Dimensional Crossover in Spin Diffusion: A manifestation of the Quantum Zeno Effect

الأصل · EN

The Quantum Zeno Effect (QZE) implies that a too frequent (ωϕ→ ∞) 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 3-d cubic lattice, ``observe'' each other with a frequency ωϕ ∝ √Jₓ²+Jy²+Jz²/ℏ, where J's are the coupling constants. This leads to a ``diffusive'' spread of a local excitation characterized by the constants Dμ∝ Jμ²/ωϕ. Thus, a strongly asymmetric interaction (e.g. Jy/Jₓ₍z₎≫ 1), would hinder diffusion in the perpendicular directions (Dₓ₍z₎→ 0) manifesting the QZE. We show that this effect is present in numerical solutions of simple 2-d 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. New experimental designs are proposed.