Fast algorithm for calculating two-photon absorption spectra
  We report a numerical calculation of the two-photon absorption coefficient of electrons in a binding potential using the real-time real-space higher-order difference method. By introducing random vector averaging for the intermediate state, the task of evaluating the two-dimensional time integral is reduced to calculating two one-dimensional integrals. This allows the reduction of the computation load down to the same order as that for the linear response function. The relative advantage of the method compared to the straightforward multi-dimensional time integration is greater for the calculation of non-linear response functions of higher order at higher energy resolution. 
Yoshiyuki Kurokawa(University of Tsukuba), Shintaro Nomura(RIKEN),   Tadashi Takemori(University of Tsukuba) and Yoshinobu A...