Topological Effect of Reduced Quantum Trajectory in Coherence and Decoherence

The topological expression of the reduced quantum trajectory is given by using ø-mapping topological current theory. The topological expression is used in study of the coherence and the decoherence. We find the expression of vorticity for decoherence has a similar form as that for coherence. Atopological reason leading to the decoherence is given and a new parameter is defined to indicate the coherence degree. The parameter is different from the damping factor because it relates to the topological structure of the reduced quantum trajectory.