Dynamics of coupled quantum spin chains

Static and dynamical properties of weakly coupled antiferromagnetic spin chains are treated using a mean--field approximation for the interchain coupling and exact results for the resulting effective one--dimensional problem. Results for staggered magnetization, N\'eel temperature and spin wave excitations are in agreement with experiments on $\rm KCuF_3$. The existence of a narrow longitudinal mode is predicted. The results are in agreement with general scaling arguments, contrary to spin wave theory.