Observable eigenstate overlap in a nonlinear mean-field quantum model

The soliton effect is defined in nonlinear physics by the transformation of a nonlinear time-dependent dynamical system into an equivalent linear spectral eigenproblem whose invariant eigenvalues unambiguously define all the dynamical properties of the original system. We point out the existence of such an effect in a non-relativistic isotropic two-electron mean-field quantum-dot model. It yields the prediction of observable modulation of radiation absorption between its two lowest-energy zero-angular-momentum nonlinear eigenstates (i.e. eigenstates which include electron-electron interaction: hence their non-orthogonality). Characteristic values for such a possible experiment are given in the case of GaAs. Furthermore it provides an intriguing nonlinear definition of the fine-structure constant solely in terms of these eigenstates.