Realization Of Yangian Research Articles

A Realization and Truncation of Yangian Algebra in theGeneralized Hydrogen Atom with a U(1) Monopole

We establish an extended hydrogen atom associated with aU(1) monopole in which a realization of Yangian Y(sl(2)) isproposed and the energy spectrum is also given. By solvingthe RTT relation R(u−v)[T(u)⊗T(v)] = [T(v)⊗T(u)]R(u−v)for the truncation T(3) = 0, the obtainedmodel is shown to be related to the truncated Yangian.

A Realization of Yangian and Its Applications to the Bi-spin System in an External Magnetic Field**The project supported by National Natural Science Foundation of China

Yangian Y(sl(2)) is realized in the bi-spin system coupled with a time-dependent external magnetic field. It is shown that Y(sl(2)) generators can describe the transitions between the “spin triplet” and the “spin singlet” that evolve with time. Furthermore, new transition operators between the states with Berry phase factor and those between the states of nuclear magnetic resonance are presented.