  We consider a d-dimensional crystal with an arbitrary harmonic interaction
and an anharmonic on-site potential, with stochastic Langevin heat bath at each
site. We develop an integral formalism for the correlation functions that is
suitable for the study of their relaxation (time decay) as well as their
behavior in space. Furthermore, in a perturbative analysis, for the
one-dimensional system with weak coupling between the sites and small quartic
anharmonicity, we investigate the steady state and show that the Fourier's law
holds. We also obtain an expression for the thermal conductivity (for arbitrary
next-neighbor interactions) and give the temperature profile in the steady
state.
