I was told that quantum chaos is just a system whose Hamiltonian's classical version shows chaotic behavior. However, I just wondering
what happens when one eigenstate of this Hamiltonian evolves?
what the chaotic (nonlinear, of course) Hamiltonian looks like in quantum version (for Hamiltonian should be a linear one)?
I know that mean-field theory could reduce the linear Hamiltonian into a nonlinear form, but it is not an exact form.
Maybe a good start point is the BEC equation and GP equation. I hope you can help me here.
For the second question, after a whole year, I think the many-body interaction will directly introduce the nonlinearity. However I still have no idea of how the eigenstate will evolve under "quantum chaotic" Hamiltonian.