Resonance solutions of the nonlinear Schrodinger equation in an open double-well potential

The resonance states and the decay dynamics of the nonlinear Schrodinger (or Gross-Pitaevskii) equation are studied for a simple, but flexible, model system, the double delta-shell potential. This model allows analytical solutions and provides insight into the influence of the nonlinearity on the decay dynamics. The bifurcation scenario of the resonance states is discussed as well as their dynamical stability properties. A discrete approximation using a biorthogonal basis is suggested which allows an accurate description even for only two-basis states in terms of a nonlinear, non-Hermitian matrix problem.