Role of the finite collision duration in femtosecond laser studies of semiconductors

The use of femtosecond laser pulses to excite electron-hole plasmas in semiconductors has become a major method of studying fast processes in this system in recent years. Transition times from the central Γ valley in GaAs to the satellite X and L valleys are comparable to the reciprocal of the frequency of the phonon involved in these transitions, bringing into question the use of standard perturbation theory approaches. We present an initial investigation of the role of retardation arising from the finite collision duration required for such a transition to occur, through the use of a path-integral form of the quantum kinetic equation. A secondary self-scattering process and a probability of completed collisions are used to cast this equation ina semi-classical form.