Energy transport in stochastically perturbed lattice dynamics
Abstract
We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order \-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/t, for the energy current correlation in equilibrium. This is in agreement with previous studies using a different method.
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