If the modes have very different decay rates, one of them can serve as a thermal reservoir for another, cf. The quantum situation changes if the resonating modes are dissipative. On the quantum side, nonlinear resonance is in some sense simpler in the absence of dissipation, as its primary signature is the familiar level repulsion. However, the actual picture in nonlinear resonance is more complicated, extending to dynamical chaos. This is reminiscent of the energy oscillations between two coupled harmonic oscillators with close frequencies. In conservative classical systems, nonlinear resonance leads to energy oscillations between the resonating modes. These mesoscopic systems provide unprecedented access to studying, using, and controlling this complicated phenomenon. Recently, nonlinear resonance has attracted particular interest in the context of nano- and micro-mechanical vibrational systems 7, 8, 9, 10, 11, 12, 13, 14, 15 and microwave cavities used in quantum information 16, 17. The resonance has been observed in a broad range of systems, from celestial bodies to ecological systems to molecules 3, 4, 5, 6. It goes back at least to Laplace and Poincare on the classical side and to the Fermi resonance on the quantum side 1, 2. The study of nonlinear resonance has a long history in quantum and classical mechanics. The resonance effects are most pronounced where both the numerator and the denominator of the corresponding fraction are comparatively small integers, for example, where one of the frequencies is twice or three times the other. The nonlinear resonance occurs where two vibrational frequencies in the system are commensurate, i.e., their ratio is a rational number. The results provide insight into recent experimental results by several groups and suggest new ways of characterizing and controlling nanomechanical systems. Depending on the initial conditions, with increasing time it can display an extremely sharp or a comparatively smooth crossover between different regimes. Where the decay of both modes is slow compared to the rate of resonant energy exchange, the decay is accompanied by amplitude oscillations. We demonstrate the possibility of a strongly nonmonotonic dependence of the decay rate on the amplitude if one of the modes serves as a thermal reservoir for another mode. We show that such coupling can lead to anomalous decay of the modes where they go through nonlinear resonance, so that their amplitude-dependent frequencies become commensurate. Many nontrivial aspects of the vibration dynamics arise from the coexistence of several nonlinearly coupled modes. Because of the small size of nanomechanical systems, their vibrations become nonlinear already for small amplitudes.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |