Tunnel effect and analysis of the survival amplitude in the nonlinear Winter’s model

In this paper we show how the nonlinearity term affects the tunnel effect and the survival amplitude in the nonlinear Win- ter’s model. In particular, in the case of attractive nonlinearity large enough it turns out that the tunnel effect is going to disappear. Furthermore, the difficulty in giving a rigorous and appropriate definition of quantum resonances by means of the notions already used for linear equations is also highlighted.