"Paradoxical" coexistence of continuum of 'bound' waves and discrete set   of unlimited motion states
  We have combined two remarkable phenomena: resonance tunneling and Anderson localization. It results in unexpected spectrum reverse to usual notions. It is demonstrated by the quantum system with chaotic distribution of potential resonance tunneling traps over the whole coordinate axis. The corresponding spectrum contains continuum of 'bound' states (Anderson's localization) and discrete tunneling resonances of unlimited wave propagation. It is in contrast to the usual situation with discrete bound and continuum of scattering states. 
V.M. Chabanov, B.N. Zakhariev