Regular and erratic quantum dynamics in spin 1/2 rings with an XY Hamiltonian

The dynamics of spin polarization driven by the XY Hamiltonian of a spin 1/2 ring of an arbitrary length is studied analytically and numerically. The initial polarization localized on a single spin splits into sub-packets propagating around the ring in opposite directions. A simple analytical approximation for the spin polarizations is found for a large ring for times less than half the period of the wave propagation around the ring. The initially regular appearance of the polarization transforms into erratic behavior at longer times due to the complex interference of the spin–wave packets. The dynamics of polarization of the ring is compared with that of a linear spin 1/2 chain.