Abstract
It is shown that the Peierls vector integral of motion can extended such that it applies also to anharmonic phonon systems, provided they remain translationally invariant. This hints at the possibility of ballistic transport. In the classical regime it is in agreement with the existence of propagating solitons in the Toda and the Fermi-Pasta-Ulam chains. For quantal energy transport it provides new aspects for the concept of Umklapp scattering and, as regards energy transport in disordered materials, for speculations about a possible constructive role of anharmonicity.
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