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The production of a sterile species via active-sterile mixing in a thermalmedium is studied in an exactly solvable model. The \emph{exact} time evolutionof the sterile distribution function is determined by the dispersion relationsand damping rates $\Gamma_{1,2}$ for the quasiparticle modes. These depend on$\wtg = \Gamma_{aa}/2\Delta E$, with $\Gamma_{aa}$ the interaction rate of theactive species in absence of mixing and $\Delta E$ the oscillation frequency inthe medium without damping. $\wtg \ll1,\wtg \gg 1$ describe the weak and strongdamping limits respectively. For $\wtg\ll1$, $\Gamma_1 = \Gamma_{aa}\cos^2\tm ;\Gamma_{2}=\Gamma_{aa}\sin^2\tm$ where $\tm$ is the mixing angle in the mediumand the sterile distribution function \emph{does not} obey a simple rateequation. For $\wtg \gg 1$, $\Gamma_1= \Gamma_{aa}$ and $\Gamma_2 = \Gamma_{aa}\sin^22\tm/4\wtg^2$, is the sterile production rate. In this regime sterileproduction is suppressed and the oscillation frequency \emph{vanishes} at anMSW resonance, with a breakdown of adiabaticity. These are consequences ofquantum Zeno suppression. For active neutrinos with standard model interactionsthe strong damping limit is \emph{only} available near an MSW resonance\emph{if} $\sin\theta \lesssim \alpha_w$ with $\theta$ the vacuum mixing angle.The full set of quantum kinetic equations for sterile production for arbitrary$\wtg$ are obtained from the quantum master equation. Cosmological resonantsterile neutrino production is quantum Zeno suppressed relieving potentialuncertainties associated with the QCD phase transition.

Production of a sterile species via active-sterile mixing: an exactly solvable model