Slowly varying time-dependent local perturbations in metals: a new approach

When a local time-dependent perturbation in a metal is switched on and then off, it is desired to calculate the probability P( epsilon ) for the system to be excited to a state of energy h(cross) epsilon . For a strong but slow perturbation V(t) the authors show that the problem reduces to the calculation of an evolution operator for a time-independent one-body potential W(V(t)) which is a functional of V(t). They calculate W for potentials possessing a time-independent phase-shift representation. For such potentials they calculate the evolution operator, and hence P( epsilon ), for a Fermi sea both at zero and finite temperature. They give simple applications of their results to problems such as X-ray photoemission spectroscopy and energy dissipation of an atom scattered from a metal surface. The relationship to a recent solution of the problem, at zero temperature, using a time-dependent Tomonagon representation is indicated.