We apply the model of stimulated neutrino transitions to neutrinos travelling through turbulence on a non constant density profile. We describe a method to predict the location of large amplitude transitions and demonstrate the effectiveness of this method by comparing to numerical calculations using a model supernova (SN) profile. The important wavelength scales of turbulence, both those that stimulate neutrino transformations and those that suppress them, are presented and discussed. We then examine the effects of changing the parameters of the turbulent spectrum, specifically the root-mean-square amplitude and cutoff wavelength, and show how the stimulated transitions model offers an explanation for the increase in both the amplitude and number of transitions with large amplitude turbulence, as well as a suppression or absence of transitions for long cutoff wavelengths. The method can also be used to predict the location of transitions between anti-neutrino states which, in the normal hierarchy we are using, will not undergo Mikheev-Smirnov-Wolfenstein transitions. Lastly, the stimulated neutrino transitions method is applied to a turbulent 2D supernova simulation and explains the minimal observed effect on neutrino oscillations in the simulation as being due to excessive long wavelength modes suppressing transitions and the absence of modes that fulfill the parametric resonance condition.

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. Lastly, 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 J0.

Large amplitude oscillations between the states of a quantum system can be stimulated by sinusoidal external potentials with frequencies that are similar to the energy level splitting of the states or a fraction thereof. Situations where the applied frequency is equal to an integer fraction of the energy level splittings are known as parametric resonances. We investigate this effect for neutrinos both analytically and numerically for the case of arbitrary numbers of neutrino flavors. We look for environments where the effect may be observed and find that supernovae are the one realistic possibility due to the necessity of both large densities and large amplitude fluctuations. In conclusion, the comparison of numerical and analytical results of neutrino propagation through a model supernova reveals that it is possible to predict the locations and strengths of the stimulated transitions that occur.

Here, the transition probabilities for a single neutrino emitted from a point proto-neutron source after passage through a turbulent supernova density profile have been found to be random variates drawn from parent distributions whose properties depend upon the stage of the explosion, the neutrino energy and mixing parameters, the observed channel, and the properties of the turbulence such as the amplitude C*. In this paper we examine the consequences of the recently measured mixing angle ?13 upon the neutrino flavor transformation in supernova when passing through turbulence, in order to provide some clarity as to what one should expect in the way of turbulence effects in the next supernova neutrino burst signal. We find that the measurements of a relatively large value of ?13 means the neutrinos are relatively immune to small, C*≲1%, amplitude turbulence but as C* increases the turbulence effects grow rapidly and spread to all mixing channels. For C*≳10% the turbulence effects in the high density resonance mixing channels are independent of ?13 but nonresonant mixing channels are more sensitive to turbulence when ?13 is large.

Neutrinos are fundamental particles which only interact via gravity and the weak force, which makes them uniquely hard to observe and study experimentally. There are three flavors in the Standard Model (SM) of particle physics, however there has been experimental results that suggest the existence of a theoretical fourth neutrino flavor, called the sterile neutrino, with the three flavors in the SM being active neutrinos. Sterile neutrinos would interact only via the gravity, which means we would only be able to detect them through neutrino oscillations. A potential environment in which active to sterile oscillations could be highly probable to occur is supernovae, due to a large amount of neutrinos being created through nuclear fusion as well as high and varying densities of matter through which the neutrinos propagate. To investigate the evolution of neutrinos in supernova environments and the possibility of stimulated sterile neutrino oscillations, we create a code to simulate the evolution of neutrinos through a supernova density profile.