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理论物理通讯：英文版

A Realization of Yangian and Its Applications to the Bi—spin System in an External Magnetic Field

JINShuo, XUEKang

Published Jan 1, 2003• 0 citations
OpenAlex

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 are presented.

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Jilin Normal University Journal•Jan 1, 2007•0 citations
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.
Yangian Y(sl(2))Y(sl(2))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))Y(sl(2))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.
Linear canonical transformation and time transformation are used within the formalism of path integrals in coherent state representation to solve the problem of an interacting spin with arbitrary time-dependent external magnetic fields. The Factorization technique is used to solve the equation of motion. Examples of the calculation of the transition probability in terms of elementary functions and special functions for solvable systems are presented. For completeness Berry's phase is also derived under adiabatic expansion.