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We propose a new approach to explore CPT violation of neutrino oscillationthrough a fluctuating matter based on time-dependent geometric quantities. Bymapping the neutrino oscillation onto a Poincare sphere structure, we obtain ananalytic solution of master equation and further define the geometricquantities, i.e., radius of Poincare sphere and geometric phase. We find thatthe mixing process between electron and muon neutrinos can be described by theradius of Poincare sphere that depends on the intrinsic CP-violating angle.Such a radius reveals a dynamic mechanism of CPT-violation, i.e., bothspontaneous symmetry breaking and Majorana-Dirac neutrino confusion. We showthat the time-dependent geometric phase can be used to find the neutrino natureand observe the CPT-violation because it is strongly enhanced under theneutrino propagation. We further show that the time-dependent geometric phasecan be easily detected by simulating the neutrino oscillation based onfluctuating magnetic fields in nuclear magnetic resonance, which makes theexperimental observation of CPT-violation possible in the neutrino mixing andoscillation.

Exploration of CPT violation via time-dependent geometric quantities embedded in neutrino oscillation through fluctuating matter