Tunneling electro-conductance of atomic Bose condensates

We consider interaction of an electron with a Bose condensate of atoms having electron affinity. Though states of the electron attached to atoms form a continuous band, tunneling through this band is strongly suppressed by quantum fluctuations of the condensate density. We adapt standard field theory methods originally developed for description of a particle propagating trough a disordered potential and present an exactly soluble analytical model of the process. In contrast with the standard description, we take into account inelastic processes associated with quantum transitions in the condensate. Possibilities of the experimental observation of the phenomenon are discussed.