Statistical Dynamics of the Gunn Instability near Threshold

The threshold behavior of the Gunn instability is investigated. A coupled mode equation for the fluctuating electric field is reduced to a nonlinear Langevin equation that describes the stochastic motion of a single mode. The steady-state probability density for the field fluctuations is expressed in a simple exponential form, as in the case of a single mode laser. It is found that the probability density has two peaks in a region below threshold, one of which appears at the zero field and the other at a nonzero value of the field intensity. This gives rise to a hysteresis effect for the threshold behavior of the Gunn instability. The conclusion is that the Gunn instability is an example of first-order phase transitions in systems far from thermal equilibrium.