One-dimensional Quasi-periodic System Of Heat Conduction Properties

By making use of the method of transfer matrix and the Rubin-Green formula, we have studied the transmission coefficient and heat conduction in one-dimensional quasi-period systems (including Fibonacci chain, Period-Doubling chain and Thue-Morse chain).Besides, we have also studied the influence of on-site potential, the ratio of masses, and the ratio of force constants on the transmission coefficient and heat conduction. We have also calculated the transmission coefficient of the Fibonacci chain when introducing the disorder of on-site potential and the force constants.The results show that:With the on-site potential increasing whiling fixing the ratios of atom masses and force constants, transmission coefficient of the low-frequency region all decrease, and the transmission spectrums all move to the higher frequency region, but the transmission peaks of the latter two chains in the higher frequency region are more and become more intensive than the former. Meanwhile, the transmission spectrums move to the lower frequency region with the ratios of atom masses increasing, but the transmission spectrums of the Period-Doubling chain in the middle and high frequency region appear transmission platforms. Besides, the transmission spectrums of three chains move to the higher frequency region with the increasing of the ratios of force constants between zero and one, but the transmission spectrums of the first and third chains move to the lower frequency region with the increasing of the ratios of force constants above one, but the transmission spectrum of the second chain moves to the two ends, and the band gap in the middle frequency region becomes wider and wider. When introducing the binary random disorder of the on-site potential to the Fibonacci chain, transmission coefficient of the low-frequency region decreases, and the transmission spectrum moves to the higher frequency region, and the transmission coefficient decreases with the increasing of probability distribution and the size of the system. When introducing the total disorder of the on-site potential and the binary random disorder of the force constants, the transmission spectrums of the Fibonacci chain become narrower. Meanwhile, with the increasing of on-site potential, the ratios of atom masses and force constants, the heat conductivity all decrease. When they are large enough, the thermal conductivity will tend to zero. Otherwise, the thermal conductivity of the Thue-Morse chain will converge when the system is in the certain size. In the figure ofκ-ω2, the thermal conductivity shows a slowly increasing trend in the way of steps, and tends to be a certain value in the high-frequency region.We can artificially adjust the transmission spectrum by changing the on-site potential, the ratio of masses and force constants, blocking out the certain frequencies within the frequencies of waves, and then find out the phonon states we need. It can be used to produce the band hinder wave filter and the frequency-choosing component.