Feigenbaum scenario in the dynamics of a metal–oxide semiconductor heterostructure under harmonic perturbation. Golden mean criticality

Experimental investigations and theoretical analysis on the dynamics of a metal–oxide semiconductor heterostructure used as nonlinear capacity in a series RLC electric circuit are presented. A harmonic voltage perturbation can induce various nonlinear behaviours, particularly evolution to chaos by period doubling and torus destabilization. In this work we focus on the change in dynamics induced by a sinusoidal driving with constant frequency and variable amplitude. Theoretical treatment based on the microscopic mechanisms involved led us to a dynamic system with a piecewise behaviour. Consequently, a model consisting of a nonlinear oscillator described by a piecewise second order ordinary differential equation is proposed. This kind of treatment is required by the asymmetry in the behaviour of the metal–oxide semiconductor with respect to the polarization of the perturbing voltage. The dynamics of the theoretical model is in good agreement with the experimental results. A connection with El Naschie’s E-infinity space-time is established based on the interpretation of our experimental results as evidence of the importance of the golden mean criticality in the microscopic world.