We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order \varepsilon\^-1 the local spectral density (Wigner function) evolves according to a linear transport equation describing inelastic collisions. For an energy and momentum conserving chain the transport equation predicts a slow decay, as 1/\sqrt{ t}, for the energy current correlation in equilibrium. This is in agreement with previous studies using a different method.
Categories: math.PR cond-mat.stat-mech math-ph math.MP