Self-tunnelling oscillations in non-linear quantum mechanics and the electron-transfer problem

A small quantum system with a non-linear self-consistent potential may display a spontaneous symmetry breaking of the ground state. This simple result, which can be interpreted also as a spontaneous self-localization of the wavefunction, results in the presence of several equivalent ground states, which do not exist simultaneously. There is a virtual degeneracy in the system. The addition of a stochastic perturbation (noise) to such a system provides the possibility of tunnelling among the different equivalent ground states. The tunnelling process can lock itself in into a characteristic frequency related to the dynamics of the system and not contained in the input noise. A self-pulsating quantum system is then generated based on the intrinsic non-linearity of the dynamics and the presence of noise, which is used as a seed. We inquiry into the relevance of these phenomena for electron transfer processes in large biomolecules. By combining non-linearity and noise a controlled transfer rate can be achieved in what is effectively a quantum-switch regulated by external perturbations; a mechanism that could be at work in many electron-transfer processes in proteins