S. Aubry

Laboratoire Leon Brillouin, CEA Saclay, 91191-Gif-sur-Yvette, France

References

Two resonant and weakly coupled linear oscillators exchange periodically their energy. This phenomena drastically changes when the oscillators are anharmonic because their frequencies depend on their amplitude. Generally resonance does not persist which blocks energy transfer.
However, in very special but highly interesting situations, for a specific initial energy and at arbitrarily weak coupling, the initial resonance may persist during complete energy exchange. This phenomena called Targeted Energy Transfer (TET) may occur not only between two well-tuned classical (called conjugate) anharmonic oscillators but also in complex aperiodic systems between two well-tuned discrete breathers. A simple example of conjugate oscillators consisting of a Morse oscillator weakly coupled to a rotor with well tuned inertia momentum can be investigated analytically. This system may model a discrete breather associated with a chemical bond and a rotobreather located at specific sites relatively far apart of a large molecule. In this example, TET generates the chemical dissociation of this bond shortly after the associated rotor is excited. This hyper selective chemical reaction being ultrafast, the rotor energy has no time to thermalize in the system.
TET can be extended for resonances by higher order harmonics (Fermi resonance). Chemical dissociation may also occur as well by this mechanism for the above rotor-Morse oscillator system but for different parameters. TET also persist in the quantum case. It is then related to the existence of a quantum pathway of almost degenerate eigenenergies which connects the two quantum states where only the donor oscillator or only the acceptor oscillator is excited.