Quantum mechanical methods for getting geometric phases for mixed states are analyzed. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases are derived by SU(2) transformations of mixed states wgeometric phase,hich are different from those used in NMR and neutron interference experiments. The mixed states are obtained as two-dimensional thermal states. The SU(2) transformations include time dependent parameters which are function of the magnetic fields interactions in times which are short relative to relaxation times. These conditions lead to a special form of the unitary transformation of the mixed thermal states by which results for geometric phase and for interference intensity are derived
Quantum mechanical methods for getting geometric phases for mixed states are analyzed. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases are derived by SU(2) transformations of mixed states wgeometric phase,hich are different from those used in NMR and neutron interference experiments. The mixed states are obtained as two-dimensional thermal states. The SU(2) transformations include time dependent parameters which are function of the magnetic fields interactions in times which are short relative to relaxation times. These conditions lead to a special form of the unitary transformation of the mixed thermal states by which results for geometric phase and for interference intensity are derived
Quantum mechanical methods for getting geometric phases for mixed states are analyzed. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases of mixed states are obtained as Pancharatnam phases which are valid also for open cycles. The geometric phases are derived here by SU(2) transformations of mixed thermal states which are different from those used in NMR and neutron interference experiments. While the zeroth order Hamiltonian is given by the interaction of a magnetic moment and constant magnetic field in the z direction, the high order perturbations assumed in the present article are composed of two oscillating magnetic fields in the same z direction. These assumptions lead to a special form of the SU(2) unitary transformation of the mixed thermal states by which results for geometric phase and for interference intensity are derived.