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

We calculate the effects of random density fluctuations on twoneutrino flavor transformations (ντ(μ) ⇀↽ νe) in the post-core-bounce supernova environment. In particular, we follow numerically the flavor evolution of neutrino states propagating through a stochastic field of density fluctuations. We examine the approach to neutrino flavor depolarization, and study the effects of this phenomenon in both the early shock reheating epoch and the later r-process nucleosynthesis epoch. Our results suggest that significant fluctuation-induced neutrino flavor depolarization effects occur in these environments only when the zero-order (without density fluctautions) evolution of the neutrino states includes adiabatic propagation through resonances (mass level crossings). In the shock reheating epoch, depolarization effects from fluctuations with amplitudes larger than 0.05% of the local matter density can cause an increase in the heating rate of the Permanent address: Department of Physics, University of California, San Diego, La Jolla, CA 92093-0319. Permanent address: Department of Physics, University of Wisconsin, Madison, WI 53706.