Spectral Properties Of Heat Current In One-Dimensional Disordered Systems

In the past 60 years,Anderson localization has received extensive attention as a ubiquitous phenomenon of wave transport in disordered media.Just as it was originally regarded as a mechanism of insulator for electron transport,Anderson localization also has a similar effect on phonon transport.In the past studies on one-dimensional disordered harmonic chains,it has been found that localization length and transmission coefficient of low-frequency phonons are monotonic functions of frequency,while high-frequency phonons are usually not paid attention because of strong scattering and negligible contribution to heat conduction.However,when studying heat conduction in the one-dimensional binary-mass disordered harmonic chain,it is found in this thesis that,completely different from low-frequency phonons,the transmission coefficients of high-frequency phonons exhibit a series of resonance line shapes.The positions of these resonance line shapes are independent of heat bath models,boundary conditions,the strength of external potential and impurity mass,and can be described by a simple formula,which implies that the resonance line shapes are relevent to ordered subsystems in the whole disordered system.In addition,various asymmetric resonance line shapes can be obtained by adjusting the strength of external potential and impurity mass.Although these resonance line shapes appearing in the diffusion scale will gradually disappear when the system size approaches localization length,it can be found by studying the logarithm of transmission coefficient that the resonance line shapes still exist in the localization scale,which implies that.there are many resonance line shapes in the localization length of high-frequency phonons.In addition to the one-dimensional binarymass disordered harmonic chain,heat conduction in the one-dimensional disordered FPUT-β model is also studied in this thesis.It is shown from the numerical results that disorder in the system qualitatively changes heat current as a function of the strength of anharmonicity.For the one-dimensional ordered FPUT-β model,due to the competition between phonon-phonon scattering effect and phonon renormalization effect,heat current first decreases and then increases with the increase of the strength of anharmonicity.For the one-dimensional disordered FPUT-β model,when disorder is weak,a peak for the heat current emerges with the increase of the strength of anharmonicity,however,when disorder is strong,monotonic increasing of the heat current shows up.Based on the competition between two effects of anharmonicity on phonons,namely,phonon delocalization and phonon-phonon scattering,these phenomena have been explained.The size effects of heat current as a function of the strength of anharmonicity further confirms that phonon delocalization effect plays an important role in the heat conduction under weak anharmonicity.By numerically calculating the spectral heat current,various effects of anharmonicity on heat conduction in the one-dimensional disordered FPUT-βmodel have been further understood.Different from harmonic chains,the spectral heat current in anharmonic chains is position dependent.This is because the phonon-phonon interaction results in phonon transition,which leads to the redistribution of the spectral heat current during the propagation of phonons.