Thanks a lot!When the electric field is strong, the Wannier state is localized, see the article
by M Dignam in Phys. Rev. B in 1994.
They are quasi-stable, they are resonant state.
See also the Dignam's article
For one dimensional tight binding lattice, without interband tunneling, the Wannier-Stark stateThanks a lot!
Why are they quasi-stable?
I take a tight-binding model, and numerically diagonalize the hamiltonian, and find out the eigenstates, i find that the eigenstates are all well-localized and of the same shape. Of course, except for those near the boundary.
For one dimensional tight binding lattice, without interband tunneling, the Wannier-Stark state
is rigorous localized state. and the eigenenergy is equidistant.
If there exists interband tunneling, the WS state is a resonant state and quasi-stable.