On the spectral gap of Kawasaki dynamics under a mixing condition revisited

We consider a conservative stochastic spin exchange dynamics which is rever sible with respect to the canonical Gibbs measure of a lattice gas model. W e assume that the corresponding grand canonical measure satisfies a suitabl e strong mixing condition. We give an alternative and quite natural, from t he physical point of view, proof of the famous Lu-Yau result which states t hat the relaxation time in a box of side L scales like L-2. We then show ho w to use such an estimate to prove a decay to equilibrium for local functio ns of the form 1/t(alpha-epsilon), where epsilon is positive and arbitraril y small and alpha=1/2 for d=1, alpha=1 for d greater than or equal to 2. (C ) 2000 American Institute of Physics. [S0022-2488(00)01103-8].