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Anomalous (non-Fourier's) heat transport is no longer just a theoreticalissue since it has been observed experimentally in a number of low-dimensionalnanomaterials, such as SiGe nanowires, carbon nanotubes, and others. Tounderstand these anomalous behaviors, exploring the microscopic origin ofnormal (Fourier's) heat transport is a fascinating theoretical topic. However,this issue has not yet been fully understood even for one-dimensional (1D)model chains, in spite of a great amount of thorough studies done to date. Fromthose studies it has been widely accepted that the conservation of momentum isa key ingredient to induce anomalous heat transport, whilemomentum-nonconserving systems usually support normal heat transport whereFourier's law is valid. But if the nonconservation of momentum is the reason,what is the underlying microscopic mechanism for the observed normal heattransport? Here we carefully revisit a typical 1D momentum-nonconserving$\phi^{4}$ model and present evidence that the mobile discrete breathers or, inother words, the moving intrinsic localized modes with frequency componentsabove the linear phonon band can be responsible for that.

Crossover from ballistic to normal heat transport in the $\phi^{4}$ lattice: If nonconservation of momentum is the reason, what is the mechanism?