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We calculate the effects of random density fluctuations on two-neutrinoflavor transformations (${\nu}_{\tau(\mu)} \rightleftharpoons {\nu}_e$) in thepost-core-bounce supernova environment. In particular, we follow numericallythe flavor evolution of neutrino states propagating through a stochastic fieldof density fluctuations. We examine the approach to neutrino flavordepolarization, and study the effects of this phenomenon in both the earlyshock reheating epoch and the later r-process nucleosynthesis epoch. Ourresults suggest that significant fluctuation-induced neutrino flavordepolarization effects occur in these environments only when the zero-order(without density fluctautions) evolution of the neutrino states includesadiabatic propagation through resonances (mass level crossings). In the shockreheating epoch, depolarization effects from fluctuations with amplitudeslarger than 0.05% of the local matter density can cause an increase in theheating rate of the material behind the shock compared to the case with noneutrino flavor transformation - but this corresponds to a significant decreasein this quantity relative to the case with adiabatic neutrino transformation.If r-process nucleosynthesis is to occur during the late stages of supernovaevolution, then the requirement of neutron-rich conditions excludes a region ofneutrino mass-squared difference and vacuum mixing angle ($\delta m^2,\\sin^22\theta$) parameter space for neutrino flavor transformation. We findthat in the presence of stochastic fluctuations, this excluded region is notsignificantly altered even for random fluctuations with an amplitude of 1% ofthe local matter density.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Effects of random density fluctuations on matter-enhanced neutrino flavor transitions in supernovas and implications for supernova dynamics and nucleosynthesis