A link between Random Matrix Theory and neutrino propagation in a turbulent medium

TL;DR

This paper explores the potential of Random Matrix Theory to model neutrino flavor depolarization caused by turbulence in supernovae, providing a new theoretical framework for understanding complex numerical results.

Contribution

It proposes using RMT to interpret neutrino flavor evolution in turbulent supernova environments, bridging a gap between numerical simulations and theoretical models.

Findings

Numerical distributions of neutrino crossing and survival probabilities align with RMT predictions.

RMT offers a promising approach to understanding neutrino depolarization effects.

The study supports the applicability of RMT in modeling complex neutrino flavor transformations.

Abstract

It is becoming ever clearer that the neutrino signal from the next supernova in our Galaxy can reveal missing information about the neutrino as well as allowing us to probe the explosion of the star by decoding the temporal and spectral evolution of the flavor composition of the signal. But this information may be lost if turbulence in the supernova `depolarizes' the neutrinos so that the observed flux for each flavor is an equal mixture of the initial - unencoded - spectra. Determining if depolarization occurs is one of the most pressing issues of this field. The most difficult aspect of studying the effect of turbulence upon the neutrinos is the lack of any theoretical models that allow us to understand the results of numerical studies. This paper makes the suggestion that Random Matrix Theory (RMT) may shine some light in this direction and presents support for this the possibility by comparing the distribution of crossing and survival probabilities obtained numerically for some `test case' calculations with the distributions one expects from RMT in the calculable limit of depolarization of N neutrino flavors.