Once-in-a-lifetime encounter models for neutrino media. II. Quasisteady states and miscidynamic flavor evolution

We extended the once-in-a-lifetime encounter (OILE) model to stochastic interactions among neutrinos. As in the original OILE model, the new model reproduces the mean-field behavior of a dense neutrino gas for time <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>t</a:mi> <a:mo>≲</a:mo> <a:mo stretchy="false">(</a:mo> <a:mi>μ</a:mi> <a:mi>γ</a:mi> <a:msup> <a:mo stretchy="false">)</a:mo> <a:mrow> <a:mo>−</a:mo> <a:mn>1</a:mn> </a:mrow> </a:msup> </a:math> , where <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>μ</e:mi> </e:math> measures the strength of the mean-field neutrino self-interaction potential and is proportional to the neutrino density, and the dimensionless “impact parameter” <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>γ</g:mi> </g:math> is a measure of the change in the flavor quantum state of a neutrino during interaction with another neutrino when the wave packets of the two neutrinos overlap. As in the mean-field case, the OILE model with random neutrino velocities experiences kinetic flavor decoherence as the flavor quantum states of the neutrinos diverge from each other. Unlike the mean-field case, however, the OILE model has a “collision term” due to the quantum entanglement among neutrinos. For <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>γ</i:mi> <i:mo>≪</i:mo> <i:mn>1</i:mn> </i:math> , this incoherent effect can drive the neutrinos into a quasisteady state that is similar to the collective precession mode in a homogeneous and isotropic neutrino gas in the mean-field approximation. Subsequently, the collision term drives the neutrino gas adiabatically through different quasisteady states and eventually to flavor equilibration. This process is an example of miscidynamic flavor evolution, with the mixing equilibria being the quasisteady precession states.