Quantum tunnelling, non-trapping and the existence of Stark ladder resonances

The authors announce results which establish the existence of Stark-Wannier resonances in one-dimension in the semiclassical regime of small Planck's constant. They also obtain estimates on the width of these resonances, including dependence of the width on the electric field in certain cases. They discuss the proofs of these results which utilise many recently developed ideas concerning resonances in quantum mechanics.