  In astrophysical environments, neutrinos may propagate over a long distance
in a magnetic field. In the presence of a rotating magentic field, the neutrino
spin can flip from left-handed neutrino to right-handed neutrino. Smirnov
demonstrated that the pure state geometric phase due to the neutrino spin
precession may cause resonantg spin conversion inside the Sun. However, in
general, the neutrinos may in an ensemble of thermal state. In this article,
the corresponding mixed state geometric phases will be formulated, including
the off-diagonal casse and diagonal ones. The spefic features towards
temperature will be analysized.
