Horseshoe chaos and subharmonic orbits in the nanoelectromechanical Casimir nonlinear oscillator

SUMMARY

The progressive miniaturization of electronic components today makes feasible to exploit the nanoscale level. At this scale, phenomena peculiar of the quantum world arise, which can be exploited to realize innovative and potential breakthrough devices. In this paper, the dynamic behavior of one such device, the Casimir nonlinear oscillator is analyzed. Using the Melnikov's method, we prove that under the effect of a weak damping and a weak periodic forcing, complex behaviors in the form of Smale's horseshoes arise, and the mechanism leading to their birth is revealed. Copyright © 2012 John Wiley & Sons, Ltd.

Nanotechnology suggests the possibility to exploit quantum phenomena to realize innovative electronic components. The Casimir oscillator is a nonlinear device, where the nonlinearity stems from a quantum electrodynamical effect: the Casimir force. In this paper, the dynamics of the Casimir oscillator is analyzed. It is shown that under the effect of periodic perturbations, the oscillator can exhibit complex dynamics in the form of Smale horseshoes and subharmonic periodic orbits.