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

TL;DR

This paper demonstrates how the Quantum Zeno Effect causes dimensional crossover in spin diffusion within a 3D lattice, with asymmetric interactions suppressing diffusion in certain directions, supported by numerical and experimental evidence.

Contribution

It introduces a novel connection between the Quantum Zeno Effect and spin diffusion anisotropy, supported by numerical simulations and experimental observations.

Findings

Asymmetric interactions hinder diffusion in perpendicular directions.

Quantum Zeno Effect manifests as dimensional crossover in spin diffusion.

Experimental evidence from paramagnetic compounds supports the theoretical model.

Abstract

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 3-d cubic lattice, ``observe'' each other with a frequency $\omega_\phi $ $\propto \sqrt{J_x^2+J_y^2+J_z^2}/\hbar $, where $J$'s are the coupling constants. This leads to a ``diffusive'' spread of a local excitation characterized by the constants $D_\mu \propto J_\mu ^2/\omega_\phi .$ 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.