Microscopic theory of ultrafast electron dynamics on metal surfaces

Ultrafast electron dynamics in image states of metals are investigated by Green function method involving off-diagonal elements of self-energy functions, which represent virtual electron transitions between different image states. The diagonal and off-diagonal elements of Green functions, which represent the electron densities of the image states with quantum numbers from 3 to 6 and the probability amplitude of electron propagation between different image states, respectively, are calculated by treating the self-energy functions within the GW approximation. The virtual electron transitions between different image states account for occurrence of quantum beats and acceleration and deceleration of the decay of electron densities, as compared with the intrinsic decay rates determined by the imaginary parts of the diagonal elements of the self-energy functions. It is quantitatively demonstrated that the effects of the virtual transitions are marked especially for image states with large quantum numbers.