Low Temperature Relaxational Dynamics of the Ising Chain in a Transverse Field

We present asymptotically exact results for the real time order parameter correlations of a class of d0ex0ex=0ex0ex1 Ising models in a transverse field at low temperatures ( T) on both sides of the quantum critical point. The correlations are a product of a T-independent factor determined by quantum effects, and a T-dependent relaxation function which comes from a classical theory. We confirm our predictions by a no-free-parameter comparison with numerical studies on the nearest neighbor spin-1/2 model.