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

Abstract

The Quantum Zeno Effect (QZE) implies that a too frequent (${\omega }_{\varphi }\to \infty )$ 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 3-d cubic lattice, ``observe'' each other with a frequency ${\omega }_{\varphi }$ $\propto \sqrt{J_x^2+J_y^2+J_z^2}/\hslash$, where $J$'s are the coupling constants. This leads to a ``diffusive'' spread of a local excitation characterized by the constants $D_{\mu }\propto J_{\mu }^2/{\omega }_{\varphi }.$ Thus, a strongly asymmetric interaction (e.g. $J_y/J_{x(z)}\gg 1$), would hinder diffusion in the perpendicular directions ($D_{x(z)}\to 0$) 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.

RevTeX, 5 pages, 3 Postscript figures, Accepted in PRB, Scheduled tentatively B1 01Mar98

References in corpus (1)

• Attenuation of polarization echoes in NMR: A study of the emergence of dynamical irreversibility in many-body quantum systems

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