TEMPORAL OSCILLATIONS OF CURRENT TUNNELING THROUGH A POINT JUNCTION

We consider scattering of quantum particles by a potential which inclu des a deltafunction whose amplitude contains a term proportional to th e density of particles. This is the simplest model of the single-parti cle tunneling through an ultrashort junction in the presence of the mu ltiparticle interactions. Solution of the scattering problem in this n onlinear model is non-unique in a certain interval of amplitudes of th e incident wave. We demonstrate that the nonlinearity gives rise to an oscillatory instability of the scattering solutions, which has a thre shold in the density of particles as well as in the single-particle en ergy. The instability must manifest itself, generating an ac component in the transmitted current.