Quantum Mechanics and Spin Systems

Hannah Troger, Ofek Bengyat, Thomas D. Galley +1 more

The standard description of the state of a spin in quantum mechanics presupposes externally fixed directions -- a classical background. Can a spin be fully described instead in relation to other quantum mechanical systems? Poulin suggested twenty years ago group averaging over rotations the joint state of a fundamental spin and a reference spin with large angular momentum which, however, yields a classical bit in a probabilistic mixture. We revisit this idea and show that when the quantum reference system is augmented to \emph{two} large spins, the standard quantum mechanical description of a spin is recovered in the limit of large quantum numbers for the reference system.

Xiaoqin Wang

The applications of the spin exchange operator in quantum mechanics are discussed based on its properties.This method provides a convenient approach for the coupled system of two-body spin.

Ola Bratteli, Derek W. Robinson

Ronald Lee Walsworth, Isaac F. Silvera, Edward M. Mattison +1 more

We extend a nonlinear generalization of quantum mechanics, recently formulated by Weinberg, to systems of composite spin, such as atoms. We have used hydrogen (H) masers to set a limit of 3.7\ifmmode\times\else\texttimes\fi{}${10}^{20}$ eV (8.9 \ensuremath{\mu} Hz) on the magnitude of a nonlinear correction to the quantum mechanics of atomic spins. This result is of comparable magnitude to the limit recently set in a single-valued (nuclear) spin system. In the absence of nonlinear effects, the experiment provides a new and stringent test of H-maser clock performance and the applicability of standard maser theory.

John B. Parkinson, DAMIAN J. J. FARNELL