Some remarks about quantum diffusion for Hubbard models

Some exact results are given, that connect, for a general magnitude of the interaction term U, the repulsive and attractive Hubbard models, in terms o f the eigenspectra and quantum diffusion properties. In particular, it is s hown that, for some initial conditions, the quantum evolution cannot differ entiate between the attractive and repulsive models. These results apply to both fermionic: and bosonic models, in any dimension and for general filli ng, as far as the underlying structure is bi-partite.