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An effective, low temperature, classical model for spin transport in theone-dimensional, gapped, quantum $O(3)$ non-linear $\sigma$-model is developed.Its correlators are obtained by a mapping to a model solved earlier by Jepsen.We obtain universal functions for the ballistic-to-diffusive crossover and thevalue of the spin diffusion constant, and these are claimed to be exact at lowtemperatures. Implications for experiments on one-dimensional insulators with aspin gap are noted.Comment: 4 pages including 3 eps-figures, Revte

physical review letters

Low Temperature Spin Diffusion in the One-Dimensional Quantum<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>)</mml:mo></mml:math>Nonlinear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math>Model

Low Temperature Spin Diffusion in the One-Dimensional QuantumO(3)NonlinearσModel