Convergence to equilibrium of conservative particle systems on ℤ\bmd

Abstract

We consider the Ginzburg--Landau process on the lattice ℤdZd whose potential is a bounded perturbation of the Gaussian potential. We prove that the decay rate to equilibrium in the variance sense is t−d/2t−d/2 up to a~logarithmic correction, for any function uu with finite triple norm; that is, |||u|||=∑x∈ℤd‖∂ηxu‖∞<∞|||u|||=∑x∈Zd‖∂ηxu‖∞<∞.