Bistability in active circuits: Application of a novel Fokker-Planck approach

The problem of metastability in electronic circuits with negative differential resistance, originally pioneered by Landauer in 1962, is reconsidered from the viewpoint of a Fokker-Planck modeling for nonlinear shot noise (master equation). A novel Fokker-Planck approximation scheme is presented that describes correctly the deterministic flow and the long-time dynamics of the master equation. It is demonstrated that the conventional scheme of a truncated Kramers-Moyal expansion at the second order overestimates the transition rates in leading exponential order. In order to obtain the correct relative stability, the novel scheme uses a diffusion coefficient which incorporates information about global nonlinear fluctuations characterized by the whole set of higher-order Kramers-Moyal transport coefficients.