Why Bohmian velocity might not be the only quantum velocity and the role of quantum diffusion flux is super-luminal wave packets

In this short-length paper, we will present some math that play a central role in quantum hydrodynamics and that were presented by Mita in the past. In this formulation of QM, a quantity is involved which is called the diffusion flux. As we will see, this quantity plays a crucial role on the evolution of wave packets. More specifically, we will initially briefly explain some results derived in Mita's papers, by analyzing Gaussian and soliton wave packets, while our main focus is on the role of diffusion in the evolution of super-luminal wave packets. Also, A very brief discussion will be made about the presence of the osmotic velocity field in quantum dynamics