The Study On The Effection Of Yangian On The Geometric Phase

The concept of geometric phase first introduced by Pancharatnam in his study of interferencebetween light waves in distinct states of polarization and rediscovered by Berry for quantalsystems undergoing cyclic adiabatic evolution has been refined and applied during the past years.Aharenov and anandam removed the need of adiahatic external parameters and pointed out thatthe geometric phase could be considered the anholonomy associated with the curvature of theprojective Hilbert space. Samuel extended the geometric the geometric phase to noncyclic andnonunitary evolutions.Geometric phase in an important conception in quantum mechanics. Thedeeply study about geometric phase will help people to understand quantum mechanics. The Quantum Yang-Baxter Equation is one successful theory which deals with nolinearquestion. The theory of Yangian is one important development of the theory of the QuantumYang-Baxter Equation. Yangian is most used to describe symmetry the physical systems and soon. In this paper, we mainly study the impact of Yangian on geometric phase. Firstly we studythe geometric phase of the system with Hamiltonian is H₁=ω₁S_1Z +ω₂S_2Z .,and we give general formof the geometric phase of (?) and (?).The difference between them is studied.