Diagrammatical study of a nonequilibrium process: Model calculation

The Feynman rule of any quantum system explicitly depends on the initial time when it is prepared. Assuming that the initial state is in equilibrium, the complete diagrammatical rule is applied to the field-theoretical time-dependent model Hamiltonian. The explicit calculations up to the lowest nontrivial order are performed for the typical nonequilibrium processes. The equation of motion is derived by the inversion method, which is equivalent to the Legendre transformation. The subjects discussed are the calculation of the damping term, the change of the internal energy due to the adiabatic or the nonadiabatic change of the external source, and the resulting temperature shift of the system.