Equilibration of quantum many-body fast neutrino flavor oscillations

TL;DR

This paper investigates the complex flavor evolution of dense neutrino gases in astrophysical environments, showing evidence of quantum chaos, rapid entanglement, and thermodynamic equilibration driven by neutrino-neutrino interactions.

Contribution

It demonstrates that the neutrino flavor evolution in dense gases is non-integrable, exhibits quantum chaos, and can be described by a thermodynamic partition function, providing new insights into neutrino flavor dynamics.

Findings

Neutrino flavor evolution is non-integrable and exhibits quantum chaos.

Neutrinos rapidly entangle and reach flavor equilibrium.

A thermodynamic model predicts average neutrino flavor content.

Abstract

Neutrino gases are expected to form in high density astrophysical environments, and accurately modeling their flavor evolution is critical to understanding such environments. In this work we study a simplified model of such a dense neutrino gas in the regime for which neutrino-neutrino coherent forward scattering is the dominant mechanism contributing to the flavor evolution. We show evidence that the generic potential induced by this effect is non-integrable and that the statistics of its energy level spaces are in good agreement with the Wigner surmise. We also find that individual neutrinos rapidly entangle with all of the others present which results in an equilibration of the flavor content of individual neutrinos. We show that the average neutrino flavor content can be predicted utilizing a thermodynamic partition function. A random phase approximation to the evolution gives a simple picture of this equilibration. In the case of neutrinos and antineutrinos, processes like $\nu_e {\bar{\nu}}_e \leftrightarrows \nu_\mu {\bar{\nu}_\mu} $ yield a rapid equilibrium satisfying $n( \nu_e) n({\bar \nu}_e) = n( \nu_\mu) n({\bar \nu}_\mu) = n( \nu_\tau) n({\bar \nu}_\tau)$ in addition to the standard lepton number conservation in regimes where off-diagonal vacuum oscillations are small compared to $\nu-\nu$ interactions.