrals the correlation functions are necessary, in relation with the statistical Wick rules. Precisely, having in 

Quantum Nanochemistry— Volume II Quantum Atoms and Periodicity 

The density matrix as a functional of the introduced interaction current y can be developed under the form (Pelster Kleinert, 1996 Kleinert et al., 

Whit these (Feynman) rules the connected expressions are calculated following the (the modified Wick rules) prescriptions of Section 3.3.2, here particularized as  

---