Role of non-gaussian quantum fluctuations in neutrino entanglement

TL;DR

This paper investigates how non-Gaussian quantum fluctuations and entanglement among neutrinos influence their flavor evolution, using phase-space methods and exact solutions in a simplified two-beam system.

Contribution

It introduces a phase-space approach to model neutrino entanglement and quantum fluctuations, providing new insights into neutrino flavor dynamics in dense environments.

Findings

Neutrino entanglement causes strong phase-space delocalization.

Quantum fluctuations are largely non-Gaussian and significant.

The phase-space method accurately captures entanglement effects.

Abstract

The flavor evolution of neutrinos in environments with large neutrino number densities is an open problem at the nexus of astrophysics and neutrino flavor physics. Among the many unanswered questions pertaining to this problem, it remains to be determined whether neutrino-neutrino coherent scattering can give rise to nontrivial quantum entanglement among neutrinos, and whether this can affect the flavor evolution in a meaningful way. To gain further insight into this question, here we study a simple system of two interacting neutrino beams, and obtain the exact phase-space explored by this system using the Husimi quasi-probability distribution. We observe that the entanglement induced by the coupling leads to strong delocalization in phase-space with largely non-Gaussian quantum fluctuations. The link between the neutrino entanglement and quantum fluctuations is illustrated using the one- and two-neutrino entropy. In addition, we propose an approximate phase-space method to describe the interacting neutrinos problem, where the exact evolution is replaced by a set of independent mean-field evolutions with a statistical sampling of the initial conditions. The phase-space approach provides a simple and accurate method to describe the gross features of the neutrino entanglement problem. Applications are shown using time-independent and time-dependent Hamiltonians in the non-adiabatic regime.