Abstract
We consider lattice dynamics with a small stochastic perturbation of order \({\varepsilon}\) 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.
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Communicated by J. Fritz
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Basile, G., Olla, S. & Spohn, H. Energy Transport in Stochastically Perturbed Lattice Dynamics. Arch Rational Mech Anal 195, 171–203 (2010). https://doi.org/10.1007/s00205-008-0205-6
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DOI: https://doi.org/10.1007/s00205-008-0205-6