Investigation on anomalous diffusion for nuclear fusion reactions

A simple model for diffusion of a particle with initial velocity coupled to a non-Ohmic environment over a barrier is proposed. An exact expression for the passing probability of the particle over a parabolic potential barrier is obtained. It is shown that in the case of subdiffusion, more than half of the particles cannot overcome the barrier, no matter what the initial velocity is. However, in the case of superdiffusion, a minimum critical velocity needed for passing over the barrier is found, which can lead to a strong friction and make the passing probability increase with kinetic energy, but still slower than in the case of normal diffusion. Effects of quantum diffusion and zero point fluctuation are also discussed. The model is applied to solve a long-standing problem in nuclear fusion reactions, though the mechanism found in this study can have a rather broad application.

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