Three-flavor neutrino oscillations using the phase space approach

The phase-space approximation (PSA) approach, originally applied in [] to describe neutrino oscillations from a dense astrophysical source such as a core-collapse supernova in the two-flavor limit, is extended here to describe the more realistic case where neutrinos can oscillate between three different flavors. The approach is successfully validated against the exact solutions up to eight neutrinos. In all cases where the exact solution is feasible, the PSA provides excellent reproduction of the neutrino oscillation dynamics. By replacing the full problem with a set of simple mean-field equations, the PSA offers a versatile, predictive, and easily parallelizable approach for tackling three-flavor problems. This enables the simulation of large-scale neutrino oscillations, as illustrated here with simulations involving up to 300 neutrinos. Even if direct comparison to exact solutions is only feasible for small systems (up to eight neutrinos), where PSA shows excellent agreement, its applicability in the large- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>N</a:mi> </a:math> regime appears promising, although a full quantitative validation remains beyond current computational capabilities. Additionally, the method also provides insight into the system’s equilibration properties.