Theory of energy dissipation under time-dependent local perturbations

A new method to treat the energy dissipation into electron excitations by time-dependent local perturbations is presented. The probability P( epsilon ) for the electron system to be excited to a state epsilon is expressed in terms of new Green functions given by extending the Keldysh Green function formalism. As an example, the method is applied to the slowly varying noninteracting Wolff model at zero temperature. The Muskhelishvili technique, which has been used for X-ray problems, is used to solve the resulting integral equations of the Green functions. The results are identical to those given by a time-dependent Tomonagon approach and by solving directly the equation of motion for field operators.