One-dimensional superdiffusive heat propagation induced by optical phonon-phonon interactions

Abstract

One-dimensional anomalous heat propagation is usually characterized by a Lévy walk superdiffusive spreading function with two side peaks located on the fronts due to the finite velocity of acoustic phonons. In the case when the acoustic phonons vanish, e.g., due to the phonon-lattice interactions such that the system's momentum is not conserved, the side peaks will disappear and a normal Gaussian diffusive heat-propagating behavior will be observed. Here we show that there exists another new type of superdiffusive, non-Gaussian heat propagation but without side peaks in a typical nonacoustic, momentum-nonconserving system. It implies that thermal transport in this system disobeys the Fourier law, in clear contrast with the existing theoretical predictions. The underlying mechanism is related to an effect of optical phonon-phonon interactions. These findings may open a new avenue for further exploring thermal transport in low dimensions.

Transport in perturbed classical integrable systems: The pinned Toda chain

“…Although the model is chaotic in the usual sense (Section 3), it displays however some form of solitonic transport, yielding a relatively slow and unexpected decay of current correlations. In this respect, we should also mention the case of the Fermi-Pasta-Ulam-β model equipped with a substrate quadratic potential that unexpectedly exhibits landmarks of heat superdiffusion [51]. Actually, it should be noted that the presence of the underlying Toda potential seems essential here.…”

Heat transport in one dimension

“…The intricate scenario of heat transport in anharmonic chains has been enriched by the contribution contained in [25], where the authors study a model where the Hamiltonian (9) has an additional local 'pinning' potential of the form…”

Anomalous Heat Transport in Classical Many-Body Systems: Overview and Perspectives

“…However, at very low temperatures another almost-conserved quantity (the phase difference between oscillators) appears, and for a finite chain and long times the dynamics is the same as that of a generic anharmonic model, leading to KPZ scaling of correlations and anomalous transport [52,53]. Further unexpected features have been reported also in Xiong and Zhang [54], where the authors study this problem for the FPUT-β model (i.e., Equation 1) with V = V FPUT and α = 0) with an additional local, also called "pinning, " potential of the form…”

“…Actually, for the φ 4 model there is no way to argue that a ballistic regime should be observed for any finite, even if small, value of β. The ballistic behavior observed in both models for β < 0.1 seems to suggest that for small non-linearities one needs to explore considerably larger chains and integrate the dynamics over much longer times than in Xiong and Zhang [54], before phonon-like waves in both chains may experience the scattering effects due to the local potential. Moreover, the weaker quadratic pinning potential of the original model seems to still be affected by finite size corrections, even in the region β > 1.…”