Dimensional crossover in spin diffusion: A manifestation of the quantum Zeno effect

The quantum Zeno effect (QZE) implies that a too frequent $({\omega }_{\phi }\to \infty )$ observation of a quantum system would trap it in its initial state, even though it would be able to evolve to some other state if not observed. In our scheme, interacting spins in a three-dimensional cubic lattice, “observe” each other with a frequency ${\omega }_{\phi }\propto \sqrt{J_x^2{+J}_y^2{+J}_z^2}/ħ$, where the $J$’s are the coupling constants. This leads to a “diffusive” spread of a local excitation characterized by the constants $D_{\mu }\propto J_{\mu }^2/{\omega }_{\phi }.$ Thus, a strongly asymmetric interaction (e.g., $J_y{/J}_{x\left(z\right)\mathrm{}}\gg 1)$, would hinder diffusion in the perpendicular directions ${(D}_{x\left(z\right)\mathrm{}}\to 0)$ manifesting the QZE. We show that this effect is present in numerical solutions of simple two-dimensional systems. This reduction in the diffusion kinetics was experimentally observed in paramagnetic compounds where the asymmetry of the interaction network manifests through an exchange narrowed linewidth. Experimental designs are proposed.