Targeted energy transfer by Fermi resonance

The earlier theory of targeted energy transfer (TET) [S. Aubry, G. Kopidakis, A.M. Morgante, G.P. Tsironis, Physica B 296 (2001) 222] between weakly coupled nonlinear oscillators (or discrete breathers) is extended to the case where the nonlinear oscillators are resonant by harmonics (Fermi resonance). Defining new detuning and coupling functions depending on the order of the resonance, it is shown that complete energy transfer may also occur by harmonics resonance under a condition similar to those of TET. This effect is called Fermi targeted energy transfer (or FTET). heory of FTET is applied for the weakly coupled rotor-Morse oscillator system modelling selective chemical dissociation described in [A. Memboeuf, S. Aubry, preprint submitted to Physica D]. It is shown that chemical dissociation still occur by Fermi resonance at least up to resonance of order 5. Quantum FTET is also briefly discussed and shown to be related to the existence of a path of degenerate quantum states at the uncoupled limit.