Stability of spectral eigenspaces in nonlinear Schrodinger equations
  We consider the time-dependent non linear Schrodinger equations with a double well potential in dimensions d =1 and d=2. We prove, in the semiclassical limit, that the finite dimensional eigenspace associated to the lowest two eigenvalues of the linear operator is almost invariant for any time. 
Dario Bambusi and Andrea Sacchetti