Stimulated Neutrino Transformation Through Turbulence

We derive an analytical solution for the flavor evolution of a neutrino through a turbulent density profile which is found to accurately predict the amplitude and transition wavelength of numerical solutions on a case-by-case basis. The evolution is seen to strongly depend upon those Fourier modes in the turbulence which are approximately the same as the splitting between neutrino eigenvalues. Transitions are strongly enhanced by those Fourier modes in the turbulence which are approximately the same as the splitting between neutrino eigenvalues. We also find a suppression of transitions due to the long wavelength modes when the ratio of their amplitude and the wavenumber is of order, or greater than, the first root of the Bessel function $J_0$.