Forced Duffing oscillator

Exercises 8.4.5-8.4.11 deal with the forced Duffing oscillator in the limit where the forcing, detuning, damping, and nonlinearity are all weak ... 

If this expected photoemission really takes place, the resultant spectra should reflect the nonhnear dynamics of nonadiabatic vibrational motion under an external field, which is similar to classical driven oscillators such as a forced Duffing oscillator [156, 239]. Therefore various nonlinear phenomena such as limit cycle, frequency locking, and chaos (1.5-dimensional chaos) [156, 239] can be expected, which would be intrinsically originated from the quantmn dynamics. Furthermore, one may be able to control the frequency and amplitude of the photoemission by varying the laser parameters applied. It may be possible to utilize the photoemission as a new optical somce and also as finger-print signals to identify molecular species and/or molecular states. In this section we illustrate the appearance of such... 

Figure 12. The dependence of the activation energy R on the amplitude A of the harmonic driving force F(t) =A cos (1.2r) as determined [141] by electronic experiment (filled circles), numerical sumulations (open circles) and analytical calculation (solid line), based on (28) for an overdamped duffing oscillator U q) = —q2/2 +

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