Collisional Effects in The Neutrino Flavor Pendulum*

Neutrino flavor oscillation occurs because neutrinos emitted in a certain flavor are composed of a superposition of different neutrino mass states. In a dense enough environment, neutrino self-interactions synchronize flavor on large scales. In the two-flavor approximation, the resulting dynamics show similar behavior to the classical spinning top and inverted pendulum under some conditions. We explore the neutrino flavor pendulum with the addition of charged-current interactions and absorption/emission processes, investigating collisional effects in densities and time scales relevant to the isotropic and monochromatic emission of neutrinos from core-collapse supernovae, similar to neutrino the bulb model. We are able to identify the synchronized and bipolar modes of oscillation and constrain the polarization pendulum to a sphere and a circle in flavor space. We observe an unequal flavor distribution caused by symmetrical collisional rates in (anti)neutrino populations and find limits to the self-interaction energy required for this behavior.