  We realized a time-domain simulator based on the electrodynamics of Cooper
pairs and quasiparticles in Josephson junctions. The tool, based on the charge
carriers' densities of states described by the Werthamer and Harris formalisms
of Bardeen-Cooper-Schrieffer (BCS) theory, allows to analyze the behavior of
current- or voltage-controlled Josephson junction-based circuits for any signal
waveform, at a physical temperature comprised between the absolute temperature
and the critical temperature. The simulator can account for I-V curve
hysteresis depending on the McCumber parameter, or Shapiro and photo-assisted
steps in the presence of a monochromatic microwave signal. We used the
simulator to assess the behavior of MgB2-based Josephson junctions at THz
frequencies by taking into account the presence of the two anisotropic gaps of
MgB2.
