Irreversible energy gain by linear and nonlinear oscillators

A particle can gain appreciable irreversible energy ("absorption") from linear or nonlinear oscillations only by ballistic excitation ("collision") or, if excited by an adiabatic pulse of constant frequency, by undergoing resonance. For the linear oscillator it is shown that the transition from ballistic to adiabatic behavior out of resonance occurs for sin²-pulses 2–4 eigenperiod long. In the case of a linear oscillator with time-varying eigenfrequency it is shown that Cornu's double spiral represents an attractor, either for zero energy gain out of resonance or finite gain by transiting through resonance. One of the remarkable properties of nonlinear oscillators is that resonance depends on the level of excitation. It is this property which opens a new access to understanding the dominant heating process at high laser intensities, the so-called collisionless absorption phase in solids, extended cluster media, dusty plasmas, and sprays, well guaranteed by experiments and computer simulations but hitherto not well understood in physical terms.