  We propose a new approach to explore CPT violation of neutrino oscillation
through a fluctuating matter based on time-dependent geometric quantities. By
mapping the neutrino oscillation onto a Poincare sphere structure, we obtain an
analytic solution of master equation and further define the geometric
quantities, i.e., radius of Poincare sphere and geometric phase. We find that
the mixing process between electron and muon neutrinos can be described by the
radius of Poincare sphere that depends on the intrinsic CP-violating angle.
Such a radius reveals a dynamic mechanism of CPT-violation, i.e., both
spontaneous symmetry breaking and Majorana-Dirac neutrino confusion. We show
that the time-dependent geometric phase can be used to find the neutrino nature
and observe the CPT-violation because it is strongly enhanced under the
neutrino propagation. We further show that the time-dependent geometric phase
can be easily detected by simulating the neutrino oscillation based on
fluctuating magnetic fields in nuclear magnetic resonance, which makes the
experimental observation of CPT-violation possible in the neutrino mixing and
oscillation.
