A realization of Yangian and its applications to the bi-spin system

TL;DR

This paper realizes the Yangian algebra in a bi-spin system with a time-dependent magnetic field, demonstrating its role in state transitions and introducing new operators relevant to Berry phases and NMR.

Contribution

It presents a novel realization of Yangian $Y(sl(2))$ in a dynamic bi-spin system and introduces new transition operators for Berry phase and NMR states.

Findings

Yangian generators describe spin state transitions over time.

New transition operators connect states with Berry phase.

Application to NMR states enhances understanding of quantum transitions.

Abstract

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 (NMR) are presented.