Nonequilibrium Green functions depending on the observation time for ultrafast dynamics

Abstract

Nonequilibrium Green functions depending on the observation time are introduced in order to investigate ultrafast dynamics involved in photoemission from metal surfaces. Phase decay due to scattering of secondary particles (electrons and holes in the metal) accounts for the dependence of the Green functions on the observation time of a main particle (photoelectron) in the final state. The Green functions $G^{+-}$ and $G^{-+}$ striding over the forward and backward branches of the Keldysh contour represent the dynamics of the secondary particles, i.e., decay of the secondary particles and electron thermalization due to inelastic scattering of the secondary particles. Then, by applying the Green functions to two-photon photoemission from a metal surface, it is shown that the decay of photoexcited holes accelerates the decrease of the photoelectron intensity as a function of the pump-probe delay time and the electron thermalization can account for dephasing.