13 - Transition probabilities and spectral density of fluctuations of noise driven bistable systems

Summary

Introduction

One of the important problems of physical kinetics is the investigation of relaxation and fluctuation phenomena in systems which have two or more stable states. Bi- and multistable systems are studied in various fields of physics, and the causes of multistability and the types of stable states are different in different cases. For systems moving in static potential fields (disregarding the interactions that give rise to relaxation and fluctuations in a system) multistability takes place if a potential has several minima. In this case the stable states are the equilibrium states. A number of systems of this type are investigated in solid state physics; in particular, diffusing atoms and impurity centers that reorient within a unit cell (see Narayanamurti and Pôhl, 1970).

Multistability may also arise in systems driven by an external periodic field. The constrained vibrations correspond to the stable states in this case (the attractors with a more complicated structure may also appear here). In particular, nonlinear oscillators of various physical nature refer to such systems (see Landau and Lifshitz, 1976). It is well known that in a certain frequency range the dependence of the amplitude A of the constrained vibrations of a nonlinear oscillator on the resonant external field amplitude h may be S-shaped (cf. curve (c) in Figure 13.1). In the range of the non-singlevalued dependence A(h) the states with the largest and smallest A are stable.