Effects of interaction symmetry on delocalization and energy transport in one-dimensional disordered lattices

Effects of interplay between disorder and anharmonicity on heat conduction

Heat conduction through a disordered Fermi-Pasta-Ulam-β (DFPU-β) chain is studied. The presence of disorder makes the heat current behave significantly different from that of the ordered Fermi-Pasta-Ulam-β (FPU-β) chain. Thanks to the interplay between disorder and anharmonicity, a nonmonotonic-monotonic transition occurs when the disorder strength increases. That is, a peak for the heat current emerges for weak disorder; however, monotonic increasing of the heat current shows up for strong disorder. This can be understood based on the competition between two effects of anharmonicity on phonons, namely, delocalization and phonon-phonon scattering, which is shown by the spectral decomposition of heat current.

Wave-Turbulence Origin of the Instability of Anderson Localization against Many-Body Interactions

Whether Anderson localization is robust against many-body interactions and, closely related, whether a disordered many-body system can be thermalized are long outstanding issues. In this Letter, we address these issues with the wave-turbulence theory. We show that, in general, the thermalization time in one-dimensional disordered lattice systems is inversely proportional to the squared interaction strength in the thermodynamic limit. It leads to the conclusion that such systems can always be thermalized by arbitrarily weak many-body interactions and thus the localized states are unstable.

Anomalous interfacial temperature profile induced by phonon localization

Through the integration of the power spectral density, we obtain temperature profiles of both multisegment harmonic and anharmonic systems, showing the presence of an anomalous negative temperature gradient inside the interfacial segment. Via investigating patterns of the power spectral density, we found that the counterintuitive phenomenon comes from the presence of interfacial localized phonon modes. Two out-band localized modes of the harmonic model, which make no contributions to local temperature due to the absence of phonon interactions, result in the concave temperature profile and overcooling effect. For the anharmonic model, thanks to the phonon-phonon interactions, the localized modes are excited and make considerable contributions to interfacial temperature, which is clearly shown by examining the temperature accumulation function. When anharmonicity is considerably large, the negative temperature gradient is absent since the localized phonon modes are fully mixed. The presence of localized modes are evidently demonstrated by the inverse participation ratio and normal mode analysis for the isolated harmonic model. The localized modes make contribution to interfacial temperature profiles of the harmonic system when they are excited in initial conditions of simulations.

Heat perturbation spreading in the Fermi-Pasta-Ulam-β system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity

We employ the heat perturbation correlation function to study thermal transport in the one-dimensional Fermi-Pasta-Ulam-β lattice with both nearest-neighbor and next-nearest-neighbor couplings. We find that such a system bears a peculiar phonon dispersion relation, and thus there exists a competition between phonon dispersion and nonlinearity that can strongly affect the heat correlation function's shape and scaling property. Specifically, for small and large anharmoncities, the scaling laws are ballistic and superdiffusive types, respectively, which are in good agreement with the recent theoretical predictions; whereas in the intermediate range of the nonlinearity, we observe an unusual multiscaling property characterized by a nonmonotonic delocalization process of the central peak of the heat correlation function. To understand these multiscaling laws, we also examine the momentum perturbation correlation function and find a transition process with the same turning point of the anharmonicity as that shown in the heat correlation function. This suggests coupling between the momentum transport and the heat transport, in agreement with the theoretical arguments of mode cascade theory.

Phonon transport in a one-dimensional harmonic chain with long-range interaction and mass disorder

Atomic mass and interatomic interaction are the two key quantities that significantly affect the heat conduction carried by phonons. Here, we study the effects of long-range (LR) interatomic interaction and mass disorder on the phonon transport in a one-dimensional harmonic chain with up to 10^{5} atoms. We find that while LR interaction reduces the transmission of low-frequency phonons, it enhances the transmission of high-frequency phonons by suppressing the localization effects caused by mass disorder. Therefore, LR interaction is able to boost heat conductance in the high-temperature regime or in the large size regime, where the high-frequency modes are important.

Non-Gaussian normal diffusion induced by delocalization

Non-Gaussian normal diffusion, i.e., the probability density function (PDF) is non-Gaussian but the mean squared displacement (MSD) depends on time linearly, has been observed in particle motions. Here we show by numerical simulations that this phenomenon may manifest itself in energy diffusion along a lattice at a nonzero, finite temperature. The studied model is a one-dimensional disordered lattice with on-site potential. We find that the energy density fluctuations are spatially localized if the nonlinear interaction is suppressed, but may spread with a non-Gaussian PDF and a linear time-dependent MSD when the nonlinear interaction is turned on. Our analysis suggests that the mechanism lies in the delocalization properties of the localized modes.