Anomalous quantum diffusion over a saddle point and application to fusion of massive nuclei

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 memory to its initial position rather than initial velocity and the latter increases the randomness of motion. The quantum fluctuation helps the particle with a small initial velocity to cross the saddle point, however, it is harmful to the directional motion of the particle with a large initial velocity. The present model is applied to calculate the fusion probability of massive nuclei and the fusion probability curve increases slowly with the center-of-mass energy. This is in agreement with the experimental fact.