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IBM Journal of Research and Development  
Volume 32, Number 1, Page 119 (1988)
Basic Concepts in Quantum and Stochastic T...
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Bistability in active circuits: Application of a novel Fokker–Planck approach

by R. Hanggi, P. Jung
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.
Related Subjects: Quantum theory and effects