Dynamics of Bloch electrons in external electric fields. II. The existence of Stark-Wannier ladder resonances

For pt.I see ibid., vol.14, no.10, p.2817-27 (1981). The problem of the existence of the Stark-Wannier ladder for the Bloch electrons in homogeneous electric fields is considered. If the direction of the electric field coincides with one of the reciprocal lattice vectors, as is well known, the Hamiltonian of the problem can be written as a direct integral of one-dimensional-like Hamiltonians. For these Hamiltonians, the existence of Stark-Wannier ladders of well separated resonances is proved. The wavefunctions corresponding to these resonances are shown to decay exponentially along the field direction.