= Kurt Wiesenfeld
{c}
<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.<Kurt Wiesenfeld profile by Georgia Tech School of Physics>[Research section]{ref}
The school's identified https://physics.gatech.edu/user/kurt-wiesenfeld[faculty profile] links an external https://physics.gatech.edu/sites/default/files/profile/photo/kwiesenfeld-qbios.jpg[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.<Observation of Stochastic Resonance in a Ring Laser by Bruce McNamara and others>[Publisher byline and Abstract]{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 rate
$$
r(D)=r_0e^{-\Delta/D},\qquad r_0>0,\quad\Delta,D>0.
$$
This 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 gives
$$
r(D)=\frac2T=20\,\mathrm{s^{-1}},\qquad
D=\frac1{\log50}\approx0.2556.
$$
At $D=0.1$, 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.
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