Abstract
We study the spin-wave dynamics of the one-dimensional Heisenberg ferromagnet with random exchange couplings J. The problem becomes equivalent to considering an electronic wavepacket put on an initial site in a chain with correlated off-diagonal disorder, where the bonds are random in pairs. The mean-square displacement of the wavepacket versus time is shown to display asymptotically super-diffusion (σ 2( t)∼ t 3 2 ) and localization (σ 2( t)∼const), depending on whether the average over the disorder 〈1/ J〉 exists or not. In the critical intermediate case ordinary diffusion σ 2( t)∼ t is obtained. We show that the dynamical behaviour relates closely to the corresponding spectral density and the localization length singularities whose type is demonstrated.
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