  While the cosmic baryon asymmetry has been measured at high accuracy to be
6.1*10^-10, a corresponding lepton asymmetry could be as large as 10^-2 if it
hides in the neutrino sector. It has been known for some time that a large
asymmetry can be generated from a small initial asymmetry given the existence
of a sterile neutrino with a mass less than the mass of the active neutrino.
While the magnitude of the final lepton asymmetry is deterministic, its sign
has been conjectured to be chaotic in nature. This has been proven in the
single momentum approximation, also known as the quantum rate equations, but
has up to now not been established using the full momentum dependent quantum
kinetic equations. Here we investigate this problem by solving the quantum
kinetic equations for a system of 1 active and 1 sterile neutrino on an
adaptive grid. We show that by increasing the resolution oscillations in the
lepton asymmetry are eliminated and that the sign of the lepton asymmetry is in
fact deterministic. This paper also serves as a launch paper for the adaptive
solver LASAGNA which is available at http://users-phys.au.dk/steen.
