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Quantum mechanical methods for getting geometric phases for mixed states areanalyzed. Parallel transport equations for pure states are generalized to mixedstates by which dynamical phases are eliminated. The geometric phases of mixedstates are obtained as Pancharatnam phases which are valid also for opencycles. The geometric phases are derived here by SU(2) transformations of mixedthermal states which are different from those used in NMR and neutroninterference experiments. While the zeroth order Hamiltonian is given by theinteraction of a magnetic moment and constant magnetic field in the zdirection, the high order perturbations assumed in the present article arecomposed of two oscillating magnetic fields in the same z direction. Theseassumptions lead to a special form of the SU(2) unitary transformation of themixed thermal states by which results for geometric phase and for interferenceintensity are derived.

Geometric phases for a thermal two-dimensional mixed spin 1/2 system