Abstract
Geometric phase in a two-level atom with a fluctuating magnetic field is calculated by a nonunit vector ray in a complex projective Hilbert space, where the nonunit vector is a map connecting with density matrices of a quantum open system. We find that the Pancharatnam phase oscillates with evolving time. The Berry phase depends on the fluctuating parameter but it is proportional to the area spanned in the Bloch parameter space.
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