Equilibration of quantum many-body fast neutrino flavor oscillations

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 nonintegrable 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 νeν¯e⇆νμν¯μ yield a rapid equilibrium satisfying n(νe)n(ν¯e)=n(νμ)n(ν¯μ)=n(ντ)n(ν¯τ) in addition to the standard lepton number conservation in regimes where off-diagonal vacuum oscillations are small compared to ν-ν interactions. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.