The directional motion of a particle in an unbound potential in the presence of either non-Ohmic memory friction or Lévy flight is considered. Time-dependent probability passing over the saddle point of a parabolic potential is derived exactly. The results show that the Lévy flights break...

The quantal diffusion of a particle with an initial velocity coupled to a non-Ohmic environment passing over a potential top is considered. It is shown that sub- and super-diffusions hinder the directional motion of the particle in two different ways. The former makes the particle have a strong...