Kurt Wiesenfeld

Kurt Wiesenfeld is a physicist whose research includes stochastic resonance and collective dynamical behavior. Georgia Tech's School of Physics profile lists stochastic resonance, spontaneous synchronization and dynamical beam steering among his research topics.^[ref]

The school's identified faculty profile links an external portrait of Kurt Wiesenfeld.

He coauthored Observation of Stochastic Resonance in a Ring Laser by Bruce McNamara and others with Bruce McNamara and Rajarshi Roy. The publisher's abstract establishes the experimentally observed improvement in a periodically modulated optical system with added noise.^[ref] A useful theoretical question is how a random transition rate can relate to the forcing period.

For an original illustrative model, suppose a system has two states with a noise-dependent escape rateThis is an assumed activation-type form, of the kind represented by a Kramers escape rate; it is not a fitted law for the cited laser. If unforced dwell times have an exponential distribution, their mean is $1/r(D)$. A periodic forcing of period $T$ suggests comparing that time with $T/2$, the time between alternating preferences for the two states.

Take stipulated $r_0=1000{\mathrm{s}}^{-1}$, dimensionless $\Delta =1$, and $T=0.1\mathrm{s}$. The mean-dwell matching condition givesAt $D=0.1$, the mean dwell is about 22.03 seconds, far longer than the forcing half-period. At $D=0.5$, it is about 7.39 milliseconds. The calculation explains why too little noise can prevent switching, while rapid random switching can obscure a weak preference.

Matching means is only a heuristic. Exponential dwell times have a spread as large as their mean, and periodic forcing changes the rates over the cycle. The matching calculation alone does not prove phase locking or locate the optimum signal-to-noise ratio. A proposed test records transition times relative to the forcing phase and compares the full response as noise is varied.

This distinction between a simplified rate model and an observed response is central to interpreting stochastic resonance. The example is an original calculation illustrating the theoretical issue; the joint 1988 paper supplies the verified optical observation.