Multi-barrier resonant tunnelling for the one-dimensional nonlinear Schroedinger Equation

For the stationary one-dimensional nonlinear Schroedinger equation (or Gross-Pitaevskii equation), nonlinear resonant transmission through a finite number of equidistant identical barriers is studied using a (semi-)analytical approach. In addition to the occurrence of bistable transmission peaks known from nonlinear resonant transmission through a single quantum well (respectively a double barrier), complicated (looped) structures are observed in the transmission coefficient which can be identified as the result of symmetry breaking similar to the emergence of self-trapping states in double-well potentials. Furthermore, it is shown that these results are well reproduced by a nonlinear oscillator model based on a small number of resonance eigenfunctions of the corresponding linear system.