MSW Solutions to the Solar Neutrino Problem in Presence of Noisy Matter   Density Fluctuations
  We study the effect of random matter density fluctuations in the sun on resonant neutrino conversion in matter by solving numerically the evolution equation for the neutrino system including the full effect of the random matter density fluctuations of given amplitude and correlation length. In order to establish the possible effect on the MSW solutions to the solar neutrino problem we perform a global analysis of all the existing observables including the measured total rates as well as the Super-Kamiokande measurement on the time dependence of the event rates during the day and night and the recoil electron energy spectrum. We find the effects of random noise to be larger for small mixing angles and they are mostly important for correlation lengths in the range few 100 km $\lesssim L_0\lesssim$ few 1000 km. They can be understood as due to a parametric resonance occuring when the phase acquired by the oscillating neutrino state on one fluctuation length L_0 is a multiple of 2$\pi$. We find that this resonant parametric condition is mainly achieved for low energy neutrinos such as the pp-neutrinos and therefore its effect is mostly seen on the total event rates while the other Super-Kamiokande observables are very marginally sensitive to the presence of noise due to the higher energy threshold. 
A.A. Bykov, M.C. Gonzalez-Garcia, C. Pe\~na-Garay, V.Yu. Popov, and   V.B. Semikoz