MODULATIONAL INSTABILITY OF A WAVE SCATTERED BY A NONLINEAR CENTER

We consider scattering of a quantum particle by a potential which incl udes a delta function whose amplitude is nonlinear in the wave functio n. Solution of the scattering problem in this model is nonunique in a certain interval of amplitudes of the incident wave. We demonstrate th at the nonlinearity gives rise to an oscillatory instability of the sc attering solutions, which is a localized version of the well-known mod ulational instability of the nonlinear Schrodinger equation. We also c onsider a nonlinear regime slightly above the instability threshold. T he results obtained can be applied to the problem of single-particle t unneling through an ultrashort junction in the presence of multipartic le interaction. Our prediction is that the instability gives rise to a n ac component in the transmitted current.